To estimate glacier melt, we used output from the S3M Italy operational chain , which relies on the S3M snow-glacier melt model . Among the wide range of cryospheric models, S3M strikes a balance between physical complexity and computational efficiency, providing spatially explicit estimates of snow water resources and glacier melt. In this paper, we used both daily maps of Snow Water Equivalent (see Sect. ) and glacier melt (see Sect. ). Note that S3M is a cryospheric model designed to simulate snow and glacier melt processes; it does not simulate river discharge or hydrological routing. Also, in this study, SWE, air temperature and precipitation were analyzed only over glacierized areas, to characterize how snow drought conditions affected glaciers; although S3M simulates SWE both on and off glaciers, off glacier snowmelt contributions to discharge were not considered here. While the S3M Italy system simulates snow water equivalent and snowmelt both on and off glaciers at the national scale, our analysis focuses only on meltwater generated over glacierized areas. Isolating the contribution of off-glacier snowmelt would require a fully coupled hydrological model capable of representing runoff routing, groundwater storage, and evapotranspiration processes. As a result, this study concentrates on glacier melt as a distinct and directly quantifiable component of the catchment water balance, while off-glacier snowmelt remains implicitly included in the observed streamflow signal.

The model uses a hybrid temperature index and radiation-driven melt approach and is fed by hourly inputs of incoming shortwave radiation, air temperature, total precipitation, and relative humidity. Precipitation-phase partitioning relies on both air temperature and relative humidity , an approach that has proved to provide reliable estimates across mountain landscapes . The snow module also includes settling and snow hydraulics, based on a viscoplastic parametrization and the Darcy law, respectively . In S3M, equations are solved for each pixel with no exchange of mass or energy across pixels, including no wind redistribution.

In the S3M Italy operational chain, S3M works with a 200 m spatial resolution and simulates hourly snapshots of snow water equivalent (SWE), snow depth, bulk snow density, and glacier melt across the whole of the Italian territory (period: September 2010 to present). Input data are routinely obtained from the database of the Italian Regional Administrations, Autonomous Provinces, and the Italian Civil Protection. Input maps are cropped over the 20 computational domains, each corresponding to one Italian administrative region, originally derived from a 20 m digital elevation model provided by the Italian Institute for Environmental Protection and Research (ISPRA), which was resampled at 200 m resolution using an averaging method. The vertical accuracy of the DEM is therefore consistent with that of a resampled elevation dataset at 200 m resolution, and does not retain the fine scale topographic variability present in the original DEM.

Besides elevation, S3M Italy employs static glacier maps from the Randolph Glacier Inventory v 6.0. The outputs are maps of snow accumulation and melt, as well as glacier melt on snow-free glacier surfaces. S3M Italy does not include glacier movement or debris coverage. Given the relatively short study period, assuming static glacier geometry represents a reasonable simplifying assumption, whereas the implications of neglecting debris cover are further discussed in Sect. .

S3M has been extensively calibrated and validated. The original model setup was calibrated in north-western Italy based on minimizing errors with respect to snow depth from 50+ ultrasonic sensors and thousands of manual measurements at peak accumulation (period: 2010–2019). This calibration targeted the optimization of the two melt parameters, one for incoming shortwave radiation and another one for air temperature. Results returned Root Mean Square Errors and Kling-Gupta Efficiencies that are in line with the literature, 12–37 cm and 0.66–0.72, respectively. S3M Italy has been further validated with regard to its snow component at the national scale , showing little to no mean bias compared to Sentinel-1-based maps of snow depth, and root mean square errors are of the typical order of 30–60 cm and 90–300 mm for in situ, measured snow depth and snow water equivalent, respectively. Estimates of peak snow water equivalent by S3M Italy are also well correlated with annual streamflow at the closure section of 102 basins across Italy (correlation coefficient = 0.87), with the ratio between peak snow water equivalent volume and total annual streamflow volume averaging 22 % (median: 12 %).

Regarding the glacier component, only a general validation of this model suite for a different setup was published in . This validation in Aosta valley returned a correlation between simulated and observed change in thickness of 0.6. The sensitivity of the two melt parameters was found to be low in previous studies, because explicitly separating the radiation- and temperature-driven components of melt brings these parameters closer to a first-principles energy balance model than standard degree-day approaches .

To validate glacier-melt estimates, we employed a dataset of 32 ablations stakes in Aosta Valley and 39 in Lombardy, installed on the various glaciers shown in Fig.  at elevations from 2546 to 3545 m a.s.l.. Altogether, 208 measurements were collected from 2009 to 2022 by the Environmental Protection Agency of Aosta Valley and the Lombardy Glaciological Service, the two institutions responsible for glacier data collection in Aosta Valley and Lombardy, respectively (the latter in collaboration with the Regional Environmental Protection Agency of Lombardy and the Snow and Meteorology Monitoring Center of Bormio). Despite the inherent uncertainty and spatial limitations of ablation stake data , comparing modelled glacier melt to these measurements represents the most informative validation of S3M glacial melt component feasible to date.

Streamflow data for the Dora Baltea and Adda rivers were provided by the Autonomous Region of Aosta Valley and the Environmental Protection Agency of Lombardy, respectively. The dataset consisted of water-stage measurements, which were converted into flow rates using flow rating curves provided by the two respective institutions and accounting for morphological changes. For both datasets, we removed unreliable measurements to ensure data quality, mainly through visual screening. Both basins have a high degree of anthropization, especially due to hydropower, which may alter the timing and magnitude of river flow. As we will further discuss in Sect. , however, several pieces of evidence show that this alteration was minor for our scopes and at our scales.

In this paper, we will always refer to water years, defined as periods of time between 1 September and 31 August.

We characterized the snow drought events of 2022 and 2023 by using daily maps of air temperature, total precipitation, and snow water equivalent (SWE) as available from S3M Italy across our study area . These data were processed to extrapolate daily trajectories of air temperature, precipitation, and mean snow water equivalent across select elevation bands over glaciers (every 500 m between 2000 and 4500 m a.s.l.). In this context, SWE was used to describe snow storage conditions over glaciers during these drought events.

To highlight the deviations from typical conditions, we first computed daily quartiles of air temperature, total precipitation, and snow water equivalent over the period 2010–2023, and then plotted these quartiles along with the trajectories of daily air temperature, total precipitation, and snow water equivalent for 2022 and 2023. Air temperature and snow water equivalent data were smoothed using a 10 d moving average to better highlight key events during these two years at different elevations. Precipitation data were cumulated by elevation band.

We also calculated seasonal anomalies for air temperature and precipitation in 2022 and 2023 relative to the mean seasonal values from 2010 to 2023. Each season corresponded to a three-month period according to meteorological conventions for this region: winter (December, January, February), spring (March, April, May), summer (June, July, August), and autumn (September, October, November).

To validate S3M Italy for the glacier component, we compared point mass balance data from 32 ablation stakes with co-located glacier melt model estimates. Since each ablation-stake data reports the mass balance over a certain period of time (usually, from summer to summer), for each data point we accumulated glacier melt for the same location and the same period of time. Subsequently, we computed the correlation index, bias (mean difference between simulated and observed values), a confusion matrix, the Root Mean Squared Error, and the coefficient of determination between observed and modelled cumulative glacier melt.

A rigorous quantification of glacier melt contribution would require knowing the proportion of total discharge that is directly attributable to glaciers, and thus a complex glacio-hydrologic model incorporating evapotranspiration, groundwater recharge, and flow routing processes. Lacking such a model, we adopt a simplified approach, estimating this contribution as the ratio of cumulative glacier melt to total observed discharge over a given period . We acknowledge that this approach likely overestimates the absolute glacier contribution, since observed streamflow integrates losses due to evapotranspiration and groundwater recharge from all runoff components. Therefore, the reported glacier contribution should be interpreted as an indicator of the relevance of glacier melt for streamflow generation, rather than as an exact partitioning of runoff sources.

We converted cumulative glacier melt in mm into a flow rate with units matching streamflow (m³ s⁻¹), by multiplying glacier melt by the pixel area (40 000 m²). Then, we computed weekly ratios between cumulative, basin wide glacier melt and cumulative streamflow as a proxy for the contribution of glacier melt to streamflow. We chose a weekly resolution for our analysis in order to account for the time needed by glacier melt to reasonably influence streamflow at the closure sections. Since no definitive estimate of this lag time is available for these regions, this temporal resolution should be seen as a trade-off between shorter (such as daily) or longer (such as monthly) resolutions, which would both be inevitably too short or too long to capture driving factors of the glacier-streamflow interaction. We also evaluated the relationship between annual and daily glacier melt and streamflow to gain further insights.

Despite the significant spatial mismatch between stake measurements and a 200 × 200 m² model, melt-estimate biases were generally within a ±1 m w.e. range (Fig. ). Overall, S3M slightly underestimated glacier melt, with mean biases of −0.89 m w.e. in Lombardy and −0.39 m w.e. in Aosta Valley. Corresponding RMSE values are 1.66 m w.e. and 1.15 m w.e., respectively.

The model performed best between 2800 and 3200 m a.s.l., which is the most critical zone, as a significant portion of glacier mass currently lies at these elevations (see Fig. ). At lower elevations, the model generally underestimated melt, likely due to the model struggling to represent the presence of debris on the glacier surface or other tongue processes. Above about 3300 m a.s.l., the model exhibited a more variable behavior depending on region and elevation, with evidence of both over and underestimation of melt. This likely reflects uncertainties in representing snow accumulation and melt processes at high elevations. Overall, these biases suggest that our estimates of glacier contribution to streamflow are conservative.

In Aosta Valley, both 2022 and 2023 were warmer than the 2010–2023 average, particularly during winter (DJF) and summer (JJA) (Figs.  and ). Daily temperatures remained above the climatological median for prolonged periods, especially during the early-summer heatwave of 2022. Seasonal anomalies show that winter 2022 exhibited the strongest positive anomalies across elevation bands, followed by summer, whereas spring anomalies were generally smaller.

In contrast, spring 2023 was markedly cooler, with locally negative anomalies at lower elevations that favoured late-spring snowfall events, while winter and summer remained warmer than average. A comparable pattern emerged in Lombardy, although winter 2022 was slightly colder than average at the lowest elevations before predominantly above-average summer temperatures.

Warmer-than-average conditions during summer were driven by different mechanisms in 2022 vs. 2023. In 2022, warm spells during late-spring and early summer played a key role, with distinct periods of high temperatures observed in May, June, and July (see again Fig. ). 2023, on the other hand, saw later and more concentrated hot spells, mainly during July and August, coupled with a cooler spring. Results were similar in Lombardy (Fig. ), with 2022 characterized by distinct warm spells in late-spring and early summer (e.g., 11–28 May), while 2023 experienced later and more concentrated hot spells, particularly in August (e.g., 10–27 Augsut).

In terms of precipitation (Fig. , right column), Aosta Valley experienced a markedly drier-than-average 2022, particularly in winter and spring, with widespread negative anomalies across elevation bands. Precipitation deficits generally ranged between about −25 % and −30 % at mid to high elevations. After near-average conditions in September and October, precipitation deficits re-emerged from November onward. At the highest elevations (4000–4500 m a.s.l.), cumulative precipitation remained closer to the climatological median, generally within the interquartile range.

By contrast, 2023 exhibited a generally wetter pattern at lower elevations, particularly between 2000 and 3000 m a.s.l., largely driven by a small number of intense storm events. Spring precipitation was moderately above average at these elevations, while cumulative precipitation remained close to climatological values at higher elevations (3000–4500 m a.s.l.).

A similar pattern emerged in Lombardy (Fig. ). The year 2022 was predominantly drier than average across most seasons and elevations, with particularly severe winter deficits at 2000–2500 m a.s.l. (around -30 % to -65 %). In contrast, 2023 was characterized by generally wetter conditions, especially in summer, when precipitation at 2000–2500 m a.s.l. was approximately +30 % to +35 % above average. However, winter precipitation remained substantially below normal, comparable to 2022.

Fig.  summarizes the seasonal temperature anomalies across elevation bands. In both regions, positive temperature anomalies generally increased with elevation, with winter 2022 exhibiting the strongest warming (up to about +3 °C), followed by summer. Compared with 2022, spring 2023 showed substantially smaller and locally negative temperature anomalies, particularly at lower elevations. This cooler spring favored late-spring snowfall events and delayed snow depletion on glaciers, despite above average temperatures returning during summer.

Both 2022 and 2023 saw substantial and widespread snow water equivalent (SWE) deficits over glaciers across all elevations in Aosta Valley (Fig. ). In 2022, the snow water equivalent anomaly reached approximately -76 % across the 2000–3500 m a.s.l. range. This deficit decreased slightly at higher elevations, recording -64 % for 3500–4000 m a.s.l. and -47 % for 4000–4500 m a.s.l.. Similarly, 2023 exhibited substantial snow water equivalent deficits, though with slightly different altitudinal patterns. The anomaly was approximately -75 % from 2000–3500 m a.s.l., -71 % at 3500–4000 m a.s.l., and -64 % at 4000–4500 m a.s.l..

While this significant snow water equivalent deficit persisted in both 2022 and 2023 in Aosta valley, the timing of snow accumulation and melt differed notably: 2022 saw an earlier than usual end to the snow accumulation season at all elevations (up to two months), which was directly attributable to the combined effect of consistently higher temperatures and lower precipitation. This premature end of accumulation inevitably led to an earlier onset of the snowmelt season, which reduced the duration of snow cover on glacier, with seasonal snow depletion and initial ice exposure occurring approximately 1.5 months earlier than usual at 2000–2500 m a.s.l. in 2022. Conversely, in 2023, the lower temperatures during spring, coupled with late-spring snowfalls as visible in Fig. , extended the snow accumulation season closer to its average end date.

Similar to the patterns observed in Aosta Valley, Lombardy also faced severe and widespread snow water equivalent (SWE) deficits across all analyzed elevations in both 2022 and 2023 (Fig. ), clearly highlighting severe snow drought conditions. In 2022, SWE deficits ranged between approximately −70 % and −63 % across elevations from 2000 to 3500 m a.s.l., generally decreasing with altitude and becoming substantially smaller at the highest elevation band (3500–4000 m a.s.l.). A similar situation was observed in 2023, with SWE deficits ranging from about −71 % to −56 % between 2000 and 3500 m a.s.l., again showing a marked reduction at the highest elevations.

The 2022 and 2023 droughts markedly altered hydrology in both catchments, with extremely low river flows highlighting an intense summer hydrologic drought following the winter snow drought (Fig. ): annual mean streamflow in 2022 and 2023 was approximately -32 % lower than the 2011–2021 average, contrasting with a higher-than-usual glacier melt (∼+ 148 % mean annual glacier melt compared to 2011–2021).

Specifically, a clear contrast was observed during the 2022 water year. Along the Dora Baltea at Tavagnasco, average annual streamflow was among the lowest recorded during the study period (64.5 m³ s⁻¹), while annual mean glacier melt reached its maximum value (14.9 m³ s⁻¹). Similarly, along the Adda river, mean annual streamflow was low (60 m³ s⁻¹), despite the highest glacier melt contribution of record (9.5 m³ s⁻¹).

In 2023, both mean annual streamflow and glacier melt were slightly lower than in 2022 at both sites. At Tavagnasco (Dora Baltea), mean streamflow increased to 69.9 m³ s⁻¹ while glacier melt averaged 10.2 m³ s⁻¹. At Gera-Lario-Fuentes (Adda), mean streamflow was 61 m³ s⁻¹ and glacier melt averaged 8.3 m³ s⁻¹. Despite enhanced glacier melt in both years, streamflow remained below long-term average conditions (Fig. ), indicating that glacier melt could not fully compensate for precipitation deficit and reduced snowmelt during drought.

Glacier melt contribution to streamflow during summer doubled, or nearly tripled, in both catchments during 2022 and 2023 compared to pre-2022 water years (Fig. ). This increase in glacier melt and the concurrent decline in streamflow highlighted a clear signature of snow droughts on the link between glacier melt and water supply – a signature that resolves around four significant mechanisms (Fig. ).

The first mechanism is an earlier-than-usual start of the glacier-melt season (defined here as the week when glacier contribution first exceeded 5 %): in both Aosta Valley and Lombardy, the 2022 melt season began six weeks earlier than the median for 2011–2021. This earlier-than-usual start took place also in 2023: two weeks ahead of the median in Aosta Valley and three weeks ahead in Lombardy.

The second mechanism is an increase in the contribution of glaciers to streamflow during the whole of the melt season, and not just the peak summer-melt period. In 2022, peak glacier-melt contribution to streamflow reached 75 % in Tavagnasco, while it reached 65 % in 2023, two to three times the usual contribution for this region (31.5 %). At Fuentes, the impact was even more pronounced: in 2022, peak contribution nearly quadrupled (83 %), and in 2023, it almost tripled (61 %) compared to the median values (22.6 %).

The third mechanism is a potential shift in the timing of the seasonal glacier melt peak, which was particularly evident in Tavagnasco in 2022, when reduced summer rainfall led to an earlier and more distinct glacier melt peak. During this year, peak contribution occurred two weeks earlier than usual, shifting from the median timing of week 34 (22–28 August) to week 32 (8–14 August). At Fuentes, the glacier melt peak during 2022 was recorded during week 34, that is, close to the median timing (week 33, 15–21 August), although an earlier sub-peak was already observed in week 31 (1–7 August). In 2023, on the other hand, sporadic rainfall during summer increased short-term discharge variability, making the identification of a distinct glacier melt peak less robust and partially masking melt driven signals.

The fourth and final mechanism observed is a potential prolongation of the melt season, which underpinned a higher-than-usual glacier melt contribution than the median even during late summer/early autumn. In Tavagnasco, glacier melt in 2022 accounted for 33 % of the streamflow even during week 38 (25–19 September), which was significantly above the median of 13 %. Similarly, at Fuentes, glacier melt during week 37 (12–18 September) reached 31 %, compared to the median of 11 %. This effect was even more pronounced in 2023 due to higher late-summer temperatures, as shown in Fig. . During 2023, in Tavagnasco, glacier melt during week 39 (26 September–2 October) contributed 44 % of streamflow, well above the median of 13 %, while in Fuentes, the contribution during week 39 was 15 %, compared to the median of 7 %.

Despite these four general mechanisms, glacier melt contribution to streamflow remained sensitive to short-term meteorological events, such as temperature drops and early or late snowfalls (Fig. ). For instance, between April and May 2023, streamflow quickly increased in Aosta valley due to the seasonal freshet, which continued until June. Then, streamflow decreased slightly as seasonal snow waned. In June, glacier melt increased, quickly becoming a dominant contributor to streamflow. Glacier melt peaked in late August, coinciding with the peak of the glacier melt season. A sudden drop of temperatures between late August and early September, however, led to a quick and sudden glacier melt decrease, and to a pairwise decline in streamflow (Fig. a and b). In early September, finally, glacier melt rapidly rose as temperature increased again, growing to 63 m³ s⁻¹ in Tavagnasco and 42.3 m³ s⁻¹ in Fuentes.

This study employed S3M Italy for glacier melt estimates.

In its current operational setting, this model does not account for glacier movement and debris cover on glaciers . As already pointed out, glacier evolution over the relatively short 13-year study period is expected to influence melt outputs only modestly compared to the interannual variability driven by climatic conditions . In this sense, coupling S3M with simplified glacier-evolution schemes (e.g., parameterized retreat models; ) or more advanced ice-flow modelling approaches and emulators would allow for a dynamic representation of glacier geometry and its feedback on melt and runoff.

On the other hand, thick debris typically acts as a protective layer for the underlying ice , which may have led to a local overestimation of glacier melt at very low elevations (note that these elevations are outside the validation range we considered in Fig. ). To account for both aspects, future research with S3M should explore the inclusion of spatially distributed estimates of debris cover, such as that by . Another direction of future work is the adoption of enhanced melt models that are specifically designed for debris-covered glaciers .

S3M Italy also employs static glacier maps from the Randolph Glacier Inventory v 6.0 , which is a globally complete inventory intended to capture the world's glacier outlines near the beginning of the 21st century . Consequently, these static glacier outlines may overestimate current glacier extent, particularly during the drought years taken into consideration. To assess this discrepancy, we leveraged more recent glacier outlines provided by the Aosta Valley Autonomous Region (2019 data) and the Lombardy Glaciological Service (SGL) (2021 data) and compared them against the Randolph Glacier Inventory v 6.0 used by S3M Italy. Our analysis revealed a glacier area loss of 7 % in Aosta Valley between 2000 and 2019. Lombardy experienced a 18.7 % reduction in glacier coverage from 2000 to 2021. We then quantified the effect of these changes in glacier area by computing glacier melt contribution to streamflow using the updated regional glacier inventories. Compared with the RGI v6.0 glacier outlines, the updated inventories reduced the estimated mean annual glacier contribution from 10.5 % to 6.4 % during 2011–2021 and from 23.8 % to 19.1 % during 2022–2023 in Tavagnasco. In Fuentes, the corresponding values decreased from 4.9 % to 2.9 % and from 22.8 % to 11.1 %, respectively. While the reduction in glacier area caused an expected decrease in the absolute glacier contribution to streamflow, the amplification observed during 2022 and 2023 compared to historical patterns remains robust. In Tavagnasco, mean annual glacier contribution increased from 6.4 % (2011–2021) to 19.1 % (2022–2023), corresponding to nearly a threefold increase. In Fuentes, the increase was from 2.9 % to 11.1 %, equivalent to almost a fourfold amplification. In terms of peak weekly contributions, the median annual peak during 2011–2021 was 28.4 % in Tavagnasco, compared to 61.1 % in 2022 and 53 % in 2023. In Fuentes, the median baseline peak was 13 %, whereas peak values reached 47.5 % in 2022 and 35.2 % in 2023 (up to nearly fourfold amplification).

Our estimate of glacier contribution to discharge is based on the ratio between modelled glacier melt and observed streamflow. This simplified metric does not explicitly account for evapotranspiration losses or groundwater recharge. Because these processes remove water from the runoff signal, our approach likely leads to a modest overestimation of the absolute glacier contribution to discharge. However, because the investigated basins are largely energy limited, evapotranspiration is expected to remain small relative to other hydrologic fluxes . The values reported here should still be interpreted primarily as indicators of the relative importance and temporal variability of glacier melt as a driver of streamflow, rather than as a rigorous partitioning of runoff sources.

Both the Adda and Dora Baltea basins include artificial reservoirs, which may have impacted the natural timing of water transit and thus our quantification of glacier contributions to streamflow. While reservoir impacts depend on energy market fluctuations , we in general expect hydropower to shift runoff from early to late summer, as spring freshet is accumulated to meet later peaks in energy prices. With regard to our study region, a recent study by has reconstructed the naturalized streamflow of the Adda basin close to Fuentes, and demonstrated that the effect of high-elevation reservoirs is below 10 % when comparing naturalized and measured streamflow. As for Aosta Valley, another study performed in the context of the Regional Water Protection Plan (https://pta.regione.vda.it/, last access: 5 March 2026) confirmed the same order of magnitude between naturalized and measured streamflow. In both regions, the largest percentage discrepancies between naturalized and measured streamflow is expected during winter, when nonetheless streamflow is low and glaciers do not contribute to runoff. By July, these differences decrease markedly, tend to less than 10 %, and remain minimal throughout the remainder of summer and fall. The importance of glaciers in sustaining summer water supply during droughts regardless of reservoir operations is also clear if one looks at annual rather than weekly time scales. In fact, the mean annual glacier melt contribution in Aosta Valley more than doubled from 6 % (2011–2021) to 18 % (2022–2023). In Lombardy, the increase was even more pronounced, with glacier melt contribution nearly quadrupling from 4 % (2011–2021) to 15 % (2022–2023).