The glacier model experiments used mesoscale meteorological variables to calculate surface mass balance for the Khumbu Glacier catchment in combination with a debris-covered glacier evolution model to represent the surface processes that modify mass balance (Fig. 2A). Our approach produced a total of six simulations of Khumbu Glacier to 2100 CE from the three Coordinated Regional Downscaling Experiment (CORDEX) South Asia region RCMs (NOAA, CCCma, IPSL; Lutz et al., 2016) under two RCPs (RCP4.5 and RCP8.5; Collins et al., 2013) to explore the impacts of possible variability in future precipitation amount and distribution in tandem with warming on glacier evolution. Before we used the RCMs to force the future climate scenarios, we evaluated their capabilities against observations of present-day weather and climate. The experimental design represents an advance compared with previous glacier modelling efforts by including in each simulation; (1) mesoscale meteorological phenomena, including sublimation, (2) the redistribution of surface mass by snow avalanching, and (3) the feedbacks between debris transport, ice flow and mass balance. This section describes the experimental design for the glacier modelling workflow, downscaling of the present-day RCMs using meteorological data from automatic weather stations (AWS) in the Khumbu Valley, downscaling of the future RCMs for both RCPs, the surface energy and mass balance calculations using COSIPY (Sauter et al., 2020) and the debris-covered glacier evolution modelling using iSOSIA (Rowan et al., 2015). A reference simulation and sensitivity experiments were carried out for the period 2013–2015 CE, and the simulations of future glacier change represented the period 2015–2100 CE. Additional information about the development and testing of the modelling approach is provided in Appendix A.

The spin-up simulation from the ice-free model domain to represent the late Holocene glacier was forced using a simple approximation of mass balance. The ice-free model domain was found by subtracting the estimated ice thickness (Farinotti et al., 2019) from a 30 m digital elevation model (DEM) acquired from the Shuttle Radar Topography Mission (Farr et al., 2007). The ice-free model domain incorporated the full hydrological catchment including the steep hillslopes in the Western Cwm that provide snow to the glacier surface by avalanching. As a starting point for our transient simulations of Khumbu Glacier, we reconstructed the late Holocene glacier from the ice-free domain using an ELA of 5325 m a.s.l. and an atmospheric lapse rate of -4.0 °C km⁻¹ in a 5000 year simulation. Accumulation above the ELA was calculated as a function of elevation 0.2 mm m⁻¹ up to a maximum of 2.0 m water equivalent (w.e.) per year and ablation was calculated as a function of elevation 0.5 mm m⁻¹ up to a maximum of 2.0 m w.e. a⁻¹. This simulation continued through the LIA forced by a step change in mean annual air temperature (MAAT) equivalent to 1.5 °C colder than the present day over 500 years following the approach of Rowan et al. (2015, 2021). Ice-marginal moraines denoting the late Holocene (1.3 ± 0.1 ka) glacier extent and thickness (Hornsey et al., 2022) were used to constrain the spin-up simulation.

The late Holocene simulation was forced to present-day (2015 CE) conditions using three surface mass balances (one from each RCM) calculated using the Coupled Snowpack and Ice-surface Energy and Mass Balance model in Python (COSIPY v1.3) (Sauter et al., 2020). These simulations were evaluated against a range of observations of present-day glaciology and previous glacier model experiments (Fig. 3), and the experiment using the NOAA RCM was identified as the starting point for all future simulations because this was most representative of the observed glacier. We simulated only the active section of the glacier beyond 2015 CE and added the dynamically detached debris-covered tongue simulated at the present day to the model domain as a static topographic feature for the future simulations. The volume of the detached tongue was calculated by using the simulated present-day velocity field to separate the simulated present-day ice volume where velocities declined below 10 m a⁻¹. Thus, we arrived at the present-day from the LIA maximum simulation by forcing the LIA glacier with the 2015–2020 CE mass balance for 200 years.

We used the output from the present-day simulation with the 2095–2100 CE mass balance calculated using COSIPY to force the model to 2100 CE over a period of 85 years. The glacier model simulations continued from the present day to 2100 CE forced by distributed glacier surface mass balances calculated for each of the three RCMs and two RCPs using COSIPY. The three RCMs and two future RCPs represented a range of possible future climates with distinctly different precipitation trends – equivalent to dry, moderate, and wet scenarios for warming of 1.4–2.2 °C under RCP4.5 and 3.8–4.1° under RCP8.5 (Table 1; Fig. 2D; Sect. 2.3). We used time slices representing the present day (2015–2020 CE) and the end of the 21st Century (2095–2100 CE) to calculate surface mass balance, and the preceding decade was used to evaluate these time slices (see Sect. 3.3). We used this step forcing, whereby the future mass balance was imposed and the glacier adjusted to this from the start of the century in question, rather than interpolating mass balance over time to reduce the computational expense of the surface mass balance and glacier modelling (∼ 24 h per simulation).

Estimates from a global glacier modelling study indicate that avalanching contributes up to 18 % of regional accumulation to glaciers in the monsoon-influenced Himalaya (Kneib et al., 2025) and observations of high-elevation Himalayan glaciers, including Khumbu Glacier, suggest that up to 75 % of accumulation occurs by avalanching rather than direct snowfall (Fig. 1D) (Benn and Lehmkuhl, 2000; Laha et al., 2017). Avalanching affects mountain glaciers in two ways; (1) by moving snow from steep hillslopes onto the glacier surface thus increasing accumulation from that calculated from direct snowfall onto the glacier surface, and (2) by redistributing snow across steep sections of the glacier surface (Kneib et al., 2025). We examined the uncertainty in accumulation resulting from the application of a calculation in iSOSIA to move snowfall from slopes susceptible to avalanching (see Sect. 2.6). If avalanching was not considered in iSOSIA, then the accumulation of snow calculated using COSIPY within the catchment but outside of the glacier outline would have no impact on accumulation resulting in an underestimation of ice volume, and the steep sections of the glacier would hold more mass than expected. For example, when avalanching was not simulated and accumulation occurred at a uniform rate of 2.0 m w.e. a⁻¹ across the Western Cwm accumulation area, Khumbu Glacier had a similar extent but a volume more than double that of the glacier simulated with avalanche redistribution of snow, because mass was not redistributed effectively across steep sections of the glacier surface (result not shown).

The first meteorological observations for the Nepal Himalaya were collected during the 1970s and found a trend of diurnal precipitation on ridges and nocturnal precipitation in valley floors (Ageta, 1976) reflecting cloud development from orographic convection during the day. Continuously recording AWS were first installed in the region in the 1990s at the Pyramid Observatory near Lobuche village, where Bollasina et al. (2002) analysed of the monsoon from meteorological observations collected between 1994 and 1999, finding that the onset (decay) of the Indian Summer Monsoon was distinguished by higher (lower) daily precipitation totals, mean relative humidity and atmospheric pressure and a reduced (increased) diurnal range in atmospheric temperature. Bollasina et al. (2002) identified two daily profiles in precipitation and wind direction thought to be related to the monsoon. In addition, five-day and ten-day precipitation cycles were observed linked to oscillations in the Tibetan High. A new AWS was installed at the Pyramid Observatory at 5035 m a.s.l. in September 2000 as part of a network in the Dudh Koshi valley of six AWS between 2680 to 5700 m a.s.l., in addition to some short-lived higher-elevation stations, maintained by the Ev-K2-CNR network. The Pyramid Observatory AWS included a snow depth sensor between 2009 and 2010, but the data were discontinuous and inconsistent, and the measurement period ended in December 2010. A second AWS was installed in the same location by the GlacioClim network in 2013 (Sherpa et al., 2017) provides a longer period of continuous data collection. More recently, a network of 5 AWS including the highest elevations in the Khumbu catchment were installed by the National Geographic project at Phortse (3810 m a.s.l.), Everest Base Camp (5315 m a.s.l.), Camp 2 (6464 m a.s.l.), the South Col (7945 m a.s.l.) and the Balcony (8430 m a.s.l.) (Matthews et al., 2020). However, at time of writing, there are no continuous records of high-elevation meteorological variables that span a longer period than 15 years, making the calculation of climate normals impossible. In this study, we analysed data from these various sources for evaluation of mesoscale trends in the upper Khumbu Valley and for use to downscale RCMs and evaluate the results of our calculations. The location of the AWS is shown in Fig. 1C. Gaps in the air temperature and precipitation data were filled using interpolated data from neighbouring stations where required (as described in Appendix A).

The AWS data were used to make a reference simulation in COSIPY of the surface energy fluxes and mass balance of the Khumbu Glacier catchment between 2013–2015 for model development and sensitivity experiments (Figs. 4 and 5). We compiled 14 years of meteorological observations from the two AWS provided by the GlacioClim network at the Pyramid Observatory (5050 and 5035 m a.s.l.) and the West Changri Nup Glacier AWS (5363 m a.s.l.) (Sherpa et al., 2017). All meteorological data were collected for the period December 2010 to November 2019, apart from precipitation which was only recorded between December 2012 to November 2016. All meteorological data (excluding precipitation) used for the reference simulation were taken from the West Changri Nup AWS. Given the frequency of missing precipitation data from the AWS, the undercatch of snow associated with tipping bucket rain gauges, and the scarcity of high-elevation precipitation measurements, precipitation was not varied with elevation in the reference simulation. Precipitation data for the reference simulation were collected from the GlacioClim Geonor precipitation gauge at the Pyramid Observatory (5035 m a.s.l.) because this precipitation gauge provides a longer period of continuous observations than the other gauges and avoids errors due to low precipitation amounts measured by tipping bucket gauges, which are known to systematically underestimate snowfall particularly during high winds (Sherpa et al., 2017). Precipitation was measured at 15 min intervals using a Geonor T-200BM sensor mounted 1.8 m above the surface. Evaporation from the bucket was blocked by a layer of oil, but some loss did occur, as evidenced by precipitation values below 0 mm. Noise from wind and evaporation were corrected for by compensating any negative change over the 15 min time step with the neighbouring positive value such that accumulated precipitation was unchanged. Periods with prolonged evaporation were set to zero. Undercatch of snowfall by rainfall gauges was corrected through precipitation phase partitioning using wind speed observations (Wagnon et al., 2009). Air temperature was interpolated to match the height of the precipitation gauge using hourly lapse rates that averaged -5.89 °C km⁻¹. COSIPY was run for both elevations using the non-adjusted temperature data for 5336 m a.s.l. and the adjusted temperature data for 5035 m a.s.l. and it made little impact on the model results. Simulated meteorological variables were evaluated at the highest elevations using the National Geographic AWS stations at Camp 2 (6464 m a.s.l.) and the South Col (7945 m a.s.l.) using data for May–November 2019 (Matthews et al., 2020).

Direct solar radiation across the model domain was corrected for the slope, azimuth, and shadowing potential of each pixel (Wohlfahrt et al., 2016; Sauter et al., 2020). A footprint-weighted correction was also applied to horizontal measurements of net radiation. The fraction of diffuse incoming shortwave radiation was estimated by using the ratio of total shortwave (global) radiation and potential shortwave radiation to define a clearness index (Wohlfahrt et al., 2016). This clearness index was used to calculate diffuse radiation, which was calibrated with data from the Neustift eddy covariance station in the Austrian Alps (Wohlfahrt et al., 2008). Pressure was distributed across the domain by first calculating sea-level pressure (cf. Lente and Ősz, 2020) and then interpolated with the barometric equation. The relative humidity gradient was calculated as -0.002 % m⁻¹ using data from the Ev-K2-CNR and the GlacioClim AWS networks, and evaluated by comparison with measurements made by the National Geographic network AWS ranging in elevation from 3810–8430 m a.s.l. (Matthews et al., 2020) to capture trends at higher elevations. The distributed radiative fluxes were compared with the same high-elevation stations for 2019 to assess the efficacy of this method across the domain. Wind speed was assumed to be uniform across the domain.

Six RCMs were assessed on their fidelity to present-day climate using hindcasting (Biemans et al., 2013) with an emphasis on temperature seasonality and seasonal precipitation dynamics given the importance of these variables for glacier mass balance. RCMs from the CORDEX South Asia domain were dynamically downscaled from CMIP5 GCMs by the Indian Institute of Tropical Meteorology to a 50 km spatial resolution (Lutz et al., 2016) and collected for the grid box containing Khumbu Glacier (27.9065056° N, 86.4352951° E). Three of the six CORDEX South Asia RCMs (NOAA, CCCma, IPSL) spanning a range of possible future precipitation conditions (Table 1) were selected as discrete scenarios for the glacier surface energy and mass balance calculations. The three remaining RCMs were discounted due to being intermediate to those selected for our experiments (i.e. close to the future precipitation scenario represented by CCCma) or particularly poor at reproducing seasonal temperature and precipitation cycles. For example, despite the annual precipitation sums from the CSIRO RCM being closest to observed values and having the potential to be the “driest” scenario examined, analysis of precipitation seasonality indicated that the monsoon signal was completely absent with this RCM instead showing a strong dominance of winter precipitation.

The present-day RCM results were downscaled using quantile mapping, also known as “distribution mapping”, using 14 years of observations collected between January 2006 and November 2019 from three AWS as described in Sect. 2.2. Parametric quantile mapping (Piani et al., 2010) was used to downscale the RCM to a daily time step at the resolution of the DEM, whereby a statistical relationship between the raw climate model outputs and observations was formed by substituting the RCM results with observations at a cumulative density function of the prescribed distribution (e.g., a Gaussian distribution for temperature; Luo et al., 2018; a gamma distribution for precipitation; Piani et al., 2010). This correction was applied to the raw RCM outputs to produce a third downscaled dataset which had an improved the fit to the observations (Fig. 2C and D). The quantile mapping approach was chosen because this is effective for downscaling precipitation and reduces errors in the standard deviation, the coefficient of variation, and the skewness of distributed values relative to other methods (Lafon et al., 2013; Reiter et al., 2018). The AWS data were used to disaggregate the daily downscaled present-day and end-of-century climate model outputs to an hourly resolution for energy balance modelling. All meteorological variables, excluding precipitation, were downscaled using the MELODIST Python tool (Förster et al., 2016). Seasonal means were applied for precipitation to reproduce the “nocturnal peak” seen during the monsoon that MELODIST was unable to replicate (Figs. A1, A2 and A3). Further information on the meteorological data analysis and RCM downscaling are provided in Appendix A.

Two future emission scenarios (RCP4.5 and RCP8.5) were available from CORDEX South Asia, which represent intermediate and high emissions by 2100 CE relative to the present day. These two emissions scenarios are frequently used in climate impact studies enabling the comparison of our results with studies that use other climate/glacier model projections. The two future emissions scenarios were analysed for each of the three CORDEX RCMs to account for the inherently high uncertainties in future precipitation trends associated with climate models and the interplay of changing precipitation with atmospheric warming. The same statistical downscaling approach and disaggregation used for the three present-day RCMs described in Sect. 2.3 was applied to the raw CORDEX RCM daily outputs for the three future RCM time slices under RCP4.5 and RCP8.5. The temperature change between the present day and the future time slices was preserved and there was no evidence of any imposed strengthening in the monsoon resulting from downscaling. An increase in the frequency of days per year outside of the monsoon season with high precipitation amounts (defined here as over 15 mm of daily precipitation) accounted in large part for the higher annual precipitation amounts relative to the present day that were found in four out of the six RCMs. However, the total future annual precipitation increase was on average 8.8 % greater in the downscaled climates relative to the raw RCMs, suggesting that this positive trend was inflated by downscaling. The downscaled climates reduced the frequency of precipitation, although, as in present day observations, monsoon precipitation occurred frequently and could be characterised as predominantly drizzle in the future.

COSIPY is a leading open-source method for estimating glacier surface mass balance and has previously been applied to glaciers in High Mountain Asia. COSIPY includes a calculation of sublimation, which is an important ablation process for high-elevation glaciers because ablation can still occur if the latent heat flux is negative through sublimation, even in instances where surface temperature and/or air temperature are well below the melting point (Bonekamp et al., 2021; Brun et al., 2023; Huintjes et al., 2015). COSIPY resolves all energy fluxes (F) at the ice surface that contribute to surface melt (Qmelt): 1F=SWin⋅1-α+LWin+LWout+Qsens+Qlat+Qg+Qliq Where SW_in is incoming shortwave radiation, α is albedo, LW_in and LW_out are incoming and outgoing longwave radiation, and Qsens, Qlat, and Qg are the sensible, latent, and ground heat fluxes (Oerlemans, 2001) and Qliq is the heat flux from liquid precipitation; the latter variable is often neglected in ablation calculations (Cuffey and Paterson, 2010) but is of particular importance here as the Indian Summer Monsoon brings a significant amount of liquid precipitation to the lower reaches of Khumbu Glacier. The resulting F is equal to the energy available for surface melt (Qmelt) when surface temperature (Ts) is at melting point (0 °C). Ts is used to calculate LW_out, Qsens, Qlat, Qg and to partition solid and liquid precipitation. When Ts exceeds the melting point it is reset to 0 °C (273.15 K) and the residual F fluxes equal Qmelt. In this instance, subsurface melt is triggered when the energy fluxes, for example, penetrating SW_in warm the ice layer so that Ts exceeds the melting point of ice (Sauter et al., 2020).

The COSIPY model domain was taken from the 30 m DEM that was resampled to 200 m grid spacing following a reference simulation for 2013–2015 and sensitivity analyses, which revealed minimal impact on the results whilst greatly reducing computational expense (Fig. 4). The sensitivity of glacier mass balance to individual meteorological variables (MAAT, radiative fluxes, relative humidity, lapse rate, precipitation amount, precipitation phase, glacier surface roughness) was calculated in sensitivity experiments using the reference simulation that perturbed these variables individually. Perturbations were made within the range of the possible uncertainties for each variable that arise from a combination of the choice of observations or climate models, the downscaling approach used, and the distribution of meteorological variables (see Sect. 3.1). The values used for perturbations of MAAT and precipitation amount were similar to those expected for possible future climate forcings. We tested a range of lapse rates from -3.0 to -6.0 °C km⁻¹ while maintaining the same ELA based on the range of monthly values calculated from regression of NASA MODIS land surface temperature data for the Central Himalaya, which resulted in a difference in ice volume of 0.4 × 10⁹ m³ and no change in glacier length at the present day (result not shown).

The downscaled and disaggregated CORDEX RCM daily climate variables (temperature, precipitation, the radiation components, wind speed, relative humidity and atmospheric pressure) were used to force COSIPY for the periods 2015–2020 and 2095–2100 CE. While snowfall measurements can be used as an input to COSIPY, there are no good-quality measurements of snowfall in the Everest region and so precipitation was partitioned into rainfall and snowfall using the snow transfer scheme within COSIPY (Sauter et al., 2020). COSIPY was forced using hourly meteorology with nine variables to calculate the energy balance and mass balance components at an hourly time step from the sum of accumulation by solid precipitation, deposition, and refreezing of melt water percolation, and ablation by melt and sublimation. The exchange processes at the surface, including energy release and consumption with phase changes, control temperature distribution and phase changes within the glacier (comprised of horizontal ice and snow layers), and accounts for meltwater refreeze and percolation with the meltwater produced from the surface melt calculations acting as an input. The impacts of supraglacial debris on ablation and of snow avalanching on accumulation were handled in iSOSIA, as described in the next section.

The second-order shallow ice approximation model (iSOSIA) is a 3-D higher-order ice-dynamical glacier evolution model that solves for the flow of ice including longitudinal and transverse stress gradients that are imposed on ice flow through high-relief topography (Egholm et al., 2011). This glacier model simulates the evolution of debris-covered glaciers by incorporating the feedbacks between debris transport, mass balance and ice flow (Rowan et al., 2015) and includes two processes that are important for many Himalayan glaciers; (1) the redistribution of snow by avalanching that is estimated to account for up to 75 % of accumulation, and (2) the formation and evolution of a supraglacial debris layer that insulates the ice surface to modify ablation (Rowan et al., 2015). While previous versions of this glacier model used depth-integrated ice flow, this version simulates ice flow through Khumbu Glacier in 3-D as the ice thickness is divided into 20 vertical layers to calculate englacial debris transport (Rowan et al., 2015). The glacier model has a variable time step that can adjust up to a maximum of 0.1 years to allow greater computational efficiency.

The distributed surface mass balances calculated using COSIPY using the downscaled RCMs for the periods 2015–2020 and 2095–2100 CE were used as inputs to the glacier model with no change in forcing applied between these two periods. The model domain topography was the same in iSOSIA as that used in COSIPY. Surface processes within the glacier model modified the distribution of accumulation and ablation but this was not updated into the surface topography used in COSIPY. Simulated accumulation was the result of the total snowfall in each cell and avalanching of snow imposed for the accumulated snowpack from hillslopes by removing snow and ice from hillslopes greater than 28° and redistributing this mass across less steep surfaces using a non-linear hillslope flux model (Roering et al., 1999). The avalanching routine was found to be sufficient to prevent snow and ice accumulation on slopes that are observed to be free of glacier ice such as the southwest face of Sagarmatha (Mt. Everest) while allowing accumulation on steep sections of the glacier (Rowan et al., 2015) resulting in accumulation rates at the glacier surface in line with the limited available observations for Himalayan glaciers of 2 m w.e. a⁻¹ (Benn and Lehmkuhl, 2000).

Rock avalanching is responsible for much of the debris accumulation on the glacier surface but there is little information about the magnitude and frequency of these events, so headwall erosion was assumed to be uniform at 1 mm a⁻¹ (Rowan et al., 2021). Debris produced by headwall erosion was delivered to the glacier surface using a similar non-linear hillslope flux model to snow avalanching. The reduction in ablation beneath supraglacial debris from clean-ice values was represented as a reciprocal function that scaled clean-ice ablation (bclean) to give sub-debris melt (bdebris) as a function of debris thickness (h): 2bdebris=bclean×h0h+h0 where h0 is a constant representing the characteristic debris thickness at which the reduction in ablation due to insulation by supraglacial debris is 50 % of the value for an equivalent clean-ice surface (Anderson and Anderson, 2016; Rowan et al., 2021). The observed heterogeneity of surface ablation required a parameterisation of sub-debris melt representing the effects of differential ablation, which was represented in Eq. (2) using a value for h0 of 0.8 m (Bartlett et al., 2021; Rowan et al., 2021; Strickland et al., 2023). We note that Eq. (2) represents an empirical calculation of the impact of supraglacial debris on glacier surface melt that is calibrated to observations of sub-debris melt rates for glaciers in the Central Himalaya (Rowan et al., 2021) and as such, changes in surface energy balance processes including vapour fluxes within the debris-covered section of the glacier are not included.

The spatially averaged mass balance was most sensitive to changes in MAAT (perturbed by ±1.5, 2.0 and 3.0 °C), LW_in and SW_in (±10 % and 20 %). Perturbations of relative humidity (±10 % and ±20 %) had the least impact on mass balance. The use of a seasonal lapse rate of 5.38 °C km⁻¹ yielded a spatially averaged mass balance that was 5.6 % less than the reference calculation value, while a diurnal lapse rate gave a mass balance that was only 0.45 % lower because the reference lapse rate was close to the mean of the day/night lapse rates, whereas the environmental lapse rate (6.50 °C km⁻¹) gave a mass balance that was 1.24 % higher than the reference value. The relatively small difference in mass balance due to the choice of lapse rate is due to the extremely high elevation of Khumbu Glacier, which means that MAAT is below 0 °C in the accumulation area for much of the year and a higher lapse rate does not affect rain/snow partitioning. The largest difference in mass balance due to the choice of lapse rate occurred just below the ELA and resulted in a difference of ±24 % in spatially averaged mass balance for this section of the glacier. The National Geographic AWS on Mt. Everest provided an opportunity to examine lapse rates at the highest elevations. For the period April–November 2019, the observed lapse rate was 4.68 °C km⁻¹ between Phortse (3810 m a.s.l.) and Everest Base Camp (5315 m a.s.l.), and 5.36° km⁻¹ between Camp II and South Col, similar to the value used in this study. The lapse rate above 8000 m a.s.l. was about 1.2 °C km⁻¹ greater than that below 5600 m a.s.l. between the two highest AWS at the South Col (7945 m a.s.l.) and the Balcony (8430 m a.s.l.) indicating that in the highest-elevation sections of the catchment, lapse rates may be best represented by values considered suitable for the free atmosphere.

Coupled parameter testing was carried out to perturb precipitation and MAAT simultaneously. The most significant change in spatially averaged mass balance followed a 3 °C increase in MAAT and 20 % decrease in precipitation amount. The change in ablation following an increase in temperature of 1.5 °C was compensated by accumulation resulting from 20 % higher precipitation. The impact on mass balance of two precipitation phase (rain/snow) partitioning schemes was investigated and compared with the default snow transfer function in COSIPY; (1) using threshold temperatures of 0.5, 2.0, and 3.5 °C, and (2) using a calculation that smoothly scaled rain/snow partitioning from 100 % solid precipitation at -1 °C to 0 % solid precipitation at 4 °C. The height of the 0 °C isotherm during months that experienced significant ablation (May–September) fluctuated around 5125–6250 m a.s.l., which correlated with the elevations that experienced the greatest mass balance change with lapse rate. While the lapse rate used to distribute MAAT did not have a significant impact on glacier-wide mass balance, the elevation of the 0 °C isotherm from the pre-monsoon until the end of the monsoon was sensitive to the air temperature distribution.

The glacier ice surface roughness (z0) value was 1.7 mm (Table 2), which is a reasonable estimate for clean-ice glaciers (Mölg et al., 2012). The z0 values reported in the literature vary widely, even for clean-ice glaciers, and do not consider debris-covered glacier surfaces, and so two substantially different z0values were tested as end-members of the likely range in z0 values for Khumbu Glacier. Values for z0 of 0.1 mm from Midtre Lovénbreen in Svalbard (Irvine-Fynn et al., 2014) and August-One Glacier in China (Guo et al., 2018), and a value of 6.9 mm for the clean-ice section of Haut Glacier D'Arolla (Brock et al., 2006) were all tested in the reference simulation. Adjusting z0 had minimal impact on mass balance, although a higher (lower) z0 did result in slightly increased (decreased) mass balance.

The reference simulation represented the period 2013–2015 CE and was forced with AWS data using the model parameters in Table 2. Turbulent fluxes and energy balance components across Khumbu Glacier were explored across the 2013–2015 reference period to assess the performance of COSIPY and understand their relative spatial importance (Fig. 5). The glacier-wide clean-ice mass balance for the three-year reference period was -3.4 m w.e., which equates to -1.13 m w.e. a⁻¹. Maximum ablation was up to 16.2 m w.e. over three years (Fig. 4). High precipitation events were observed to offset some ablation if they occurred outside the core monsoon season (e.g., in October 2013 and May 2014) but did not influence monsoon season ablation when high air temperatures and strong incoming radiative fluxes rapidly remove snow cover and drive melting. Higher minimum temperatures in winter 2013–2014 CE relative to the other winters did not significantly influence accumulation rates, which remained similar to those in 2014–2015 CE. Low precipitation amounts during the 2015 monsoon (286 mm in 2015, compared to 330.8 mm in 2013, and 333.9 mm in 2014) resulted in lower accumulation in the upper reaches of the glacier. The precipitation gradient was calibrated to 1 × 10⁻⁵ % m⁻¹ to match observed accumulation rates. However, this gradient largely arises from avalanching (Benn and Lehmkuhl, 2000) which is challenging to represent in COSIPY and was instead handled in the glacier model (Sect. 2.6).

The energy available for ablation peaked in the pre-monsoon and monsoon, bringing higher rates of sublimation and subsurface melt in April–June (Fig. 5). Simulated sublimation occurred at all elevations, with the highest cumulative loss near the South Col (EB7910) where sublimation dominated mass balance and only slightly slowed from December until May. Sublimation rates were increasingly tied to seasonality with distance down-glacier, with rates on the lower section of the tongue (EB4980) increasing from April until the start of the monsoon in July. Calculated subsurface melt was negligible at or above the ELA (5950 m a.s.l.) whereas at lower elevations sub-surface melt dominated mass balance with a stronger seasonal cycle related to surface temperature. The interannual variability in subsurface melt was linked to surface temperature, although low simulated subsurface melt rates in the first year of the reference simulation were largely due to persistence of the initial snow cover that shielded the subsurface from relatively warm air temperatures until the subsurface adapted to local conditions. Refreezing occurred across the entire glacier, with a staggered onset due to increased elevation, and the absolute values were low (Fig. 5). The higher latent heat flux during the monsoon resulted in higher deposition of snow to the glacier at the lower elevations, with negligible rates at higher elevation. Similar absolute values and patterns are seen for condensation.

Calculated incoming shortwave radiation matched well with AWS observations, indicating that the radiation model in COSIPY performed well across the extreme relief of the Khumbu Glacier catchment. Net shortwave radiation contributed the largest energy input to the glacier surface at lower elevations, correlating most strongly with the energy available for melt, with a mean correlation coefficient of 0.79. There was high temporal variability related to variable cloud cover exhibited in the hourly incoming shortwave radiation forcing and fluctuating albedo during the warmer months with the melting of the snowpack. The high incoming shortwave radiation the upper reaches of the glacier indicate that low net shortwave radiation is not due to topographic shading. Net shortwave radiation was correlated with albedo (r=0.86), and the persistence of snow throughout much of the year reduced the energy available for melt. Net longwave radiation also contributed to the energy available for melt as the pattern of both fluxes corresponded. Between 5900–7900 m a.s.l., net longwave radiation sometimes exceeded zero during the monsoon, most likely due to heavy cloud cover and increased temperatures relative to the glacier surface. The latent heat flux was almost zero at the lower elevation sites as the arrival of the monsoon resulted in higher relative humidity, and this pattern was similar, but dampened, at higher elevation. At the South Col (EB7910) the energy available for melt correlated most closely with the sensible heat flux (Fig. 5).

Grid spacings for the model domain of 30, 50, 200 m and 1 km were tested to ensure that that the COSIPY calculations captured orographic effects without unnecessary computational expense (Fig. 4). The simulated maximum accumulation rate did not change significantly with grid spacing, giving accumulation rates of 2.1–3.9 m w.e. at 6500–7000 m a.s.l. in the reference simulation. The 1 km grid spacing contained only 27 glacier points, and gave a similar spatial mean mass balance to the finer-resolution calculations, but there were large gaps in mass balance calculated across the glacier that affected the height of the ELA and significantly reduced the calculated maximum accumulation value. The 30 and 50 m grid spacings captured greater spatial variability in mass balance relative to the 200 m resolution calculation, particularly at elevations between 5200–5400 m a.s.l. (Fig. 4). However, as the ELA, and the calculated maximum and minimum mass balances were not significantly different between these finer-resolution calculations, the 200 m grid spacing was used throughout to benefit from the much reduced computational expense.

The downscaled climate variables from the three RCMs for the present-day time slices (2015–2020 CE) were evaluated against 14 years of observations from three AWS to assess the representation of means, seasonality, diurnal cycles, day-to-day variability, and interannual variability (Fig. 2C and D). All three downscaled RCMs showed good agreement between MAAT (-2.15 ± 0.05 °C) and observed air temperature from the Pyramid AWS (Figs. A1 and A2). The representation of the monsoon was greatly improved by the RCM downscaling; temperature seasonality was well resolved following quantile mapping and the monthly mean and minimum air temperatures were similar to observations across the present-day time slice (Fig. A1). The monsoon stabilised air temperatures and reduced the range between minimum and maximum temperatures in the downscaled RCMs, which was in better agreement with AWS observations, but was not present in the raw RCMs prior to downscaling. We note that the downscaled maximum air temperature was at times higher than observations amongst all RCMs during the post-monsoon and winter (Fig. A1) but the distribution of downscaled air temperatures was similar to observed values (Fig. A2). Gamma-distribution quantile mapping substantially improved the absolute precipitation values relative to the AWS observations compared to those in the raw RCMs; the overestimation of winter precipitation and relative underestimation of monsoon precipitation amounts in the raw RCMs was reduced and downscaled results show a clearer monsoon signal (Fig. A3). When compared with AWS observations, RCM downscaling slightly overcorrected the seasonal precipitation pattern with a slight underestimation of winter precipitation for the most extreme winter events. Across the three present-day RCM simulations, the surface mass balance calculated using the NOAA RCM was more positive than that for the ISPL and CCCma RCMs and most similar to the mass balance calculated from meteorological observations, and remained the most positive mass balance in the end-of-century time slices (Fig. 6).

COSIPY was used to calculate clean-ice surface mass balance from the downscaled RCMs, and the insulating effects of supraglacial debris were calculated in iSOSIA. The simulated glacier geometry and dynamics were compared with remotely sensed observations of ice thickness, supraglacial debris distribution, velocity, and surface elevation change for the present-day glacier (Fig. 3) and varied depending on the RCM used as forcing (Fig. 7). The experiment using the NOAA RCM was identified as the starting point for all future simulations because this was most representative of the observed glacier at 2015 CE (Fig. 3). The distributed surface mass balances calculated using COSIPY were most similar to observed values after the calculated surface mass balances were integrated with the glacier model to include accumulation by snow avalanching and the reduction in surface melting beneath supraglacial debris; the active glacier extent was underestimated if supraglacial debris is not simulated (Fig. 8). The supraglacial debris-mass balance feedback in the glacier model reproduced the observed reversed mass balance gradient and peak in ablation below the Khumbu Icefall (Fig. 1D).

The simulated glacier area was 7.8 km² and similar to that obtained from structural mapping in 1979 CE (Nakawo, 1986). Radio-echo sounding in 1999 CE obtained ice thickness estimates close to the active terminus of ∼ 160 m (Gades et al., 2000) and simulated ice thickness at the terminus was 130 m (Fig. 3A). The simulated thickness at the active glacier terminus thickness was approximately 175 m in 1999 CE, which agreed well with observations from DEMs of difference that show thinning here of up to 55 m between 1984–2018 CE (Fig. 3D and E) (King et al., 2020). Simulated surface elevation change in the ablation area was -30 m over 20 years to the present day and similar to values derived from satellite observations for 1984–2018 CE (King et al., 2020). Simulated present-day glacier velocities (Fig. 9) reached a maximum of 248 m a⁻¹ and showed a similar pattern and magnitude to glacier surface velocities observed using remote sensing observations, which reach a maximum of 220 m a⁻¹ in the Khumbu Icefall (Altena and Kääb, 2020) and up to 20 m a⁻¹ in the ablation area (Quincey et al., 2009; Dehecq et al., 2019). The simulated present-day velocities in this study were a better fit to remote sensing observations than those from previous simulations that used an elevation-dependent mass balance forcing (Rowan et al., 2015, 2021) where the maximum simulated velocities were 118 m a⁻¹.

Khumbu Glacier is responding to historical climate change and will continue to shrink even if warming ceases today. Indeed, if we allow the spin-up experiment to reach equilibrium with the present-day NOAA RCM mass balance, the glacier terminus will recede by 2.1 km and the maximum ice thickness will decrease from 246 to 206 m by 2100 CE without any additional warming. In this scenario, a supraglacial debris layer up to 1.3 m thick extends 1 km up-glacier from the terminus and partially dampens the committed volume loss, by sustaining 13 % more ice volume than would be the possible for a clean-ice glacier surface with the same mass balance (Fig. 10A). The committed glacier volume loss due to historical warming in the absence of any further climate forcing is 10 %–23 % of the present-day glacier mass (Fig. 10C) with the associated uncertainty represented by this range of values arising from the parameterisation of the impact of supraglacial debris evolution on surface melting.

Now considering the effects of additional warming under the RCP scenarios for the NOAA experiment, we find that greater warming occurs in winter than in the monsoon under both RCPs and results in an increase in annual precipitation amount of about 15 % made up of a greater increase in non-monsoon precipitation than monsoon precipitation (Fig. 2E). The climate forcing from the downscaled NOAA RCM under RCP4.5 is 1.4 °C warmer than the present day (-0.75° in 2095–2100 CE compared with -2.15° in 2015–2020 CE) and annual precipitation increases by 14.8 % from 581.4 mm at present day to 664.8 mm a⁻¹ by 2100 CE with monsoon (June–September) precipitation increasing by 5.4 % and non-monsoon season (December–February) precipitation increasing by 14.1 % (Fig. 2E). Under RCP8.5, the downscaled climate forcing is projected to be 3.8 °C warmer than present day (1.65 °C in 2095–2100 CE) with an increase in annual precipitation of 14.9 % by 2100 CE, with monsoon precipitation increasing by 9.8 % and non-monsoon precipitation increasing by 19.4 % (Fig. 2E).

In the NOAA RCM RCP4.5 experiment, the spatially averaged cumulative glacier mass balance is -0.14 m w.e. a⁻¹ in 2100 CE, which is slightly more positive than the present-day value of -0.21 m w.e. a⁻¹ (Fig. 6) and glacier volume decreases by 36 % between the present day and 2100 CE (Fig. 10C). While significant, this end-of-century glacier loss is partially offset by the concurrent increase in precipitation. In comparison, an equivalent simulation forced only by warming and without any change in precipitation results in a more linear trajectory of glacier change and 70 % loss of glacier volume by 2100 CE (cyan line in Fig. 10C) demonstrating that 34 % of potential glacier loss from warming could be compensated by the increase in precipitation that occurs as a result of warming.

The CCCma and IPSL RCMs projected greater warming from the present day by 2100 CE than the NOAA RCM under RCP4.5 with a value of 1.6 °C (+0.2 °C compared with the NOAA RCM) in the IPSL RCM experiment and 2.2 °C (+0.8 °C) in the CCCma RCM experiment. These two RCMs also projected slightly greater warming by 2100 CE under RCP8.5, with a value of 3.9 °C (+0.1 °C compared with the NOAA RCM) for the IPSL RCM experiment and 4.1 °C (+0.3 °C) for the CCCma RCM experiment.

The projected increase in precipitation amount across the three RCMs is similar between RCPs with annual totals above 600 mm by 2100 CE. The CCCma RCM gives the greatest increase in annual precipitation amount of 100 mm by 2100 CE (Fig. 2E). There is no evidence of change in the intensity of the Indian Summer Monsoon, as the seasonal split in precipitation remains similar to the present day, but the frequency of days with high precipitation (over 15 mm d⁻¹) increases by 2100 CE, giving twice as many days in the NOAA RCM experiment and up to seven times as many days in the IPSL RCM experiment.

Under RCP8.5, all experiments showed similar results for mass balance by 2100 CE with only a 10 % difference in glacier volume between the three RCMs (Fig. 10C). The CCCma RCM experiment has only a 1 % difference in volume loss between RCP4.5 and RCP8.5 by 2100 CE despite a 1.9 °C difference in MAAT – this is a surprising result given the significant temperature difference, which can be attributed to the greater number of high-magnitude precipitation events that occur under RCP8.5 in combination with the small difference in winter temperatures between the two RCPs. Indeed, in the CCCma RCM experiment under RCP4.5, the maximum winter temperature is 1.7 °C higher than for the other RCMs, resulting in ablation and rainfall (rather than snowfall) during the winter.

Sources of uncertainty in our results arose from each step of our glacier modelling workflow, and we considered how the experiments could be designed to reduce these uncertainties. Here we discuss the potential sources of uncertainty associated with the choice of RCMs, the downscaling of the RCMs, the use of time slices rather than continuous mass balance calculations, the representation of future precipitation in the RCMs, and the representation of avalanching in the glacier model.

A single RCM was not considered sufficient to represent both present-day climate and potential future climatic extremes, but the climate-mass balance forcing ensemble was limited in size due to the small number of RCMs available. The use of three RCMs allowed the implications of uncertainties in understanding of local climate for glacier evolution to be evaluated. A multi-model mean approach using all the CORDEX South Asia RCMs (as widely used elsewhere) was not considered sufficient to represent present-day and future climate conditions in the Khumbu Valley because this approach gives equal weighting to models irrespective of their performance (Pierce et al., 2009) and does not enable intercomparison of results for future climate conditions.

Five-year downscaled RCM time slices were chosen to reduce computational expense associated with COSIPY and the integration with iSOSIA. To ensure that the five-year periods selected were representative, the preceding decade was used for comparison with the time-slice results (results not shown). The use of quantile mapping with 14 years of AWS data as the downscaling method limited the influence of any natural variability by ensuring that the period did not reflect an extreme phase of natural climate oscillation. This comparison was particularly important for the future time slices, where large uncertainties arise between RCMs, and observational data cannot be used for evaluation of the downscaled climate or the resulting mass balance. We note that this experimental design could be improved by interpolating the mass balance over time and coupling the COSIPY and iSOSIA models such that mass balance was calculated dynamically for the evolving ice surface, but this was beyond the scope of our experiments. However, the experiments were repeated using addtional mid-Century (2045–2050 CE) mass balance forcings to investigate if this produced a different end-of-Century result. These experiments produced near-identical results in 2100 CE to the experiments with no mid-Century forcing, in part because the response time of the simulated glaciers was longer than the 40-year period between the present-day and future time slices. Thus, a mid-century surface mass balance forcing was not considered necessary in our experiments and instead we used a step forcing for mass balance rather than interpolation between mass balance calculations in the glacier model.

The differences in simulated glacier change and response time between RCM forcings were at times greater than those resulting from the RCP due to differences in projections of precipitation. Whilst the three selected RCMs performed well in representing annual precipitation cycles from the six available CORDEX RCMs, we note that this representation was still fairly poor, although substantially improved by quantile mapping (Fig. 2D). The poor representation of monsoon dynamics in the present-day RCMs highlights an additional uncertainty associated with future precipitation scenarios and that these results should be treated as a set of possible scenarios.

The CORDEX CMIP5 and CMIP6 projects only produced dynamically downscaled RCMs for two future emissions scenarios (RCP4.5 and RCP8.5) and as such the implications of other RCPs for glacier evolution could not be assessed. The downscaled future climates were compared with those from other studies using CORDEX results, and showed similar annual and seasonal regional temperature trends strongly linked to the choice of RCP, and similar positive precipitation trends with poor agreement between RCMs (Kaini et al., 2019; Sanjay et al., 2017). The relationship between precipitation and warming in the two future emissions scenarios was less clear than that for air temperatures because the monsoon-influenced Himalaya has particularly poor RCM consensus and high levels of uncertainty in future precipitation trends with warming relative to other regions in High Mountain Asia (Sanjay et al., 2017).

A potentially large uncertainty in the glacier model arose from the parameterisation of avalanching, as this mass balance variable is poorly constrained, with no direct observations of the avalanche contribution to the mass balance of Khumbu Glacier and high regional variability (Kneib et al., 2025). Avalanching was included in iSOSIA by slope-dependent diffusion and resulted in increased accumulation along the glacier surface in the Western Cwm and improved the agreement between simulated and estimated accumulation rates and distribution (Fig. 1D). Future work to resolve the impact of low frequency–high magnitude avalanche events on accumulation rates would be useful to refine this calculation but the contribution of avalanches to glacier accumulation over decadal time scales remains extremely challenging to measure (Purdie et al., 2025).

Our study addresses fine-scale temporal (hourly) and spatial (100 m) glacier surface processes, including avalanching and sublimation, that affect glacier surface mass balance across the elevation range of Khumbu Glacier, but further observations of meteorological and glaciological conditions at the highest elevations would be beneficial, and are needed if micro-scale processes are to be included in glacier models (Brun et al., 2023; Khadka et al., 2021; Mölg et al., 2014; Shaw et al., 2022). Analysis of meteorological observations from AWS across the Dudh Koshi catchment indicated that precipitation gradients were weak, slightly negative or absent, confirming the observations of Salerno et al. (2015) and Yang et al. (2017). To test the sensitivity of precipitation to elevation, COSIPY was forced by a gridded climate distributed using weak negative, weak positive, and no precipitation gradients distributed across the model domain using a linear regression with elevation from the 100 m resolution DEM. The results of these experiments were used to force iSOSIA and the simulated historical glacier evolution was similar, resulting in only a 10 m difference in the maximum ice thickness between simulations with different precipitation gradients (result not shown).

The mass balance sensitivity to seasonal and daily variations in lapse rate showed a lesser impact on glacier-wide mass balance than in other studies, due to the large elevation range of Khumbu Glacier whereby a smaller fraction of the glacier relative to total area is located along the zero degree isotherm (e.g., compared to Yala Glacier in Nepal; Immerzeel et al., 2014). Seasonal and daily lapse rates that accounted for marked lower values during the monsoon season and at night gave a mean annual value of 5.54 °C km⁻¹, which produced glacier-wide mass balance and ice thickness simulations that were closest to geodetic observations and represented the maximum rates of surface lowering in the upper ablation area where the debris layer is thinnest (Fig. 3D and E).

Sublimation simulated in our study occurred at all elevations with the highest rate of ice loss due to sublimation (-0.12 m w.e. a⁻¹) in the upper reaches of the Khumbu Glacier catchment near to South Col (about 7495 m a.s.l.) where sublimation dominated ablation with only minor seasonality (Fig. A6). Whilst this amount of ice loss by sublimation is not negligible, it is almost half that found in the point-based calculations after adjusting for the different time periods represented by our studies (Matthews et al., 2020), which is likely due to the assumed uniformity of wind speed across the model domain in COSIPY. Future work to improve the calculation of sublimation in distributed surface mass balance calculations for high-elevation glaciers would be valuable.

While we have considered the effects of mesoscale meteorology on glacier mass balance, smaller-scale processes operating close to the land surface could also be important. Katabatic winds were suggested to explain a local 15-year decrease in maximum air temperatures and precipitation over glaciers while minimum air temperatures continued to rise (Salerno et al., 2023). However, this effect was found to be short-lived (Shaw et al., 2025) and the impact of microscale near-surface cooling on the duration and extent of mesoscale precipitation and accumulation is likely to be minimal and therefore unlikely to significantly affect glacier-wide mass balance (Mott et al., 2020; Shaw et al., 2024). Observations from the Camp 2 AWS (6464 m a.s.l.) indicate that surface energy fluxes may be sufficient to cause non-negligible melting of glacier surfaces despite freezing air temperatures (Matthews et al., 2020). Results from an ice core from South Col Glacier (>8000 m a.s.l.) combined with COSIPY experiments suggested that ablation may also take place at even at the highest elevations (Potocki et al., 2022). However, a subsequent study found no evidence of glacier mass change, and identified large uncertainties associated with simulating mass balance at these extreme elevations where sub-daily air temperature gradients and the duration of snow cover strongly affect ablation and accumulation (Brun et al., 2023). Future work is needed to reduce these uncertainties, as very few observations exist of accumulation processes and the upper limit of ablation processes for high-elevation Himalayan glaciers.

Current global greenhouse gas emissions are following the trajectory of the intermediate emissions scenario RCP4.5, while the high emissions scenario RCP8.5 could be described as “low possibility but high impact” (Pedersen et al., 2020). However, as represented in the RCMs used in our study, mountain regions are warming more rapidly than the global mean such that a global temperature rise of 1.5 °C will lead to 2.1 ± 0.1 °C of warming in High Mountain Asia (Kraaijenbrink et al., 2017; Pepin et al., 2022) although the occurrence of elevation-dependent warming above 5000 m a.s.l. is debated (Gao et al., 2018). The high temperatures projected under RCP8.5 could potentially be offset partly by increased precipitation, given that high-magnitude precipitation events from winter Westerly disturbances increased by a factor of seven between present day and 2100 CE in the IPSL RCM under RCP8.5.

We found no evidence of future increases in precipitation offsetting RCP8.5 warming; net glacier mass balance was strongly negative in all RCP8.5 experiments and insufficient to maintain any actively flowing glacier. Under RCP8.5, glacier mass balance in the monsoon-influenced Himalaya may therefore shift from being driven by accumulation during the monsoon to predominantly during winter. Monsoon precipitation would only result in snow accumulation at the very highest elevations and would be insufficient to maintain flowing glaciers. This outcome is avoidable by limiting anthropogenic warming to within RCP4.5, which, due to the associated increase in precipitation, could sustain nearly two thirds of the current glacier volume until 2100 CE and potentially for two centuries further into the future.

A recent global glacier modelling study forced by an ensemble of 10 GCMs projected mass loss of 64 % for Khumbu Glacier by 2100 CE (Rounce et al., 2023). In comparison, our experiments project less severe rates of decline, resulting in 30 % less mass loss under the RCP4.5 future climate scenario than in the global study (Fig. 10C). One difference between these results is that rather than using the global glacier inventory outline to define the glacier margins we consider only the actively flowing glacier and so exclude 20 % of the starting glacier volume in the detached tongue. We would expect the two sections of the glacier to evolve along different paths; while the active glacier responds to climate change as projected in our experiments, thick supraglacial debris mantling the detached tongue could allow this ice mass to survive and slowly decay in situ for many decades beyond the present day. The decay of the detached tongue may however increase due to erosion of the surface by ice cliffs and supraglacial water bodies that are expanding across the former glacier surface (King et al., 2020).

Our experiments only consider the rapidly changing active glacier, and we expect that the debris-covered tongue would melt more slowly than projected in the global modelling study, but as we do not consider the stagnant tongue to be part of the present-day glacier the ice volume simulated at the start of our experiments is smaller than that represented by Rounce et al. (2023) and other studies based on the RGI glacier inventory. The dynamically detached debris-covered tongue represents about 20 % of the present-day glacier volume and contains ice estimated as up to 360 m thick. The mean present-day ablation rate across this section of the glacier simulated in Rowan et al. (2021) is -0.54 m w.e. a⁻¹ which can be used to estimate the life expectancy of the debris-covered tongue assuming no input of ice from the active glacier and no change in ablation rate due to thickening of supraglacial debris or the development of ice cliffs and supraglacial ponds. While the thickest part of the detached tongue may survive for ∼ 600 years, the mean life expectancy of this ice mass is 176 ± 148 years from the present day meaning that the former debris-covered tongue will vanish by 2200 CE.

The dynamic response time of large glaciers to climate change is of the order of centuries. For this reason, we start our simulations from the late Holocene (∼ 1 ka) moraine extent when Khumbu Glacier was last considered dynamically stable (Hornsey et al., 2022; Rowan et al., 2015). The relationship between glacier response time and mass balance becomes less important after 2100 CE when the glacier is so small that ice flow has little impact on glacier volume change. Global and regional glacier modelling studies typically start their simulations in the current Century (e.g., 2000–2007 CE in Marzeion et al., 2020; 2000 CE in Rounce et al., 2023) and a further complication arises from the use of global glacier inventories as a starting point for glacier modelling studies as such inventories cannot capture the current dynamic state of glaciers that are imbalanced, and include all ice-covered areas rather than identifying only actively flowing ice. However, satellite-derived velocity products could be used identify where ice flow within glacier outlines declines to negligible rates (Dehecq et al., 2019).

The RGI 7.0 inventory for Khumbu Glacier is based on imagery from 1999 CE (RGI 7.0 Consortium, 2023) where the detached debris-covered tongue represents 20 % of the glacier volume contained within this outline (Fig. 1C). Simulations that integrated the stagnant tongue into the model domain rather than as part of the flowing ice improved the representation of simulated ice flow compared to observed values, supporting our conclusion that the debris-covered tongue has been dynamically detached from the active glacier for 50–100 years (Rowan et al., 2021). Field observations support the concept of active and stagnant sections co-existing in contact with each other as englacial optical televiewing indicated that thrusting occurs at several sites, denoted by skewed internal debris layers and of basal ice that has been thrust to the glacier surface, near to the active glacier terminus from the direction of Khumbu Icefall (Miles et al., 2021). Our simulations show that development of supraglacial debris at the active glacier terminus reduced net volume loss by 13 % (Fig. 8). Dynamic detachment of debris-covered tongues could allow these glaciers to move closer to equilibrium with a rapidly changing climate, the local mass balance gradient is a more important control on glacier change for both clean-ice glaciers and debris-covered Himalayan glaciers.