The Dunde Glacier is located in the western part of the Qilian Mountains on the Northeastern TP. It is a typical continental glacier, with an elevation ranging from 4400 to 5500 m (Guo et al., 2015). The ice cap covers an area of approximately 60 km², with an average annual elevation change rate of -0.501 ± 0.08 m yr⁻¹ (Hugonnet et al., 2021). The region experiences pronounced annual and daily temperature variations, with a mean annual temperature of approximately -5 °C and annual precipitation ranging from 300 to 400 mm. Meltwater from the glacier primarily feeds into the Tataleng and Haerteng rivers, which provide an important water source to their respective drainage basins. The observation site was situated on the surface of the Dunde Glacier (38°6^′23^′′ N, 96°24^′54^′′ E) at an elevation of 5317 m a.s.l., as shown in Fig. 1, and served as the primary observation site for this study.

Meteorological variables, including air temperature, air pressure, relative humidity, wind speed and direction, incoming and outgoing shortwave radiation, and incoming and outgoing longwave radiation, were primarily measured at the study site using a Campbell-ClimaVUE50 automatic weather station (AWS1) located at 5317 m a.s.l. Glacier surface height was measured independently using a Campbell SR50 sonic ranging sensor installed at AWS1. The sensor records the distance between the instrument and the glacier surface, from which temporal changes in surface height were derived. Occasional gaps in the AWS1 records were filled using linear relationships established from concurrent observations at the nearby auxiliary station (AWS2). The glacier surface temperature used in this study was derived from the observed outgoing longwave radiation, assuming a constant surface emissivity of 0.98. Details of the sensors used to measure each variable are provided in Table 1.

The point surface mass balance at the Dunde Glacier was measured using a single stake installed near AWS1 following the glaciological method described by Paterson (1994). During the observation period from 26 April to 31 December 2023, snow pits were excavated during periods of snow cover to measure snow layer density and stratigraphy. The measurements included the stake height above the glacier surface; the thickness and density of snow, firn, and superimposed ice layers, where present; and the stratigraphic structure of the snow-pit profiles (Pu et al., 2008). These measurements were used to calculate the net point surface mass balance over the observation period.

Precipitation was treated separately from other meteorological variables due to the lack of continuous in situ measurements at AWS1. Precipitation at 4970 m a.s.l. was reconstructed using ERA5 reanalysis data following a two-step procedure. First, precipitation amounts were corrected for gauge under-catch as a function of air temperature and wind speed during precipitation events, following Ma et al. (2019). Second, a constant scaling factor of 1.16 was applied to the daily precipitation totals. To suppress unrealistically small precipitation signals, daily precipitation was set to 0 when ERA5 precipitation in the corresponding grid cell was lower than 0.45 mm, consistent with the criteria adopted in previous studies (Yang et al., 2013). After reconstructing the precipitation at 4970 m a.s.l., precipitation at 5317 m a.s.l. was estimated by extrapolating the reconstructed precipitation using three constant precipitation gradients (ΔP1, ΔP2, and ΔP3), following Zhu et al. (2022).

Turbulent fluxes were measured using a Campbell IRGASON eddy covariance (EC) system during the period from 14 May to 12 October 2023. The EC method is a widely adopted micrometeorological technique that enables real-time, accurate, and continuous monitoring of atmospheric turbulence. All raw turbulence data were recorded at a frequency of 10 Hz, including the three-dimensional wind components, virtual temperature, and water vapor concentration.

Turbulence data were processed using EddyPro software. A flux averaging interval of 30 min was applied during data processing. Prior to flux calculation, the raw high-frequency data were screened using the instrument-provided quality flags to identify and remove invalid or unreliable measurements. This quality-flag-based filtering was applied at the high-frequency level before covariance calculation, and no interpolation was performed for the removed samples. Turbulent fluctuations were subsequently defined using the detrending options implemented in EddyPro. Time lags between wind components and scalar quantities were compensated using covariance maximization based on circular correlation techniques, which is recommended for open-path EC configurations (Moncrieff et al., 1997, 2005). Coordinate rotation was applied using the double-rotation method to correct for sensor tilt and streamline distortion (Kaimal and Kristensen, 1991). Flux correction was then applied to the calculated fluxes. Spectral corrections were first implemented to ensure that density corrections were based on environmentally representative fluxes. Density fluctuation effects were corrected using the Webb–Pearman–Leuning (WPL) formulation (Webb et al., 1980). The effects of humidity on sonic temperature and temperature-related covariances were corrected following the approach of Schotanus et al. (1983). Spectral attenuation resulting from both low-frequency and high-frequency losses was addressed using spectral correction schemes based on analytical transfer functions and reference cospectral formulations derived from the Kaimal spectrum (Kaimal et al., 1972) and its subsequent developments (Moore, 1986; Moncrieff et al., 1997, 2005; Massman, 2000, 2001). After the above processing steps, residual outliers in the 30 min flux data were further removed by excluding the following time intervals: periods with mean horizontal wind speed lower than 1 m s⁻¹ or higher than 8 m s⁻¹; periods when the absolute value of vertical wind velocity exceeded 0.15 m s⁻¹; and periods when the wind direction corresponded to directions obstructed by the mounting structure. After this additional screening, 72 % of the EC turbulent flux data were retained.

This study used the roughness lengths of momentum derived from EC measurements to calculate turbulent fluxes. The EC data, with a 30 min temporal resolution, provided three-dimensional wind speed components, which are then used to calculate friction velocity (u*) and Obukhov length (L) as follows: 1u*=u′w′‾2+v′w′‾21/4,2L=-Tvu*3gκw′Tv′‾, where u′ and v′ represent the fluctuations in the horizontal wind components around their 30 min mean values, w′denotes the fluctuation in the vertical wind component, Tv is the 30 min averaged virtual temperature (K), g is the acceleration due to gravity (9.8 m s⁻²), and κ is the von Kármán constant (0.4). The momentum roughness length (z0m) was then retrieved using friction velocity and L, according to the following equation: 3z0m=exp⁡-κuu*-ΨvzLz, Here, z0m is the momentum roughness length, and u represents the 30 min averaged wind speed. The term Ψv is the stability correction function for momentum. Under stable conditions zL>0, it follows the formulation of Holtslag and de Bruin (1988), while under unstable conditions zL<0, it follows the Businger-Dyer expression described by Paulson (1970).

Stable conditions: 4-ΨvzL=zL+bzL-cdexp⁡-dzL+bcd,

Unstable conditions: 5x=1-16zL0.25,6ΨvzL=log⁡1+x2⋅1+x22-2⋅arctan⁡x+π2, where the constants are a = 1, b = 2/3, c = 5, and d = 0.35; z is the measurement height. To provide a reference for future studies without reliance on EC data, we parameterized the scalar roughness lengths (z0t and z0q) as functions of the momentum roughness length z0m, which was derived from EC data. This parameterization follows the methods proposed by Andreas (1987) and Smeets and van den Broeke (2008), which have been shown to provide accurate estimates of scalar roughness lengths over glaciers. Hereafter, these two parameterization schemes are referred to as A87 and SvdB, respectively. In this study, we performed quality control on the 30 min z0m values following the procedures outlined by Conway and Cullen (2013) and Li et al. (2016). Detailed processing steps can be found in Radić et al. (2017). After filtering, 183 valid z0m data points remained, with inferred z0m values ranging from 1.14 × 10⁻⁵ to 2.08 × 10⁻² m. We finally selected the median of the quality-controlled z0m values (1.2 × 10⁻⁴ m) as the representative roughness length for evaluating the performance of the different turbulent flux parameterization schemes. For the measured sensible and latent heat fluxes, the same general quality control procedures as those applied to z0m were adopted. However, with respect to the neutrality and wind speed criteria, flux calculations were allowed to include data satisfying |z/L| < 2 and u > 1 m s⁻¹. After screening, 592 turbulent flux data points were retained for subsequent model calculations and evaluation.

Variations in the performance of different turbulent flux parameterizations primarily arise from their respective approaches to computing turbulent exchange coefficients and applying atmospheric stability corrections. These methodological differences directly affect method accuracy under varying temperature gradients, humidity gradients, and wind speed conditions, leading to discrepancies in the simulated LE and H. In this study, we evaluate two categories of bulk aerodynamic methods for calculating turbulent fluxes over glacier surfaces. The first category comprises methods in which the bulk exchange coefficient (C) is formulated as a function of surface roughness lengths and atmospheric stability. The second category includes bulk methods that explicitly incorporate a simplified katabatic (glacier wind) parameterization.

Within this framework, we analyze five bulk methods that are commonly applied to glacier surfaces. These include (i) a simplified bulk formulation without explicit stability corrections (Clog); (ii) and (iii) bulk methods that account for atmospheric stability through the bulk Richardson number (CRib1 and CRib2); (iv) a method based on the full Monin–Obukhov similarity theory, employing universal stability functions with iterative closure (CM–O); and (v) a bulk method derived from a simplified katabatic flow model that explicitly considers glacier wind effects (Ckat). The detailed formulations of methods (i) through (v) are described in the following subsections.

Model performance was evaluated by comparing 30 min turbulent fluxes (H and LE) simulated by each method with eddy covariance (EC) measurements, using standard statistical metrics including the root mean square error (RMSE), mean bias error (MBE), and mean absolute deviation (MAD). For consistency between modeled and observed fluxes, turbulent fluxes were defined as positive when directed from the atmosphere toward the glacier surface, and negative in the opposite direction. The naming of the turbulent flux methods follows the convention of Radić et al. (2017).

For the two methods in which parameter calibration does not involve roughness length, namely Ckat and Clog, the empirical parameters were recalibrated against the quality-controlled 30 min EC observations. Specifically, Cturb and Cturb2 were calibrated for the Ckat method, whereas Ch was calibrated for the Clog method (see Sect. 3.2.1 and 3.2.2 for details). The calibration followed a coarse-to-fine parameter-search procedure. First, the approximate orders of magnitude of the parameters were determined from values reported in previous studies, and relatively broad parameter intervals around these values were explored. The parameter space was then progressively narrowed around combinations that produced smaller discrepancies between the modeled and observed fluxes. The objective function was defined as the sum of the root mean square errors (RMSEs) of the modeled latent and sensible heat fluxes relative to the corresponding EC observations: 7Jθ=RMSELEmodθ,LEobs+RMSEHmodθ,Hobs where θ=(Cturb,Cturb2) for the Ckat method and θ=Ch for the Clog method. The search intervals were iteratively refined until the parameter combination yielding the minimum value of J was identified. The resulting optimal values were Cturb=0.0001, Cturb2=0.007, and Ch=0.0005. RMSE was therefore used as the criterion for parameter selection, whereas MBE and MAD were used only for the subsequent evaluation of model performance.

Because the same EC observational record was used both to constrain the parameterizations – through empirical-parameter recalibration for Ckat and Clog and through the EC-derived representative z0m for CRib1, CRib2, and CM–O – and to calculate the comparison statistics, the subsequent assessment does not constitute an independent validation. The statistics reported in Sect. 4.3 should therefore be interpreted as an observation-constrained assessment of model–observation agreement for the Dunde Glacier.

We used the publicly available MATLAB implementation of the coupled energy balance–snow and firn model (EBFM; van Pelt et al., 2012, 2019), obtained from the EBFM-glacier repository at commit 620f835. The surface energy balance (SEB; W m⁻²) is expressed as 26Qm=Sin+Sout+Lin+Lout+H+LE+Qrain+Qsub, where Qm is the energy available for melt; Sin and Sout are the incoming and reflected shortwave radiation, respectively; Lin and Lout are the incoming and outgoing longwave radiation, respectively; Qrain is the heat supplied by rainfall; and Qsub is the subsurface heat flux. The energy-balance terms are formulated such that surface temperature is the only unknown variable. Surface temperature was determined iteratively by solving Eq. (26), with melt energy initially set to zero. If the calculated surface temperature exceeds the melting point, it is constrained to the melting point and the energy-balance terms are recalculated. Any resulting positive energy residual is then used for melt.

The mass balance (MB, mm w.e.) is calculated as follows: 27MB=∫QmLm+Psnow+QLLs+Cendt, Psnow is the solid precipitation; Cen denotes refreezing; and QL is the mass exchange due to sublimation. Lm is the latent heat of ice melt (∼ 3.34 × 10⁵ J kg⁻¹), and Ls is the latent heat of evaporation/sublimation. The model was applied at the AWS site as a point-scale simulation, and spatial interpolation and topographic-correction routines were therefore not used. Incoming and outgoing shortwave and longwave radiation, surface albedo, snow depth, and rainfall were prescribed directly from the AWS observations. Except for the settings described here, all EBFM parameters were retained at the default values supplied with the public code. A precipitation-phase threshold of 273.75 K was used to distinguish snowfall from rainfall. The turbulent-flux parameters were adjusted only in the experiments designed to evaluate the effects of recalibrating the turbulent-flux methods on SEB model performance. In the baseline simulations, these parameters were assigned the standard values reported in the original publications of the respective turbulent-flux methods. In the recalibrated simulations, the parameter values that minimized the discrepancies between the modeled and observed turbulent fluxes were used for the corresponding methods. All other model settings and forcing data were kept identical between the paired simulations.

Figure 2 shows the temporal evolution of near-surface meteorological conditions during the observation period from 14 May to 12 October 2023. The daily mean Ta at the Dunde Glacier ranged from -14.1 to 3.3 °C, with an average of -4.0 °C (Fig. 2a). The warmest months were July and August, averaging -1 °C. October was the coldest month, with a mean daily Ta of -9.5 °C. The mean daily Ts ranged from -17.2 to 0 °C, with an average of -5.4 °C (Fig. 2d), and exhibited pronounced seasonal variability. Over the study period, the mean surface temperature deficit (Ta-Ts) was 1.4 °C, reaching its highest values in July and September (1.9 °C) and its lowest value in June (0.7 °C). To isolate diurnal variability from the dominant seasonal signal, Fig. 2c and f present the detrended mean diurnal cycles of Ta and Ts. After detrending, both variables displayed clear and consistent single-peak and single-trough diurnal patterns. The earlier Ts peak is interpreted to reflect the rapid radiative response of the glacier surface to incoming solar radiation; Ta responds more slowly owing to the thermal inertia of air and gradual development of convective mixing. At night, however, both the glacier surface and air cool synchronously under stable stratification and weak turbulence, resulting in the coincident early morning Ts and Ta minima. Generally, Ta was higher than Ts for most of a given day, indicative of a persistent near-surface temperature inversion layer over the glacier surface (Fig. 2t and u).

Mean daily relative humidity at the Dunde Glacier was 56.3 %, with notable seasonal variability (Fig. 2g). The highest seasonal average occurred in May–June (62.6 %), whereas September–October was the driest season (50.7 %). On a daily scale, relative humidity was characterized by a distinct midday minimum and nighttime maximum (Fig. 2i).

Daily mean wind speeds ranged from 1.7 to 10.5 m s⁻¹, averaging 4.1 m s⁻¹, with marked seasonal variability (Fig. 2j). The strongest winds occurred during May–June (average of 5.51 m s⁻¹), while June–August recorded the weakest winds (average of 3.6 m s⁻¹). On a daily scale, wind speed exhibited a pronounced diurnal cycle, with the mean daily cycle showing a peak-to-trough difference of approximately 1.5 m s⁻¹ (Fig. 2l). Wind direction was presented using circular statistics. Nighttime wind speeds exhibited limited variability, consistent with stable atmospheric stratification. Prevailing wind directions were westerly and northwesterly (Fig. 2m and o), highlighting the dominant influence of the mid-latitude westerlies on regional meteorological conditions.

Daily mean atmospheric pressure at the Dunde Glacier during our study period ranged from 527.9 to 538.4 hPa, with an average of 534.4 hPa (Fig. 2p). The highest seasonal mean atmospheric pressure occurred in June–August (535.2 hPa) and the lowest in May–June (530.6 hPa). On a daily scale, atmospheric pressure exhibited a distinct double-peak, double-trough daily pattern (Fig. 2r). Overall, atmospheric pressure variations were relatively small over the study period and therefore likely played only a minor role in modulating turbulent fluxes.

Figure 3 shows that the observed daily mean LE ranged from -35.9 W m⁻² (21 August 2023) to 10.4 W m⁻² (11 July 2023), with an average of -9.6 W m⁻² over the study period, indicating persistent sublimation/evaporation from the glacier surface. There was notable seasonal variability, with the absolute mean seasonal LE being highest in May–June (-15.1 W m⁻²), lowest in September–October (-8.1 W m⁻²), and moderate in June–September (-10.4 W m⁻²), reflecting varying intensities of moisture exchange between the glacier and the atmosphere (Fugger et al., 2022).

In contrast, observed H was generally positive, averaging 6.9 W m⁻², indicating continuous heat transfer from the atmosphere to the glacier. There were pronounced seasonal variations, with high mean H values in May–June (9.3 W m⁻²) and September–October (9.2 W m⁻²), and a monthly peak in September (10.1 W m⁻²). The lowest values were recorded in June–September, which averaged 5.4 W m⁻², and June exhibited the lowest monthly average (3.1 W m⁻²), coinciding with the period when the surface temperature deficit reached its minimum. During June, both Ta and glacier Ts increased; however, the glacier surface warmed more rapidly than the overlying air, reducing the surface temperature deficit to its lowest level. As a result, the monthly mean H reached its minimum in June.

Overall, the absolute magnitude of LE generally exceeded that of H. This resulted in a predominantly negative total turbulent flux (LE + H), averaging -2.9 W m⁻², indicating net heat loss from the glacier through turbulent exchange. From May to mid-September, the total turbulent flux was negative (glacier losing energy), while from mid-September to mid-October, it became positive (glacier receiving energy). June exhibited the strongest turbulent flux (-8.0 W m⁻²), whereas September recorded the weakest (1.5 W m⁻²). These findings underscore the overall state of heat loss from the glacier through turbulent fluxes during the study period.

In this section, we evaluate the performance of five turbulent-flux methods (Ckat, Clog, CRib1, CRib2, and CM–O) across different timescales using observation-constrained model configurations. Specifically, the Ckat and Clog methods were applied using empirical parameters recalibrated against the quality-controlled 30 min EC observations. In contrast, the CRib1, CRib2, and CM–O methods were applied using the representative momentum roughness length (z0m = 1.2 × 10⁻⁴ m) derived from the EC observations. Where required, the scalar roughness lengths were determined using the A87 and SvdB parameterizations. Unless otherwise stated, all results presented in this section are based on these recalibrated or observation-constrained model configurations. Model–observation agreement was quantified using the quality-controlled 30 min EC turbulent-flux observations. Because the same EC observational record was also used to recalibrate Ckat and Clogand to derive the representative momentum roughness length used by the other methods, the statistics presented here do not represent independent validation and should be interpreted as an observation-constrained evaluation for the Dunde Glacier.

To assess the influence of turbulent-flux parameter recalibration on glacier mass-balance simulations, three representative turbulent-flux configurations – Clog, CRib2, and CM–O + SvdB were implemented in the coupled energy balance–snow and firn model at the point scale. These configurations were selected because they represent three structurally distinct categories of turbulent-flux parameterization: a simplified bulk formulation without explicit stability corrections, a bulk-Richardson-number-based stability-correction method, and a full Monin–Obukhov similarity-theory method combined with a scalar roughness-length parameterization, respectively. The selection was intended to examine the effects of recalibration across methods with different formulations and levels of complexity while keeping the coupled-model analysis concise and focused. Because the remaining configurations showed broadly comparable overall performance in the preceding turbulent-flux evaluation, the subsequent mass-balance analysis focused on these representative configurations rather than providing an exhaustive comparison of all seven evaluated configurations.

For each selected configuration, paired simulations were conducted using the original and recalibrated turbulent-flux parameter values. In the baseline simulations, the turbulent-flux parameters were assigned the standard values reported in the original publications of the respective methods. In the recalibrated simulations, the corresponding parameter values that minimized the discrepancies between the modeled and observed turbulent fluxes were used. All other model settings and forcing data were kept identical between the paired simulations. Incoming and outgoing longwave radiation, incoming and outgoing shortwave radiation, snow depth, surface albedo, and rainfall were prescribed using the in situ observations at AWS1 to ensure a controlled experimental setup.

Under this framework, the coupled model simulated glacier surface temperature, surface height (SH), and cumulative mass balance (CMB). Because continuous stake-based mass-balance observations were unavailable for the exact modelling period, an observation-constrained reference simulation was constructed to provide a continuous reference CMB time series. In this simulation, the measured meteorological variables and quality-controlled EC turbulent fluxes were prescribed as model forcing. Gaps in the EC turbulent-flux record were filled using the recalibrated CRib2 configuration, whose parameter values minimized the discrepancies between the modeled and observed turbulent fluxes. The CMB simulated under this observation-constrained setup was therefore used as the reference CMB for evaluating the paired simulations. Because the recalibrated CRib2 configuration was used to fill gaps in the EC record, this reference CMB is partially dependent on CRib2 and is therefore not fully independent of the recalibrated CRib2 simulation.

The observation-constrained reference simulation was further compared with independent in situ measurements as a consistency check. The simulated surface temperature and surface-height variations agreed closely with the corresponding in situ observations. In addition, the independently measured point surface mass balance at AWS1 was -303 mm w.e. from 26 April to 31 December 2023, as indicated by the open star in Fig. 7, which was close to the final observation-constrained reference CMB of -298.6 mm w.e. Although the stake-observation period extended beyond the modelling period, little additional mass-balance change occurred after mid-to-late October because of the persistently cold conditions. The close agreement between the two estimates supports the use of the observation-constrained reference CMB for model evaluation.

We first ran the SEB models using the original parameter values for the three turbulent flux methods (the Clog, CRib2, and CM–O + SvdB methods). These gave RMSE values for Ts of 3.3, 8.8, and 3.2 °C, respectively. The R values between modeled and measured Ts exceeded 0.78 for all three schemes. The RMSE values for surface height change ranged from 0.16 to 0.18 m, while the CMB estimates were -238.4, -225.8, and -242.4 mm w.e., respectively, all deviating markedly from the observation-constrained reference value of -298.6 mm w.e. Following parameter calibration, all three schemes exhibited improvements in model performance. The CRib2 method showed the greatest improvement, giving a CMB value of -238.6 mm w.e., equating to an error reduction of 17.6 % relative to the uncalibrated result. In parallel, the RMSE values for Ts and surface height decreased by 68.2 % and 16.7 %, respectively. The models based on the CM–O and CRib2 methods achieved relatively high overall accuracy after optimization, with R values of 0.88 and 0.87 for Ts, respectively, and 0.94 for surface height in both cases (Table 4).

Aerodynamic roughness length (z0m) over glacier surfaces spans several orders of magnitude, and the reported ranges vary substantially among different glacier types and climatic settings. Compared with previous studies, the range inferred in this study (10⁻⁵–10⁻² m) is consistent with values documented in the literature. For example, calculated values over August-one Glacier on the TP were approximately 10⁻⁵ to 10⁻² m (Guo et al., 2018), while observations from the Greenland Ice Sheet (Haven et al., 2026) documented ranges of roughly 10⁻⁶ to 10⁻² m. These comparisons indicate that the values derived here are physically reasonable and consistent with established glacier surface characteristics. Previous studies of continental glaciers on the TP have predominantly relied on SEB models to investigate glacier change and its underlying mechanisms. In most of these studies, roughness lengths, together with other meteorological parameters, were adjusted to improve the simulated cumulative mass balance produced by the surface energy mass balance framework. In such cases, parameter selection primarily aimed to optimize overall SEB model performance rather than to explicitly constrain turbulent flux representation. Moreover, the lack of independent turbulent flux observations has limited the ability to constrain simulated sensible and latent heat fluxes, thereby introducing substantial uncertainty into SEB-based flux estimates. This limitation, in turn, hampers our understanding of continental glacier change and its underlying mechanisms. By contrast, direct observations of roughness length and turbulent fluxes can provide observational constraints for parameter calibration in SEB models. This allows the simulated turbulent fluxes to better reflect actual surface conditions, thereby improving our understanding of glacier change. Given this importance, it is therefore essential to characterize the observed variability and magnitude of roughness lengths themselves, particularly across different glacier types and climatic regimes.

Available observations suggest possible systematic differences in the characteristic magnitude and range of z0m among glacier types. Reported values from studies over the Greenland Ice Sheet collectively span approximately 10⁻⁶–10⁻² m, although the specific intervals vary among studies depending on observational period and methodology (Meesters et al., 1997; Lenaerts et al., 2014; Van Tiggelen et al., 2020). For maritime glaciers on the TP, the limited available observations – primarily from Parlung No. 4 Glacier – indicate values between 10⁻⁴ and 10⁻² m (Guo et al., 2011). In contrast, continental glaciers on the Tibetan Plateau often show lower characteristic magnitudes but broader reported ranges, spanning approximately 10⁻⁵–10⁻¹ m, although most of these estimates are derived from SEB model calibration rather than independent turbulent flux observations (Giesen et al., 2008; Guo et al., 2018; Sun et al., 2018). Taken together, these comparisons suggest that continental glaciers tend to exhibit lower but more widely distributed roughness lengths than maritime glaciers, which are generally characterized by relatively higher and narrower ranges. The broad z0m range derived from the observational data in this study further suggests that surface roughness conditions over continental glaciers can vary considerably over time. A plausible reason why such variability is more clearly captured in the derived values is the comparatively slow evolution of continental glacier surfaces, which allows changes in roughness length to be tracked more consistently in the observational record.

It should also be emphasized that most previous measurements were confined to short ablation season campaigns, whereas the present study spans a longer observation period from May to October. The wider range identified here may therefore partly result from the extended temporal coverage. Furthermore, the observation site is located in the accumulation zone, where melt intensity is relatively weak and surface evolution is comparatively gradual. This may allow changes in surface roughness to be tracked over a longer portion of the seasonal cycle. Nevertheless, given the scarcity of long-term eddy-covariance measurements over continental glaciers, additional observations are still required to evaluate the reliability and broader applicability of these findings.

The paired simulations demonstrate that uncertainties in turbulent-flux parameterization can propagate into the simulated surface temperature, surface-height change, and cumulative mass balance. Because all other forcing data and model settings were held constant, the improvements in the recalibrated simulations can be attributed primarily to the revised turbulent-flux parameters. The simultaneous improvement in Ts, surface height, and CMB indicates that observationally constraining turbulent heat exchange can improve not only the instantaneous surface energy balance but also the integrated mass-balance response.

The magnitude of the improvement differed among the three representative configurations. The particularly large reduction in surface-temperature RMSE for CRib2 suggests that its original parameter setting was less suitable for the atmospheric and glacial conditions of the Dunde Glacier and was therefore more sensitive to recalibration. By contrast, the original Clog and CM–O + SvdB configurations already produced comparatively smaller surface-temperature errors, leaving less scope for improvement. Nevertheless, recalibration improved the CMB estimates for all three configurations, indicating that even relatively modest changes in turbulent heat exchange can accumulate over time and affect the modeled mass balance.

Despite these improvements, all recalibrated configurations still underestimated the magnitude of the observation-constrained reference cumulative mass loss. This residual discrepancy indicates that uncertainties in turbulent heat fluxes are not the only source of error in the point-scale SEB simulations. Potential contributions may include uncertainties in surface temperature, precipitation partitioning, subsurface heat storage, snow and ice density, and the representation of snow and firn processes. Therefore, recalibrating turbulent-flux parameters improves SEB model performance but does not eliminate uncertainties arising from other model components and observational constraints.

In addition, the modeled surface-height time series exhibited smaller short-term variability than the observations, particularly following snowfall events. This difference is likely related to the absence of a seasonal snow-compaction scheme in the version of EBFM used in this study. Rather than explicitly simulating the rapid densification of low-density fresh snow immediately after snowfall, this model version assigns a relatively high initial density to fresh snow and subsequently treats its compaction in a manner more representative of firn. Consequently, rapid post-snowfall changes in surface height may be dampened in the simulations. In addition to this model limitation, wind-driven snow redistribution may also contribute to the larger short-term variability observed in the field. Wind erosion, transport, and redeposition can produce rapid local changes in snow depth and surface height, thereby increasing the variability of the observed surface-height record.

Because the three configurations represent distinct formulations and levels of structural complexity, the improvements obtained across all three indicate that the benefits of observationally constrained turbulent-flux parameters are not limited to a single method type, although the magnitude of the response remains method dependent.

Our analysis above demonstrates that the optimization of turbulent flux parameterizations markedly enhances the accuracy of glacier surface energy and mass balance simulations under the broader range of conditions represented by the observation period. However, the ability of SEB models to simulate turbulent fluxes under extreme events remains uncertain and warrants further investigation. Between 8 and 11 July 2023, the Dunde Glacier experienced a typical humid heatwave (Dong et al., 2024). During this event, the mean air temperature reached 2.4 °C, substantially higher than the July mean outside the heatwave period (-1.5 °C). Nighttime air temperature from 9 to 11 July consistently exceeded 0 °C, exhibiting reduced daily fluctuations, and then sharply dropped below freezing on 12 July immediately after the heatwave event (Fig. 8a). Mean relative humidity during the humid heatwave reached 94.3 %, markedly higher than during the non-heatwave period in July (89.1 %). The concurrent anomalies in air temperature and humidity during this humid heatwave were accompanied by pronounced anomalies in turbulent fluxes.

To clarify turbulent flux behaviors under such anomalous climatic conditions, we compared turbulent fluxes during the humid heatwave (8–11 July 2023) with those during the non-heatwave period (the remainder of July 2023) based on quality-controlled observational data. H increased markedly during the humid heatwave, reaching a daily average of 17.5 W m⁻², this being nearly 2.5 times higher than the non-heatwave average (7.5 W m⁻²). Moreover, the daily variation in H during the heatwave event ranged from 7.5 to 26.5 W m⁻², substantially exceeding the range observed during the non-heatwave period (-1.5 to 22.1 W m⁻²). This extraordinary increase in H during the humid heatwave indicates that substantial heat was transferred from the atmosphere to the glacier during this event. Concurrently, the magnitude of LE decreased during the humid heatwave period. During the non-heatwave period, LE remained negative, with an average value of -25.2 W m⁻². Such negative LE values are a common characteristic of continental glaciers on the TP. However, during the humid heatwave, the magnitude of negative LE decreased markedly, with an event-mean value of -3.1 W m⁻²; on 11 July, the daily mean LE became positive, reaching 5.1 W m⁻². This change was further reflected in daily LE variations, with a range of -7.6 to 5.1 W m⁻² during the humid heatwave, which was markedly different from the range of -58.8 to -2.6 W m⁻² observed during the rest of July. This shift indicates a weakening of upward latent heat transfer and, at times, a reversal to downward latent heat transfer, consistent with reduced sublimation and occasional condensation or deposition at the glacier surface (Zhang et al., 2017). Such weakly negative LE values, and occasional positive values, are more commonly observed over maritime glaciers and in high-latitude Arctic regions. In maritime settings, they are primarily associated with relatively high air temperatures and abundant precipitation, whereas in Arctic regions they are linked to weak solar radiation, which may occasionally cause glacier surface temperatures to fall below air temperature (Kuipers Munneke et al., 2009, 2018; Yang et al., 2011).

The glacier surface transitioned into a state of net turbulent energy gain, with the mean total turbulent flux (LE + H) reaching 14.4 W m⁻² during the humid heatwave. In contrast, the non-heatwave period in July was characterized by net turbulent energy loss, averaging -13.8 W m⁻². This contrast underscores a distinct shift from turbulent heat loss to heat gain under humid heatwave conditions. Concurrently, rising Ta during the humid heatwave promoted snowmelt on the glacier surface, leading to rapid snow metamorphism characterized by grain growth and rounding. As the humid heatwave persisted, continued melting may have locally removed portions of the seasonal snow cover, potentially exposing underlying ice. This reduction in surface albedo enhanced melt energy, triggering intense ablation (nighttime albedo values were not interpreted because albedo cannot be meaningfully observed without incoming shortwave radiation). Thus, although short-lived, the humid heatwave substantially altered the glacier surface energy balance through both enhanced turbulent heat input and changes in surface conditions, including reduced albedo.

We further evaluated the ability of the five methods to simulate turbulent fluxes under extreme weather events. Among the five turbulent flux methods tested, all captured the pronounced increase in H during the humid heatwave, with the CRib1 and CM–O schemes combined with the SvdB scalar roughness length parameterization performing best. Although the mean values simulated by CRib1 + SvdB and CM–O + SvdB (16.7 and 16.4 W m⁻², respectively) were slightly lower than the observed value (17.5 W m⁻²), their performance was still superior to that of the other schemes. The Ckat method exhibited the poorest performance, simulating a mean H of only 7.9 W m⁻². Meanwhile, the mean H values during the humid heatwave simulated by the Clog, CRib1 + A87, CRib2 and CM–O + A87 methods were 12.7, 14.3, 14.7, and 14.4 W m⁻², respectively. For LE, all methods exhibited noticeable deviations from the observations. Among the five evaluated methods, the Ckat scheme performed relatively better, with a mean value of -9.2 W m⁻², which may be related to its generally lower simulated fluxes throughout the study period. The next best performance was obtained by the CM–O + A87 scheme, with a mean value of -11.6 W m⁻². The remaining methods showed broadly similar results: the mean LE values simulated by Clog, CRib1 + A87, CRib1 + SvdB, CRib2, and CM–O + SvdB were -16.0, -14.1, -16.2, -14.1, and -13.0 W m⁻², respectively, all substantially deviating from the observed value of -3.1 W m⁻². Overall, the methods, particularly the CM–O + SvdB scheme, reproduced the anomalous increase in H during the humid heatwave with relatively high consistency and accuracy, and captured the reduction in the magnitude of LE during this period. However, the estimation errors for LE were non-negligible, and the models failed to reproduce the occasional reversal in LE direction (on 11 July). Part of the discrepancy between modeled and observed results may be attributed to observational limitations. The meteorological variables used to drive the models are based on half-hourly observations. Such temporal averaging may obscure short-lived near-surface temperature and humidity gradients, thereby limiting the models' ability to reproduce transient fluctuations. Nevertheless, the discrepancies identified here indicate that current parameterization schemes may misrepresent the contribution of latent heat exchange to the glacier surface energy balance under extreme humid conditions, particularly when LE weakens or reverses sign.

Under ongoing global warming, the climate system is recording notable warming and moistening trends on the TP (Wang et al., 2010). This means that the TP will likely experience an increased frequency and intensity of humid heatwave events (Zhang et al., 2025; Zhu et al., 2026). Such conditions may cause continental glaciers, such as the Dunde Glacier, to increasingly exhibit turbulent flux characteristics that resemble those of maritime glaciers, including reduced LE magnitudes and even reversals in LE direction, as well as a pronounced enhancement of H. This phenomenon warrants further investigation and is likely related to the constraint that Ts cannot exceed 0 °C. Under humid heatwave conditions, Ta continues to rise while Ts is capped, leading to an increased surface temperature deficit and consequently a substantial enhancement of H. Meanwhile, because the humidity gradient is closely coupled to the temperature gradient, LE may also undergo anomalous changes. Consequently, continued warming may drive future transitions in glacier types.