# Atmosphere Driven Mass-Balance Sensitivity of Halji Glacier, Himalayas

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}) with large interannual variability (standard deviation 0.71 m w.e. a

^{−1}) was simulated. This variability is dominated by temperature and precipitation patterns. The Halji glacier is mostly sensitive to summer temperature and monsoon-related precipitation perturbations, which is reflected in a strong correlation with albedo. According to the simulations, the climate sensitivity with respect to either positive or negative air temperature and precipitation changes is nonlinear: A mean temperature increase (decrease) of 1 K would result in a change of the glacier-wide climatic mass balance of −1.43 m w.e. a

^{−1}(0.99 m w.e. a

^{−1}) while a precipitation increase (decrease) of 10% would cause a change of 0.45 m w.e. a

^{−1}(−0.59 m w.e. a

^{−1}). Out of 22 circulation and monsoon indexes, only the Webster and Yang Monsoon index and Polar/Eurasia index provide significant correlations with the glacier-wide climatic mass balance. Based on the strong dependency of the climatic mass balance from summer season conditions, we conclude that the snow–albedo feedback in summer is crucial for the Halji glacier. This finding is also reflected in the correlation of albedo with the Webster and Yang Monsoon index.

## 1. Introduction

^{−1}or −0.19 ± 0.03 meters water equivalent per year (m w.e. a

^{−1}) and a contribution to sea-level rise of $\sim 0.7$ $\mathrm{m}$$\mathrm{m}$ from 2000 to 2018. Glacier retreat is assumed to continue in the next decades. Rounce [8] projects a HMA glacier mass shrinkage between $(29\pm 12)$% (Representative Concentration Pathway 2.6) and $(67\pm 10)$% (Representative Concentration Pathway 8.5) for the period 2015 to 2100. The changes are caused by increased temperatures, changing precipitation amounts and changes in the ratio between liquid and solid precipitation (e.g., [9]). Wei and Fang [10] report a decadal warming rate of $0.32$ $\mathrm{K}$ for the period 1961 to 2010. Nevertheless, due to heterogeneous topography, influence of large-scale circulation systems (e.g., [11,12,13,14,15,16,17,18]) and their interactions with local atmospheric circulation systems responses of glaciers largely vary in space (e.g., [19,20,21,22]). Winter-, spring- and summer-accumulation and mixed type glaciers can be found in HMA [23,24]. Summer-accumulation type glaciers are especially sensitive to changes in summer temperatures [25], e.g., due to snow–albedo feedback [26,27,28].

## 2. Halji Glacier

^{2}[45] in 2001. The glacier has an estimated maximum thickness of 83 $\mathrm{m}$ ([22], dataset: [46]) and an estimated mean flow velocity of 2.3 m a

^{−1}([47], dataset: [48]) (see Appendix A Figure A1).

^{−1}between 2000 and 2013. Shean et al. ([7], dataset: [49]) calculated an annual geodetic MB of $(-0.70\pm 9)$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ a

^{−1}between 2000 and 2018. Both studies use digital elevation model (DEM) differencing but for different periods. As reported by Ye et al. [50], the glaciers in the Naimona’nyi region (∼25 km northwest of Halji glacier) have retreated at least since 1976. The only information about the Halji glacier development pre-millennial are glacier outlines derived from satellite data and the resulting glacier areas as displayed in Figure 1. The glacier area decreased from 3.1 km

^{2}in 1974 [51] to 2.3 km

^{2}in 2001 [45]. Between 2001 and 2010, the area was relatively stable with still 2.2 km

^{2}in 2010 [52], but decreased to 1.9 km

^{2}by 2018. The 2018 outline was derived from a Sentinel 2 [53] scene found with the Google Earth Engine Digitisation Tool developed by Lea [54]. According to the outline of the Randolph Glacier Inventory 6.0 (RGI6) [45], the glacier has two ice divides (see green lines Figure 1). All other outlines have been adjusted to these divides.

**Figure 1.**The Halji glacier with multi-temporal glacier outlines and satellite image map in the background [55] (

**a**) and photo of the automatic weather station (AWS) of the Chair of Climatology (Technische Universität Berlin) installed in 2018 with a part of the glacier in the background (

**b**, photo by Benjamin Schröter). Colors within the inset map represent elevation [56].

## 3. Data and Methods

#### 3.1. COSIPY

_{M}is available melt energy, Q

_{SWin}is incoming shortwave radiation, α is snow/ice albedo, ${Q}_{LWin}$ is incoming longwave radiation, ${Q}_{LWout}$) is outgoing longwave radiation, ${Q}_{H}$ is sensible heat flux, ${Q}_{E}$ is latent heat flux, ${Q}_{G}$ is glacier heat flux and ${Q}_{R}$ sensible heat flux of rain. ${Q}_{SWin}$ and ${Q}_{LWin}$ are input parameters of COSIPY whereby ${Q}_{LWin}$ can be parametrized (see Equations (14) and (15), [42]). Cloud cover fraction is needed as input in the latter case. The decay of $\alpha $ is calculated after Oerlemans and Knap [57] with the parameters presented and studied by Mölg et al. [58] in HMA. All other terms on the right-hand side of Equation (1) depend on the surface temperature ${T}_{s}$. The resulting nonlinear equation is solved iteratively with an optimization algorithm. Due to physical constraints, ${T}_{s}$ ≤ melting point temperature ${T}_{m}$ must be fulfilled and therefore energy surplus results in ${Q}_{M}$ $>\phantom{\rule{3.33333pt}{0ex}}0$ when ${T}_{s}$ equals ${T}_{m}$. If ${T}_{s}$ < ${T}_{m}$, there is no available energy at the surface, i.e., ${Q}_{M}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0$. All energy fluxes are of positive (negative) algebraic sign towards (directed away from) the surface and presented in $\mathrm{W}$ m

^{−2}.

#### 3.2. Climate Forcing Model Input

#### 3.2.1. Automatic Weather Station Measurements

_{2}.

#### 3.2.2. Downscaling ERA5-L

#### 3.2.3. Comparison of Downscaled ERA5-L to Automatic Weather Station Measurements

^{−1}), small mean bias errors (MBE, ${p}_{sfc}$: $0.18$ $\mathrm{h}$$\mathrm{Pa}$, ${T}_{2}$: < $0.01$ $\mathrm{K}$, $S{H}_{2}$: $0.03$ $\mathrm{g}$ $\mathrm{k}\mathrm{g}$

^{−1}) and regression line slopes close to 1 (${p}_{sfc}$: 1.1, ${T}_{2}$: 0.94, $S{H}_{2}$: 1.18). All results are statistically significant with p-value < 0.01. The cumulative distribution functions in the right panels reveal that the downscaling approach in case of ${p}_{sfc}$ and ${T}_{2}$ result in a substantially improved agreement with AWS measurements. A decrease in MBE from $14.3$ to $0.2$ $\mathrm{h}$$\mathrm{Pa}$ (RMSE: from $14.3$ to $0.5$ $\mathrm{h}$$\mathrm{Pa}$) in case of ${p}_{sfc}$ and from $0.14$ to $<0.01$ $\mathrm{K}$ (RMSE: from $3.4$ to $2.3$ $\mathrm{K}$) in case of ${T}_{2}$ could be achieved. In case of $S{H}_{2}$, almost no improvement (MBE: $0.05$ to $0.03$ $\mathrm{g}$

^{−1}) can be observed. The reason might be that $R{H}_{2}$ mean of the measured values and the corresponding raw ERA5-L values differ only by $0.3$% (Measured: 77.1%, ERA5-L: 76.8%).

^{−1}) and regression line slopes are acceptable (${p}_{sfc}$: 1.05, ${T}_{2}$: 0.94, $S{H}_{2}$: 0.76).

^{−1}.

^{−1}.

#### 3.3. COSIPY Simulations

^{−1}). Therefore, for all further simulations in this study, we used a spatial resolution of $\sim 100$ $\mathrm{m}$ with the resulting 248 GGPs representing the entire Halji glacier. For all distributed simulations, we used the hpcc of the Climate Geography lab of Humboldt-Universität zu Berlin, Germany. A simulation with $\sim 100$ $\mathrm{m}$ resolution and 248 GGPs has a runtime of less than two hours for the whole ERA5-L period from January 1981 to April 2020.

#### 3.4. Sensitivity Studies and Large Scale Teleconnections

**Statistics:**To investigate the influence of the forcing variables on the interannual variability of ${B}_{clim,a}$, we calculate non-parametric Spearman’s rank correlation coefficients ${r}_{s}$ [77] between ${B}_{clim,a}$ and the different forcing variables and the intermediate variables ${Q}_{SWnet}$, $\alpha $ and net longwave radiation ${Q}_{LWnet}$. We define two significance levels with a 95% and 99% confidence interval and access the significance with the two-sided p-value of the Spearman’s rank correlation [77]. Furthermore, we start simulations with ±0.5, ±1.0, $\pm 2.0$ $\mathrm{K}$ ${T}_{2}$ and ±5, ±10, $\pm 20$% $TP$ perturbations and analyzed the resulting annual deviations of ${B}_{clim,a}$ to the original run.

**Seasonal Sensitivity Characteristic (SSC): Oerlemans and Reichert**[43] proposed calculating SSC to describe the dependency of ${B}_{clim}$ of a glacier to the local seasonal climate in a uniform and structured manner. The SSC of a glacier is a 2 × 12 matrix quantifying the ${B}_{clim}$ sensitivity to temperature and precipitation perturbations each in the 12 months of the year. For their calculation in the first step, the reference COSIPY simulation was adjusted so that the mean ${B}_{clim,a}$ is zero. Therefore, the mean forcing temperature is adjusted in the range of $\pm 2$ $\mathrm{K}$. For the Halji glacier, we applied a ${T}_{2}$ offset of $-0.37$ $\mathrm{K}$ (see Appendix A Figure A3) to arrive at a zero ${B}_{clim,a}$ for the period October 1981–September 2019. In the second step, 24 COSIPY simulations were forced with monthly ${T}_{2}$ perturbations of $\pm 0.5$ $\mathrm{K}$ and 24 COSIPY simulations were forced with monthly $TP$ perturbations of $\pm 10$%. The resulting differences of ${B}_{clim,a}$ between the positive and negative perturbation for each month are the 12 temperature values and the 12 precipitation values of the SSC. These 24 values are displayed as a bar plot. For further information, including the equations of the concept, please see Section 2, especially Equations (3) and (4) in Oerlemans and Reichert [43] and Section 3b in Reichert et al. [78].

**Indexes:**Finally, we calculate ${r}_{s}$ between ${B}_{clim,a}$ and 22 common teleconnection indexes. The temporal resolution and coverage, short and long name, reference and download location of the indexes are summarized in Table A1 in the Appendix A. In doing so, we test the relationship between COSIPY-simulated Halji glacier ${B}_{clim}$ and atmospheric drivers.

## 4. Results

^{−1}and ${B}_{clim,cum}$ is $-18.3$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ The most negative annual balance is $-2.16$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}in 1990. The most positive is $0.57$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}in 2013. The overall standard deviation of $0.71$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}reflects the quantitative interannual varability in the mass balance time series. Between 1995 and 2007 all Halji glacier annual mass balances are negative (mean $-0.53$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}). In contrast, between 2008 and 2015, the glacier balance was in equilibrium (only two negative MB-years 2012 and 2014) with a mean ${B}_{clim,a}$ of $0.0$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}over this period (see Figure 6b).

#### 4.1. Sensitivity to Climate Forcing Input Variables

_{s}between ${B}_{clim,a}$ and the forcing variables as well as four intermediate ($S{F}_{c}$, ${Q}_{SWnet}$, ${Q}_{LWnet}$ and $\alpha $) variables.

#### 4.2. Temperature and Total Precipitation Perturbations and Seasonal Sensitivity Characteristic

^{−1}). In contrast, a ${T}_{2}$ perturbation of $\pm 2$ $\mathrm{K}$ results in a disproportionate mass response ($-2.55$ and $1.31$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}). The same holds true in case of $TP$ perturbations. A yearly positive response of $0.25$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}and a negative of $-0.29$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}with a $\pm 5$% $TP$ change and a response of $0.76$ and $-1.29$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}with $\pm 20$% perturbation are found.

#### 4.3. Index Correlations

## 5. Discussion

#### 5.1. Uncertainties

#### 5.1.1. Forcing Data Uncertainties

#### 5.1.2. COSIPY Simulation Uncertainties

^{−1}([47], dataset: [48]) would result in 90 $\mathrm{m}$ ice movement over the whole period of 40 years. However, for further long-term integration of glacier change ice-dynamics will have to be integrated into the modeling framework. Snowdrift and direct sublimation of falling snow are further processes that are not resolved by the model. The model has been among others applied to the Zhadang glacier (see Section 5.1 in Sauter et al. [42]) and the Urumqi Glacier No. 1 (see Thiel et al. [95]), both located in HMA. The simulations in both cases revealed reasonable results. To assess the uncertainties stemming from all parameters and constants a full Monte Carlo simulation would have to be executed for the Halji glacier, which is not feasible in this study due to the enormous computational demand. A statistical error would affect single years, but not a long term cumulative value because the error would decrease according to the central limit theorem [96]. A systematic error would indeed affect the cumulative value of ${B}_{clim}$. Due to the significant correlation between $\alpha $ and ${B}_{clim,a}$ and experiences from Mölg et al. [58], Sauter et al. [42] and Thiel et al. [95], the Oerlemans and Knap [57] $\alpha $ parametrization is crucial for model output. We used the parameters of Mölg et al. [58]. For a sensitivity test, we varied the $\alpha $ values for fresh snow, firn and ice within the uncertainties of their study. The fresh snow $\alpha $ variance results in ±0.5 $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.\mathrm{a}$

^{−1}feedback, the firn variance in a ±0.43 $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.\mathrm{a}$

^{−1}feedback and the ice variance in a ±0.17 $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.\mathrm{a}$

^{−1}feedback. The test shows the high sensitivity to the albedo parametrization. Therefore, COSIPY simulated ${b}_{clim}$ always has to be evaluated against remote-sensing based geodetic mass balance or mass balance derived from the glaciological method through direct observations on the ground. If ${B}_{clim}$ lies within a reasonable range compared to the independent evaluation data, we understand the main purpose of applying COSIPY in identifying drivers of seasonal and interannual mass balance variability and in advancing process understanding of interactions between atmospheric drivers and ${B}_{clim}$. These analyses are feasible and justified when overall calculated ${B}_{clim}$ falls within a reasonable range. This has also been demonstrated in other studies using medium complexity energy and mass balance models similar to COSIPY (e.g., [97,98,99,100,101,102,102]).

#### 5.2. Glacier-Wide Climatic Mass Balance

^{−1}. Model simulations can be compared to ice volume changes derived by remote sensing studies of Kropáček et al. [38] and Shean et al. [7] on the mass budget of the Halji glacier. Those values are summarized in Table 6. Corresponding simulated ${B}_{clim,a}$ falls within the range of uncertainty in the case of the study by Kropáček et al. [38]. In the case of Shean et al. [7], the COSIPY simulated result is less negative than their estimate. Overall, the simulated negative ${B}_{clim}$ falls within a reasonable range and is in line with observed reduction in area, presented by the various outlines in Figure 1, the general glacier retreat in HMA (e.g., [3,4,5,6]) and in particular in western Nepal (e.g., [19,103,104]). A possible explanation for the more negative result of the Shean et al. [7] study are the simulated extreme negative MB-years 2016, 2017 and 2018. which are included in their study period, while they are not included in the Kropáček et al. [38] study.

^{−1}. The simulated mass budget between 2001 and 2010 is clearly negative. Nevertheless, this finding is not that obvious in the changes of glacier outlines between 2001 and 2010. Possibly, in this period, the negative mass balance was mainly a result of glacier thinning as opposed to area reduction. With the currently available dataset, we cannot evaluate this possibility in more detail.

^{−1}($-0.75$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}difference compared to reference simulation), which mainly affects ${B}_{clim}$ during summer. An increase in summer temperature has three main negative effects on the glacier mass budget for that kind of glacier [25]: (1) Enhanced melt, (2) lowered ratio between solid and liquid precipitation, which results in less surface accumulation, and (3) lower values of $\alpha $ as a result of a decrease in $S{F}_{c}$, which enlarges ${Q}_{SWnet}$ and results in further enhancement of melt. The latter two effects are denoted as the snow-albedo feedback [26,27,28].

## 6. Conclusions

^{−1}between October 1981 and September 2019 for the Halji glacier in northwestern Nepal. Given the lack of direct mass balance observations, simulations were compared to geodetic mass balances derived from two remote sensing studies [7,38]. The simulation results are in a reasonable range compared to both of these remote sensing studies. The simulation also reveals high interannual variability of ${B}_{clim,a}$. All results revealed the importance of the monsoon and ${T}_{2}$ and $TP$ in summer for the variability of ${B}_{clim,a}$. Only the combination of effects and resulting variability of $\alpha $ can explain the pronounced ${B}_{clim}$ variability in this season. The peak in summer of the calculated seasonal sensitivity characteristic back these findings. The variability of forcing variables in winter has a minor influence on ${B}_{clim,a}$.

^{−1}. Therefore, there is an urgent need in spatially higher resolved atmospheric datasets, to serve as forcing for long-term runs of mass balance models.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

**The following acronyms are used in this manuscript:**

AMI | Australian Monsoon Index |

AMO | Atlantic Multi-decadal Oscillation |

AO | Arctic Oscillation index |

AWS | automatic weather station |

COSIPY | COupled Snowpack and Ice surface energy and mass balance model in PYthon |

DEM | digital elevation model |

EA | East Atlantic index |

EATL/WRUS | East Atlantic/West Russia index |

ECMWF | European Centre for Medium-Range Weather Forecasts |

ERA5 | ECMWF Reanalysis fifth generation |

ERA5-L | ECMWF Reanalysis fifth generation-Land |

GDAL | Geospatial Data Abstraction Library |

GGP | glacier grid point |

GLOF | glacial lake outburst flood |

H-TESSEL | Hydrology revised Tiled ECMWF Scheme for Surface Exchanges over Land |

HMA | High Mountain Asia |

HPCC | High-Performance Computing Cluster |

IOD | Indian Ocean Dipol index |

ISM | Indian Summer Monsoon index |

MB | mass balance |

MB-year | mass-balance year |

MBE | mean bias error |

MEI | Multivariate ENSO Index |

NAO | North Atlantic Oscillation |

Nino1+2 | Nino 1+2 index |

Nino34 | Nino 3.4 index |

Nino4 | Nino 4 index |

ONI | Oceanic Nino Index |

PDO | Pacific Decadal Oscillation |

PNA | Pacific/North American index |

POL | Polar/Eurasia index |

RGI6 | Randolph Glacier Inventory 6.0 |

RMSE | root mean square error |

SCAND | Scandinavia index |

SEB | surface energy balance |

SOI | Southern Oscillation Index |

SRTM | Shuttle Radar Topography Mission |

SSC | seasonal sensitivity characteristic |

TNI | Trans-Niño Index |

WNPM | Western North Pacific Monsoon index |

WP | West Pacific index |

WYM | Webster and Yang Monsoon index |

**The following constants are used in this manuscript:**

Symbol | Description | Unit | Default Value |

M | average molar mass of air | $\mathrm{k}\mathrm{g}$ mol^{−1} | 0.02897 |

R | gas constant | kg m${}^{2}$ (s${}^{2}$ mol K)${}^{-1}$ | 8.314462 |

${T}_{m}$ | melting point temperature | $\mathrm{K}$ | 273.16 |

g | gravitational acceleration | $\mathrm{m}\mathrm{s}$^{−2} | 9.80665 |

**The following symbols are used in this manuscript:**

Symbol | Description | Unit |

${B}_{clim,a}$ | annual glacier-wide climatic mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${B}_{clim,cum}$ | glacier-wide cumulative climatic mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${B}_{clim}$ | glacier-wide climatic mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${Q}_{E}$ | latent heat flux | W m^{−2} |

${Q}_{G}$ | glacier heat flux | W m^{−2} |

${Q}_{H}$ | sensible heat flux | W m^{−2} |

${Q}_{M}$ | available melt energy | W m^{−2} |

${Q}_{R}$ | sensible heat flux of rain | W m^{−2} |

${Q}_{LWin}$ | incoming longwave radiation | W m^{−2} |

${Q}_{LWnet}$ | net longwave radiation | W m^{−2} |

${Q}_{LWout}$ | outgoing longwave radiation | W m^{−2} |

${Q}_{SWin}$ | incoming shortwave radiation | W m^{−2} |

${Q}_{SWnet}$ | net shortwave radiation | W m^{−2} |

$R{H}_{2}$ | relative humidity at 2 $\mathrm{m}$ | % |

$S{F}_{c}$ | accumulated snowfall | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

$S{H}_{2}$ | specific humidity at 2 $\mathrm{m}$ | $\mathrm{g}\mathrm{k}\mathrm{g}$^{−1} |

$TP$ | total precipitation | $\mathrm{mm}$ |

${T}_{0}$ | air temperature at reference height | $\mathrm{K}$ |

${T}_{l}$ | layer temperature | $\mathrm{K}$ |

${T}_{s}$ | surface temperature | $\mathrm{K}$ |

${T}_{2}$ | air temperature at 2 $\mathrm{m}$ | $\mathrm{K}$ |

${T}_{d,2}$ | dewpoint temperature at 2 $\mathrm{m}$ | $\mathrm{K}$ |

${U}_{2}$ | wind speed at 2 $\mathrm{m}$ | $\mathrm{m}\mathrm{s}$^{−1} |

${U}_{10}$ | wind speed at 10 $\mathrm{m}$ | $\mathrm{m}\mathrm{s}$^{−1} |

$\alpha $ | snow/ice albedo | - |

${a}_{i}$ | internal ablation | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${a}_{sfc}$ | surface ablation | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

a | thermal gradient | $\mathrm{K}\mathrm{m}$^{−1} |

${b}_{clim,a}$ | annual climatic mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${b}_{clim,cum}$ | cumulative climatic mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${b}_{clim}$ | climatic mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${b}_{i}$ | internal mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${b}_{sfc}$ | surface mass balance | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${c}_{i}$ | internal accumulation | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

${c}_{sfc}$ | surface accumulation | $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ |

h | height difference | $\mathrm{m}$ |

${p}_{0}$ | atmospheric pressure at reference height | $\mathrm{h}\mathrm{Pa}$ |

${p}_{sfc}$ | surface pressure | $\mathrm{h}\mathrm{Pa}$ |

p-value | p-value | - |

${r}^{2}$ | coefficient of determination | - |

${r}_{s}$ | Spearman’s rank correlation coefficient | - |

${z}_{0}$ | surface roughness | $\mathrm{m}$ |

## Appendix A

**Figure A2.**Scatterplot of ERA5-L air temperature at 2 $\mathrm{m}$ and model elevations of the 121 ERA5-L grid cells around the location of Halji glacier. The temperatures are the long-term means of each grid cell from 1981 to 2019.

**Figure A3.**Cumulative climatic mass balance of temperature adjusted simulation of Halji glacier from 1981 to 2020. We apply a temperature offset of $-0.37$ $\mathrm{K}$ to reach the long-term zero cumulative climatic mass balance which is needed for the computation of the seasonal sensitivity characteristic according to Oerlemans and Reichert [43].

**Table A1.**Investigated circulation, oscillation and monsoon indexes; The temporal resolution and coverage (status 1 August 2020) are displayed in the third column.

Index | Description | Temporal Resolution and Coverage |
---|---|---|

AMI [109] | Australian Monsoon Index | Seasonal (DJF), 1948–2014 |

http://apdrc.soest.hawaii.edu/projects/monsoon/seasonal-monidx.html, accessed on 22 March 2021 | ||

AMO [110] | Atlantic Multi-decadal Oscillation | Annual, 1870–2010 |

https://climatedataguide.ucar.edu/climate-data/atlantic-multi-decadal-oscillation-amo, accessed on 22 March 2021 | ||

AO [111] | Arctic Oscillation index | Monthly, January 1950–April 2020 |

https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao.shtml, accessed on 22 March 2021 | ||

EA [80] | East Atlantic index | Monthly, January 1950–April 2020 |

https://www.cpc.ncep.noaa.gov/data/teledoc/ea.shtml, accessed on 22 March 2021 | ||

EATL/WRUS [80] | East Atlantic/West Russia index | Monthly, January 1950–April 2020 |

https://www.cpc.ncep.noaa.gov/data/teledoc/eawruss.shtml, accessed on 22 March 2021 | ||

IOD [112] | Indian Ocean Dipol index | Monthly, January 1870–December 2018 |

http://www.bom.gov.au/climate/enso/indices/about.shtml, accessed on 22 March 2021 | ||

ISM [113,114] | Indian Summer Monsoon index | Seasonal (JJAS), 1948–2015 |

http://apdrc.soest.hawaii.edu/projects/monsoon/seasonal-monidx.html, accessed on 22 March 2021 | ||

MEI [115] | Multivariate ENSO Index | Monthly, January 1979–December 2019 |

https://psl.noaa.gov/enso/mei/, accessed on 22 March 2021 | ||

NAO [116] | North Atlantic Oscillation | Monthly, January 1899–February 2020 |

https://climatedataguide.ucar.edu/climate-data/hurrell-north-atlantic-oscillation-nao-index-pc-based, accessed on 22 March 2021 | ||

Nino1+2 [117] | Nino 1+2 index | Monthly, January 1950–June 2020 |

https://climatedataguide.ucar.edu/climate-data/nino-sst-indices-nino-12-3-34-4-oni-and-tni, accessed on 22 March 2021 | ||

Nino34 [117] | Nino 3.4 index | Monthly, January 1950–June 2020 |

https://climatedataguide.ucar.edu/climate-data/nino-sst-indices-nino-12-3-34-4-oni-and-tni, accessed on 22 March 2021 | ||

Nino4 [117] | Nino 4 index | Monthly, January 1950–June 2020 |

https://climatedataguide.ucar.edu/climate-data/nino-sst-indices-nino-12-3-34-4-oni-and-tni, accessed on 22 March 2021 | ||

ONI [117] | Oceanic Nino Index | Monthly, January 1950–May 2020 |

PDO [118] | Pacific Decadal Oscillation | Monthly, January 1854–February 2020 |

https://www.ncdc.noaa.gov/teleconnections/pdo/, accessed on 22 March 2021 | ||

PNA [119] | Pacific/North American index | Monthly, January 1950–April 2020 |

https://www.cpc.ncep.noaa.gov/data/teledoc/pna.shtml, accessed on 22 March 2021 | ||

POL [80] | Polar/Eurasia index | Monthly, January 1950–April 2020 |

https://www.cpc.ncep.noaa.gov/data/teledoc/poleur.shtml, accessed on 22 March 2021 | ||

SCAND [80] | Scandinavia index | Monthly, January 1950–June 2020 |

https://www.cpc.ncep.noaa.gov/data/teledoc/scand.shtml, accessed on 22 March 2021 | ||

SOI [120] | Southern Oscillation Index | Monthly, January 1951–December 2019 |

https://www.ncdc.noaa.gov/teleconnections/enso/indicators/soi/, accessed on 22 March 2021 | ||

TNI [117] | Trans-Niño Index | Monthly, January 1948–April 2020 |

WNPM [113,114] | Western North Pacific Monsoon index | Seasonal (JJAS), 1948–2015 |

http://apdrc.soest.hawaii.edu/projects/monsoon/seasonal-monidx.html, accessed on 22 March 2021 | ||

WP [80,119] | West Pacific index | Monthly, January 1950–April 2020 |

https://www.cpc.ncep.noaa.gov/data/teledoc/wp.shtml, accessed on 22 March 2021 | ||

WYM [40] | Webster and Yang Monsoon index | Seasonal (JJAS), 1948–2015 |

http://apdrc.soest.hawaii.edu/projects/monsoon/seasonal-monidx.html, accessed on 22 March 2021 |

**Figure A5.**Monthly mean deviations 1982 to 2019 from long-term monthly mean values of glacier-wide climatic mass balance (

**a**), albedo (

**b**), air temperature at 2 $\mathrm{m}$ (

**c**), accumulated snowfall (

**d**), incoming shortwave radiation (

**e**) and incoming longwave radiation (

**f**). The color bar is arranged so that deviations that act positively (negatively) on glacier-wide climatic mass balance are shown in blue (red).

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**Figure 2.**Comparison between measurements of the automatic weather station (May 2018–October 2019) and the downscaled European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis fifth generation-Land (ERA5-L) variables air pressure (

**a**–

**c**), air temperature at 2 $\mathrm{m}$ (

**d**–

**f**) and specific humidity (

**g**–

**i**) at the location of the automatic weather station. The time series are presented in the left panels (

**a**,

**d**,

**g**), the scatterplots in the middle panels (

**b**,

**e**,

**h**) and the cumulative distribution functions in the right panels (

**c**,

**f**,

**i**). A linear least-square regression model is used for the scatterplots, where the red line shows the regression line. ERA5-L-raw denotes the unscaled ERA5-L variables. In all plots, hourly values are displayed.

**Figure 3.**Measured (AWS) and ERA5-L wind speed at 2 $\mathrm{m}$. Time series without wind scaling (

**a**, ERA5-L-raw), with wind scaling (

**b**, ERA5-L), and the cumulative distribution functions (

**c**) with unscaled and scaled ERA5-L wind speed at 2 $\mathrm{m}$. In all plots hourly values are displayed.

**Figure 4.**Cumulative measured (AWS), unscaled (ERA5-L-raw) and scaled (ERA5-L) hourly total precipitation from 2 August 2018 to 2 November 2019.

**Figure 5.**Deviations of the mean annual glacier-wide climatic mass balance of the Halji glacier to the reference 30 $\mathrm{m}$ simulation for the mass-balance years (MB-years) 1982 to 2019 for different spatial resolutions ranging from 60 to 1500 $\mathrm{m}$. Corresponding glacier grid points are on the second x-axis. The red dotted lines showing the selected threshold for deviations in a tolerable range ($\pm 0.02$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}).

**Figure 6.**Simulated annual glacier-wide climatic mass balance (

**a**) and cumulative (

**b**) glacier-wide climatic mass balance of the Halji glacier from 1982 to 2019.

**Figure 7.**Monthly mean deviations 1982 to 2019 from long-term monthly mean values in percent ($\pm 100$% is maximum and minimum deviation) of glacier-wide climatic mass balance (

**a**), albedo (

**b**), air temperature at 2 $\mathrm{m}$ (

**c**), accumulated snowfall (

**d**), incoming shortwave radiation (

**e**) and incoming longwave radiation (

**f**). The color bar is arranged so that deviations that act positively (negatively) on glacier-wide climatic mass balance are shown in blue (red).

**Figure 8.**Mean (1982–2019) annual glacier-wide climatic mass balance ($\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.\mathrm{a}$

^{−1}) deviations from reference run (${B}_{clim,a}$ = $-0.48$ $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.$ $\mathrm{a}$

^{−1}) for different overall temperature and total precipitation perturbations. The values within each pixel displays the actual mean ${B}_{clim,a}$ of the corresponding perturbation simulation. Please note that the color bar of the deviations is not centered around zero, reflecting the nonlinear response to same positive and negative perturbations.

**Figure 9.**Seasonal sensitivity characteristic (SSC) after Oerlemans and Reichert [43]. Red bars are the dependence of annual glacier-wide climatic mass balance ${B}_{clim,a}$ on monthly temperature perturbations of 1 $\mathrm{K}$ and blue the dependence of ${B}_{clim,a}$ on monthly total precipitation perturbation of 10%.

**Figure 10.**Annual glacier-wide climatic mass balance (1982–2015) of the Halji glacier (upper panel), Webster and Yang Monsoon index (WYM, middle panel) and Polar/Eurasia index (POL, lower panel).

**Table 1.**Variables, instruments, measuring range and nominal accuracies of the automatic weather station located at 5359 $\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{a}.\phantom{\rule{0.166667em}{0ex}}\mathrm{s}.\phantom{\rule{0.166667em}{0ex}}\mathrm{l}.$ in the direct vicinity of Halji glacier. The full name of the instruments are Lufft WS501-UMB SmartWeather Sensor and Lufft WS100 Radar Precipitation Sensor.

Variable | Instrument | Measuring Range | Nominal Accuracy |
---|---|---|---|

Surface pressure | Lufft WS501-UMB | 300 … 1200 $\mathrm{h}\mathrm{Pa}$ | $\pm \phantom{\rule{0.166667em}{0ex}}0.5\phantom{\rule{0.166667em}{0ex}}\mathrm{h}\mathrm{Pa}\phantom{\rule{3.33333pt}{0ex}}(0\phantom{\rule{3.33333pt}{0ex}}\dots \phantom{\rule{3.33333pt}{0ex}}40\xb0\mathrm{C})$ |

Air temperature at 2 $\mathrm{m}$ | Lufft WS501-UMB | –50 … 60 $\xb0\mathrm{C}$ | $\pm \phantom{\rule{0.166667em}{0ex}}0.2\xb0\mathrm{C}\phantom{\rule{3.33333pt}{0ex}}(-20\phantom{\rule{3.33333pt}{0ex}}\dots \phantom{\rule{3.33333pt}{0ex}}50\xb0\mathrm{C}),$ |

$\pm \phantom{\rule{0.166667em}{0ex}}0.5\xb0\mathrm{C}\phantom{\rule{3.33333pt}{0ex}}(-30\xb0\mathrm{C})$ | |||

Total precipitation | Lufft WS100 Radar | 0.01 … 200 mm h^{−1} | $\pm \phantom{\rule{0.166667em}{0ex}}0.16\phantom{\rule{3.33333pt}{0ex}}$ mm or $\phantom{\rule{3.33333pt}{0ex}}\pm 10$ * |

Relative humidity at 2 $\mathrm{m}$ | Lufft WS501-UMB | 0 … 100 | $\pm 2$% |

Wind speed at 2 $\mathrm{m}$ | Lufft WS501-UMB | 0 … 75 $\mathrm{m}$ s^{−1} | $\pm \phantom{\rule{0.166667em}{0ex}}3\%\phantom{\rule{3.33333pt}{0ex}}(0\phantom{\rule{0.166667em}{0ex}}\dots \phantom{\rule{0.166667em}{0ex}}35\phantom{\rule{0.166667em}{0ex}}\mathrm{m}/\mathrm{s}),$ |

$\pm 5\%\phantom{\rule{3.33333pt}{0ex}}(>35\mathrm{m}/\mathrm{s})\phantom{\rule{3.33333pt}{0ex}}RMS$ |

**Table 2.**COupled Snowpack and Ice surface energy and mass balance model in PYthon (COSIPY) forcing variables with required units, applied downscaling approaches to ERA5-L data and approaches to create the distributed fields (interpolation) on the glacier. The second column denotes if the variable is also measured by the automatic weather station (AWS). A dash stands for no downscaling.

Variable | AWS | Downscaling | Interpolation |
---|---|---|---|

Surface pressure ${p}_{sfc}$ ($\mathrm{h}\mathrm{Pa}$) | yes | Barometric formula | Barometric formula |

Air temperature at 2 $\mathrm{m}$ ${T}_{2}$ ($\mathrm{K}$) | yes | Quantile mapping | Lapse rate |

Relative humidity at 2 $\mathrm{m}$ RH_{2} (%) | yes | Lapse rate | - |

Incoming shortwave radiation ${Q}_{SWin}$ (W m^{−2}) | yes | - | Radiation modelling [68] |

Incoming longwave radiation ${Q}_{LWin}$ (W m^{−2}) | no | - | - |

Wind speed at 2 $\mathrm{m}$ ${U}_{2}$ (m s^{−1}) | yes | Scale factor of 5 | - |

Total precipitation TP (mm) | yes | Scale factor of 2 | - |

**Table 3.**Applied spatial resolutions and resulting glacier grid points (GGPs) for the Halji glacier. Not all applied resolutions are shown.

Resolution in Arcseconds (${}^{\prime \prime}$) | 1.0 | 2.0 | 3.0 | 3.33 | 5.0 | 6.67 | 10.00 | 16.67 | 30.0 | 33.33 | 50.0 |
---|---|---|---|---|---|---|---|---|---|---|---|

Resolution in ∼m | 30 | 60 | 90 | 100 | 150 | 200 | 300 | 500 | 900 | 1000 | 1500 |

Resulting GGPs | 2735 | 688 | 303 | 248 | 110 | 59 | 28 | 11 | 4 | 2 | 1 |

**Table 4.**Spearman’s rank correlation coefficients between monthly forcing (f) and intermediate (i) variables and annual glacier-wide climatic mass balance. Grey coefficients are not significant, normal font denotes significance level 0.05 and bold and italic fonts significance level 0.01. The aggregation metrics to calculate annual and monthly values are displayed in the second row.

Variable | ${\mathit{T}}_{2}$ | ${\mathit{p}}_{\mathit{s}\mathit{f}\mathit{c}}$ | ${\mathit{R}\mathit{H}}_{2}$ | ${\mathit{U}}_{2}$ | $\mathit{T}$ | ${\mathit{S}\mathit{F}}_{\mathit{c}}$ | ${\mathit{Q}}_{\mathit{S}\mathit{W}\mathit{i}\mathit{n}}$ | ${\mathit{Q}}_{\mathit{S}\mathit{W}\mathit{n}\mathit{e}\mathit{t}}$ | ${\mathit{Q}}_{\mathit{L}\mathit{W}\mathit{i}\mathit{n}}$ | ${\mathit{Q}}_{\mathit{L}\mathit{W}\mathit{n}\mathit{e}\mathit{t}}$ | $\mathit{\alpha}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

Metric | mean | mean | mean | mean | sum | sum | mean | mean | mean | mean | mean |

Type | f | f | f | f | f | i | f | i | f | i | i |

Annual | −0.42 | −0.07 | 0.36 | −0.45 | 0.42 | 0.54 | 0.17 | −0.81 | −0.32 | 0.09 | 0.8 |

September before | −0.31 | −0.09 | 0.26 | −0.28 | 0.43 | 0.47 | −0.15 | −0.16 | 0.04 | 0.14 | 0.14 |

October | −0.49 | −0.3 | 0.43 | −0.21 | 0.36 | 0.36 | −0.0 | −0.44 | −0.05 | 0.32 | 0.44 |

November | −0.32 | −0.16 | 0.32 | −0.37 | −0.06 | 0.08 | 0.21 | −0.37 | −0.04 | 0.28 | 0.37 |

December | −0.06 | −0.02 | 0.19 | −0.17 | 0.16 | 0.19 | −0.03 | −0.14 | 0.1 | 0.13 | 0.14 |

January | −0.21 | 0.06 | −0.11 | 0.18 | 0.33 | 0.29 | 0.0 | −0.08 | −0.0 | 0.06 | 0.09 |

February | −0.55 | −0.2 | −0.09 | −0.2 | 0.18 | 0.24 | 0.05 | −0.01 | −0.35 | −0.07 | 0.05 |

March | 0.13 | 0.17 | 0.21 | 0.06 | −0.15 | −0.23 | 0.02 | 0.2 | 0.11 | 0.04 | −0.21 |

April | −0.12 | −0.04 | −0.05 | −0.08 | 0.04 | 0.12 | 0.16 | −0.03 | −0.17 | −0.08 | 0.04 |

May | −0.39 | −0.31 | 0.09 | −0.06 | 0.03 | 0.0 | 0.25 | −0.02 | −0.36 | −0.24 | 0.08 |

June | −0.68 | −0.19 | 0.51 | −0.55 | 0.03 | 0.35 | 0.22 | −0.27 | −0.36 | −0.24 | 0.31 |

July | −0.46 | 0.16 | 0.04 | −0.26 | 0.12 | 0.32 | 0.14 | −0.82 | −0.16 | −0.12 | 0.86 |

August | −0.3 | 0.01 | 0.13 | −0.37 | 0.11 | 0.31 | −0.11 | −0.9 | −0.0 | 0.01 | 0.91 |

September | 0.02 | −0.17 | 0.01 | −0.15 | 0.06 | −0.02 | −0.12 | −0.74 | 0.01 | 0.14 | 0.75 |

**Table 5.**Spearman’s rank correlation coefficient between the annual glacier-wide climatic mass balance and the Polar/Eurasia index (POL) and the Webster and Yang Monsoon index (WYM). Empty cells mark months or seasons when the index does not exist. Grey coefficients are not significant, normal font denotes significance level 0.05 and bold and italic fonts significance level 0.01.

Index | Annual | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | JJA | JJA |
---|---|---|---|---|---|---|---|---|---|---|---|---|

POL | 0.48 | 0.29 | 0.41 | –0.03 | –0.05 | –0.22 | 0.56 | 0.23 | 0.06 | 0.17 | ||

WYM | –0.42 | –0.43 | –0.35 | –0.33 | –0.17 | –0.44 | –0.43 |

**Table 6.**Comparison of simulated annual glacier-wide climatic mass balance ${B}_{clim,a}$ ($\mathrm{m}\phantom{\rule{0.166667em}{0ex}}\mathrm{w}.\mathrm{e}.\mathrm{a}$

^{−1}) with other studies using digital elevation model differences at the Halji glacier.

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**MDPI and ACS Style**

Arndt, A.; Scherer, D.; Schneider, C.
Atmosphere Driven Mass-Balance Sensitivity of Halji Glacier, Himalayas. *Atmosphere* **2021**, *12*, 426.
https://doi.org/10.3390/atmos12040426

**AMA Style**

Arndt A, Scherer D, Schneider C.
Atmosphere Driven Mass-Balance Sensitivity of Halji Glacier, Himalayas. *Atmosphere*. 2021; 12(4):426.
https://doi.org/10.3390/atmos12040426

**Chicago/Turabian Style**

Arndt, Anselm, Dieter Scherer, and Christoph Schneider.
2021. "Atmosphere Driven Mass-Balance Sensitivity of Halji Glacier, Himalayas" *Atmosphere* 12, no. 4: 426.
https://doi.org/10.3390/atmos12040426