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Supplementary Information1

Strong glacier mass loss in the Tien Shan2

over the past 50 years3

Daniel Farinotti1,2, Laurent Longuevergne3, Geir Moholdt4, Doris Duethmann1,4

Thomas Molg5, Tobias Bolch6,7, Sergiy Vorogushyn1, and Andreas Guntner15

1 GFZ German Research Centre for Geosciences, Section 5.4 -Hydrology, Potsdam, Germany6

2 Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf, Switzerland7

3 National Center for Scientific Research CNRS, UMR 6118 Geosciences, University of Rennes, France8

4 Norwegian Polar Institute, Fram Centre, Tromsø, Norway9

5 Climate System Research Group, Institute of Geography, Friedrich-Alexander-University Erlangen-10

5 Nurnberg (FAU), Erlangen, Germany11

6 University of Zurich, Department of Geography, Zurich, Switzerland12

7 Technische Universitat Dresden, Institute for Cartography, Dresden, Germany13

Substantial glacier mass loss in the Tien Shan over the past 50 years

© 2015 Macmillan Publishers Limited. All rights reserved

http://dx.doi.org/10.1038/ngeo2513

A Estimates based on GRACE data14

Launched in March 2002, the Gravity Recovery And Climate Experiment (GRACE) [1] has15

revolutionized the way large mass changes can be detected on Earth. By monitoring the temporal16

variations of Earth’s gravity field with an “unprecedented temporal and spatial resolution” [2],17

GRACE has provided new insights in mass redistribution processes of the atmosphere, the18

oceans, terrestrial water, and the cryosphere [for a review see 3].19

Consisting of two twin satellites flying in a polar orbit at about 450 km altitude and about20

200 km apart, GRACE infers on Earth’s gravity variations by constantly monitoring the distance21

between the two satellites at the micrometer level [e.g. 4]. Two types of products have been22

developed from GRACE range-rate data: The first translates satellite range-rate data directly23

into a set of localized surface mass concentrations [so-called ”mascons”, e.g. 5]; the second is a24

global spherical harmonic (SH) expansion of the gravity field, where a set of Stokes coefficients25

[e.g. 6] is the standard GRACE Level 2 product. Note that mascon- and SH-derived mass changes26

are equivalent [e.g. 7, 8]. In the present study, the SH formulation is used. A description on27

how surface mass changes can be derived from SH coefficients is given in [9]. Love numbers by28

[10] are used.29

A.1 General processing flow and challenges30

When recovering surface mass variations from GRACE products, two major difficulties have to31

be dealt with. The first is linked to the limited spectral content (i.e. the sensitivity to large32

spatial scales) of GRACE when focusing on a space-limited areas [11]. The second is given33

by the fact that GRACE (and more generally, gravity) provides information about vertically34

integrated mass changes only, which makes a separation of individual sources challenging.35

The first point leads to so-called leakage effects [12], i.e. to a loss in signal amplitude when36

concentrating GRACE on a region of interest, and a partial compensation from mass changes37

outside that region. Several methods have been developed to overcome this issue, including38

the use of a-priori information on the spatial distribution of the expected mass changes [e.g.39

13, 14]. The second point is inherently difficult, and is generally tackled by using models40

to discern between individual sources. For the region of interest in this study, the processes41

that potentially contribute to gravity variations can be subdivided into two categories, i.e. (1)42

processes related to near-surface mass transport, such as water storage in lakes, the unsaturated43

zone, aquifer systems, glaciers, the seasonal snow cover, and erosion, and (2) internal processes,44

including glacial isostatic adjustment since the Last Glacial Maximum and the Little Ice Age,45

and vertical crustal movements related to tectonic processes.46

Previous studies focusing on GRACE-derived glacier changes in High Mountain Asia showed47

that the largest uncertainties stem from the hydrological contribution [15, 16]. Recently, [17]48

showed that forward modelling (i.e. application of a spatial filter to the modelled hydrological49

contribution in order to mimic the large-scale sensitivity of the GRACE signal) can be used50

for reducing that uncertainty. Given that the processing method used for the derivation of51

the GRACE data is known, the required mathematical process is straightforward. Forward52

modelling the impact of all known contributions to the GRACE signal was previously shown53

to be the most suited method for extracting a specific storage compartment [e.g. 18, 19]. This54

general strategy is adopted here. In principle, the impact of all known mass-change contributions55

derived from models and/or independent estimates (Sections A.3 and A.4) are spatially filtered to56

match the GRACE resolution, subtracted from the total mass change derived from the GRACE57

data (Section A.2), and the residuals interpreted as glacier mass changes (Figure A.1). The so58

obtained glacier mass changes, which still refer to the GRACE resolution, are re-focussed on the59

region of interest by using a mascon adjustment approach (see Section A.5). Mass change rates60

are then obtained by computing time-series trends through a 4th order low-pass Butterworth61

filter [e.g. 20] in order to remove seasonal variations. In order to account for a wide range of62

2


possible error sources, the workflow is based on an ensemble-like approach that accounts for63

uncertainties in the (1) GRACE-derived gravity change products, (2) applied spatial filtering64

and processing strategy, (3) mass-change contributions other than glaciers subtracted from the65

total signal, and (4) methodology for re-focusing the residual mass changes.66

A.2 GRACE data67

Different sets of Stoke coefficients (called ”GRACE solutions”) can be retrieved from various68

research groups. Differences reflect varying computational strategies and are related to (i) the69

use of different background models to compute and remove the contribution of atmospheric and70

oceanic mass changes, (ii) the inversion method used to estimate the Stokes coefficients, and71

(iii) the spectral content. Although a recent global analysis suggests that long-term trends are72

similarly captured by different GRACE solutions [21], significant local differences have been73

reported to occur [e.g. 22, 23].74

In this work, a suite of 12 GRACE solutions is used in order to quantify the impact of various75

processing strategies. The different solutions can be summarized into three main categories76

including (1) unconstrained solutions, (2) stabilized solutions, and (3) regularized solutions.77

Unconstrained solutions are provided by the Center of Space Research (CSR), the German Re-78

search Centre for Geosciences (GFZ), and the Jet Propulsion Laboratory (JPL). For the CSR79

and JPL solutions, product Release 05 (RL05) is used, whilst RL05a is used for GFZ. Data80

are retrieved from ftp://podaac-ftp.jpl.nasa.gov/allData/grace/ and refer to the period81

2003-2013. Compared to RL04, ameliorations in both range-rate data processing and background82

models have resulted in lower noise level in RL05 solutions, leading to a significant reduction83

of residuals over the oceans [24] and an improved effective resolution. Unconstrained solutions84

generally show prominent North-South striping related to the amplification of uncertainties in85

the background models, and the increasing noise with increasing degree [e.g. 25]. For improving86

the signal-to-noise ratio, specific post-processing filters have to be applied. Here, three types of87

common filters are explored: (1) Gaussian smoother [e.g. 26, 9], which is the most widely used88

isotropic filter, and is generally applied in combination with a decorrelation filter, (2) decorre-89

lation filter [27, 28], which is a data-adaptive polynomial filter, and (3) DDK-4 decorrelation90

filter [29, 30], which is an anisotropic filter that uses synthetic GRACE orbital geometry and91

modelled signal covariance information to smooth and decorrelate the SH coefficients. For a92

more detailed discussion of different filtering methods, and the implications for hydrological93

applications in particular, refer to e.g. [31] or [14].94

Stabilized solutions covering the period 2003-2012 are provided by the Space Geodesy Research95

Group (GRGS) and are retrieved from http://grgs.obs-mip.fr/grace. The solutions are96

designed to avoid the striping present in the unconstrained solution. This is achieved by con-97

straining degrees 31 and above towards the mean gravity field during the inversion process98

[32, 33]. Here, RL2 and RL3 are used. RL2 is used without further filtering, whilst RL3 is99

truncated at degree 60 since first analyses for the area of interest indicate a very low signal to100

noise ratio for higher degrees (not shown).101

Regularized solutions covering the period 2003-2012 [25] mitigate the uncertainty introduced by102

the ill-conditioned inversion problem by using a Tikhonov regularization. This method has shown103

to be effective and to have limited signal attenuation. Compared to unconstrained solutions,104

regularized solutions yield an equivalent representation of the original range-rate data, but allow105

the use of SH coefficients of higher degree and order (up to degree 120) with no further filtering.106

Further differences in the GRACE data can arise from the potential substitution of low degree107

terms (degrees 1 and 2). Degree-1 coefficients, which describe the relative motion between108

the Earths centre of mass and a crust-fixed terrestrial reference frame, cannot be measured by109

GRACE and are usually either ignored or substituted from time series of geocentre motion.110

Degree-2 coefficients, associated with the Earths oblateness, are affected by large uncertainties111

3


due to the orbital geometry and short separation between the GRACE satellites [34]. Here, the112

impact of considering/ignoring the substitution of these low degrees is quantified by using degree-113

1 coefficients by [35], and degree-2 coefficients by [36]. The analyses performed for the region of114

interest indicate that for the recovered glacier-mass change, the combined effect of substituting115

or not substituting the two coefficients is below 0.1 Gt a−1. Note that GRGS solutions use a116

specific methodology for the degree-2 coefficients [33].117

The main characteristics of the various GRACE solutions are synthesized in Table A.1. Time118

series of total mass changes for the region of interest are presented in Figure A.2a. The spatial119

distribution resulting from the use of various filtering methods is presented in Figure A.3. To our120

knowledge, neither GRGS RL3 nor the regularized solutions by [25] have been applied previously.121

A.3 Subtraction of water storage variations122

When aiming at recovering glacier-mass changes, water storage variations that need to be sub-123

tracted from the GRACE signal include variations in (1) surface water storage (SWS), (2) soil124

moisture storage (SMS), (3) groundwater storage (GWS), and (3) the seasonal snow pack (SSP).125

The combination of the three components is referred to as total water storage (TWS).126

Variations in SWS, i.e. water storage variations in rivers, lakes, and wetlands, have previously127

been ignored in GRACE-based assessments of glacier mass changes, although SWS contribu-128

tions from lakes have been shown to explain large parts of the observed mass change over the129

Tibetan Plateau for example [37, 17]. Here, the impact of SWS is taken into account following130

the methods by [38]. Outlines and corresponding surface area of major lakes and reservoirs in131

the region of interest are extracted from the Global Lakes and Wetlands Database (GLWD-132

1 and 2) [39]. Changes in lake level and/or volume are either obtained from the satellite-133

altimetry based LEGOS Hydroweb database [40], or from direct observations reported from the134

Scientific-Information Center of the Interstate Coordination Water Commission of the Central135

Asia (www.sic.icwc-aral.uz). When information about changes refers to lake-level only, vol-136

ume changes are computed using a constant-area hypothesis. For some smaller lakes without137

any available observation data, volume variations are estimated from the surface area and the138

level fluctuations of the closest lake in the same river basin. Since observations from LEGOS139

Hydroweb are available until February 2010 only, SWS contributions after that date are assumed140

to be constant. Note that this has no impact for the estimates of the 2003-2009 period, which141

are used for cross validation with other approaches (cf. Sections B and C). The time series of142

the resulting SWS contribution is shown in Figure A.2b. The characteristics of the main lakes143

and reservoirs in the vicinity (< 500 km) of the study area are given in Table A.3. Lakes that144

are included in the assessment and the contribution to TWS deriving therefrom are displayed145

in Figure A.4. Note that lake storage has generally decreased over the period 2003-2009, which146

is in contrast to what was observed for the Tibetan Plateau [e.g. 41, 42].147

The contribution of TWS has been highlighted as the major source of uncertainty when recov-148

ering glacier mass-changes from GRACE data [e.g. 15, 16, 17], and GWS and SPP are known149

to strongly influence the water cycle in the study area [e.g. 43]. Yet, the actual uncertainty in150

modelling the individual compartments has not been fully determined, as authors have generally151

been considering a limited number of models, models using the same forcing data, or models152

that do not include long-term storage compartments (GWS in particular). Here, an ensemble of153

10 land surface models (LSMs) is used to better quantify errors arising from forcing data, model154

structure, and model spatial resolution. The storage compartments (i.e. SMS, GWS or SSP)155

included in the individual models, as well as the spatial and temporal resolution of the output,156

and the data used for model forcing are summarized in Table A.2. Note that GWS is included157

in a few models only, whilst some models explicitly take into account anthropogenic water use158

as well. For a detailed description of the individual models, refer to the references in the last159

column of the same Table.160

4


Time series of TWS variations as calculated by the individual models are presented in Fig-161

ure A.2c. The differences between individual models can be substantial. A 2-month phase-lag162

can be observed between models m05 (NOAH 2.7.1 at 0.25◦ resolution) and m02 (CLM v4.0)163

for example, whilst storage changes between individual models of the GLDAS suite (models164

m01, m04, m05, and m05a) can differ in amplitude by factor of two and more (Figure A.2b).165

Long-term water storage is generally negative, with trends for the period 2003-2009 between166

−0.3 and −8.6 Gt a−1 (average −3.7± 5.1 Gt a−1; see also the leftmost boxplot in Fig. A.6).167

In order to subtract TWS change from the GRACE signal, LSM outputs are converted in the168

equivalent SH representation, and then processed the same way as the corresponding GRACE169

solution (e.g. truncation at a given maximum degree, application of a given filter; see Table A.1).170

For the SH conversion (which uses global LSM data), Antarctica and Greenland are blanked for171

LSMs including these regions. Note that since LSM outputs do not contain the typical North-172

South stripes present in the GRACE solutions, no destriping filter is applied in order to prevent173

a potential removal of geophysical signals oriented in that particular direction [14]. The choice174

is additionally motivated by the data-adaptive nature of the destriping filters that makes the175

actual impact of the filtering procedure difficult to determine. The resulting spatial distribution176

of TWS, filtered the same way as the GRACE solutions, is shown in Figure A.5.177

Filtering the LSM outputs reduces the spread in the region-wide trends in total water storage178

(Figure A.6). This is in line with the findings by [17], and indicates that LSM uncertainty is scale-179

dependent. In particular, large-scale water storage variations seem to be better described by180

LSMs than variations at smaller scales. The strongest reduction in the spread between regional181

trends in total water storage is obtained by the strongest filtering method (truncation at degree182

60, Gaussian smoother with 300 km radius; option T60 G300 in Figure A.6). Despite this183

reduction, uncertainty emerging from the spread of individual LSM output remains the major184

contribution in the total error budget for the recovered glacier mass changes (see Section A.6,185

and Table A.4).186

A.4 Subtraction of further mass changes187

Processes other than water storage variations that affect total mass changes in the region of188

interest include Glacial Isostatic Adjustment (GIA), tectonic processes, and erosion [e.g. 15, 17].189

GIA is the ongoing viscoelastic relaxation of the Earth in response to the presence of large190

ice masses in the past [e.g. 44]. GIA contributions are generally associated with two dis-191

tinct events [e.g. 15], i.e. (1) the Last Glacial Maximum (LGM), with its deglaciation ter-192

minating about 19 000 years before present [e.g. 45], and (2) the more recent Little Ice Age193

(LIA), which had its coldest conditions between 1570 and 1730 [e.g. 46]. Modelling these194

effects require constraining both ice history and viscoelastic properties of the Earth. Two195

models and corresponding ice histories are considered here: ICE-5G [44, 47], retrieved from196

http://gracetellus.jpl.nasa.gov/data/pgr/, and RSES [48] (H. Steffen, pers. comm.,197

January 2014). Data are retrieved as SH coefficients and filtered with the same options as198

the GRACE solutions. Both the ICE-5G model, which does not show any significant glacieriza-199

tion in the Tibetan Plateau during the LGM, and the RSES model, which assumes the presence200

of small valley glaciers, suggest a negligible present-day GIA contribution for the Tien Shan201

(not shown). According to the two models, the effect on the recovered present-day glacier mass-202

change rate for the Tien Shan is below 0.05 Gt a−1. The contribution of the LIA have previously203

been estimated to be negligible by [15]. The presence of a larger glacierization during the LGM204

than what assumed in the ICE-5G and RSES glacial histories is controversial [e.g. 49, 50, 51, 52].205

[15] assessed that the present-day contribution associated to a potential Tibetan ice cap during206

the LGM can be up to 1±1 Gt a−1. Here, the contribution stemming from the ice-sheet hypoth-207

esis is not subtracted from the total GRACE signal, but the additionally introduced uncertainty208

is accounted for in the total error budget (Section A.6).209

5


In general, the impact of tectonic uplift and erosion processes are partially compensating each210

other [e.g. 53]. Vertical uplift in the Tien Shan is difficult to constrain because of its limited211

amplitude [54], and is generally lower than for the Tibetan Plateau [e.g. 55]. The analysis of212

Bouguer gravity anomalies over the wider Tien Shan area, however, suggest that local isostatic213

compensation is nearly complete in the region [e.g. 56]. The net contribution of tectonic uplift214

and erosion is, thus, assumed to be negligible.215

A.5 Mascon adjustment216

The mass changes obtained after subtraction of the non-glacier contributions from the total217

GRACE signal (Figure A.9) still refer to the filtered GRACE resolution. For re-focussing the218

signal to the actual glacier positions, a mascon adjustment approach is used. Mascons are surface219

mass concentrations used to represent local mass variations when inverting the GRACE derived220

gravity field [e.g. 57, 58], and widely used for estimating glacier mass changes from GRACE221

data [e.g. 59, 60, 61, 16, 62]. The interest of the mascon approach relies on the opportunity to222

incorporate a-priori information on the spatial distribution of mass variability from independent223

sources [e.g. 63]. This has been shown to yield more realistic mass changes [e.g. 19, 64, 65] than224

simple rescaling approaches since the sensitivity kernel of GRACE is not homogeneous over a225

given region but decreases from the centre of the region towards its margins [38]. Using the226

mascon approach for resolving isolated masses such as glaciers or small glacier regions, however,227

poses a tradeoff problem concerning the mascon size: A large number of small mascons with228

uniform mass distribution (the most common assumption for individual mascons) would better229

describe the high spatial variability, but increase the ill-posedness of the inversion problem since230

different distributions of the mass changes can result in the same gravity changes as seen by231

GRACE. The appropriate mascon definition is therefore critical in order to quantify the mass232

changes accurately [e.g. 63].233

In order to determine the optimal mascon repartition, the region of interest was first discretized234

in 1, 3, 7 and 16 different mascons with an equivalent size of about 6.0◦, 3.4◦, 1.8◦, and 1.2◦,235

respectively (not shown). Discretization was performed by discerning individual regions of glacio-236

logical interest. The signal of a known, synthetic mass distribution of 1 Gt in total (Fig. A.8a)237

was then filtered in order to mimic the GRACE resolution and the so obtained synthetic GRACE238

signal re-focussed on the mascons through a Bayesian inversion approach [e.g. 66, 64] in order239

to assess the total uncertainty introduced during the inversion.240

The Bayesian approach consists of propagating the knowledge provided by the GRACE signal241

through the known spatial filtering applied to that signal, and to combine it with the a-priori242

knowledge of the sub-mascon distribution of the actual mass changes that can be gained from243

the known glacier position (see below). Let mobs and mact be the vectors of observed and244

actual mass changes respectively, and f the forward model through which mact is observed (e.g.245

the effect of a spectral truncation at a specific degree and the application of a given Gaussian,246

DDK, or decorrelation filter to the GRACE data; see Section A.2), i.e. mobs = f(mact). The247

a-posteriori probability density function of mact, i.e. p(mact), can be calculated as,248

p(mact) = π(mact) exp

(−1

2rTC−1

MMr

), (1)

where π(mact) (taken as locally uniform) is the a-priori probability density function of mact,249

r = mact − f(mobs) is a vector of residuals, rT is the transpose of r, CMM is the covariance250

matrix of the observations, and C−1MM its inverse. As p(mact) is a probability function, it is251

constrained by∫p(mobs)dm = 1.252

The uncertainty introduced by the glacier representation during the inversion is quantified by253

exploring three different options: In option 1, the spatial distribution of the mass change is254

assumed to be spatially uniform within every individual mascon (Fig. A.8b). In option 2, the255

6


mass change is assumed to be uniform as well, but is localized at positions where glacier are256

known to occur (Fig. A.8c). To this end, glaciers are represented on a 1/8th degree grid, and257

every grid cell that contains a glacier according to the Randolph Glacier Inventory (RGI [67];258

see also Section C.1) is assumed to be completely glacierized. In option 3, glaciers are again259

represented on a 1/8th degree grid, but the mass change is assumed to be proportional to the260

degree of glacierization (inferred from the RGI) of that grid cell (Fig. A.8d). The resolution of261

1/8th degrees for glacier representation was chosen since tests indicated this grid size yielding262

the best compromise between numerical stability and actual description of the spatial patterns263

at GRACE resolution (not shown). Further a-priori information about glacier mass changes that264

could potentially be gained from ICESat data (see Section B) or glaciological measurements and265

modelling (see Section C) were not considered in order to ensure independence between the three266

approaches. The total uncertainty assessed for the so performed inversion approach is shown in267

Figure A.7.268

The results indicate that in general, a set of three mascons located over the central, eastern and269

northern part of the Tien Shan respectively (Fig. A.8c), is sufficient for an adequate recovery270

of the actual mass change signal: The uncertainty linked to the unknown distribution of glacier271

mass changes is up to 16 % for a truncation of the GRACE signal at degree 120 (leftmost bars in272

Fig. A.7; the filtering corresponds to the one applied for regularized GRACE solutions, and the273

relative high uncertainty reflects the need of correctly quantifying the sub-mascon mass change274

distribution), but below 4 % in all other cases. Thus, for the inversion of the actual GRACE275

signal, three mascons are used over the Tien Shan. Additional mascons are placed over the276

nearby glacierized regions of the Alay Range, the Pamirs, and the Bogda Shan (Fig. A.8c) in277

order to account for leakage from these regions.278

The above described Bayesian approach is computationally expensive when inverting whole279

time series. The approach based on iterative least-square (LS) adjustment proposed by [60]280

was therefore tested as an alternative. In the above test cases, the simple LS inversion scheme281

recovers the synthetic mass distribution within 1% of what recovered by the Bayesian inversion.282

The computationally cheaper LS approach is therefore used for all analyses.283

The quality of the mascon fit is evaluated with the root mean square error of the residuals of the284

LS adjustment (post-fit residuals) and the portion of explained variance. Depending on noise285

structure and processing method, glacier mass changes modelled by mascons explain between286

60 and 95% of the variance in the residual GRACE signal (Fig. A.10). In general, DDK-287

filtered options (Fig. A.10c,f,i) have lowest residuals, followed by stabilized GRGS solutions288

(Fig. A.10j,k). As expected from Figure A.7, in contrast, the higher spatial information of289

the regularized solutions (Fig. A.10l) also translates to higher post-fit residuals. The spatial290

distribution of these residuals, moreover, suggests that glacier mass is indeed changing within291

each of the three sub-regions defined by the mascons, and that glacier mass changes are relatively292

low for regions R3a and R6 (for region definition, see Fig. 5e in the main article). It is additionally293

to note that fitting a limited number of mascons acts as a supplementary filter in the estimation294

process. In fact, any noise which does not have the same spatial structure as imposed by the295

mascon definition (Fig. 2e in the main article), is rejected (Figure A.10). The inclusion of sub-296

mascon mass distributions adds further spatial constrains. Generally speaking, homogeneous297

mascons require larger mass changes than concentrated mass distributions for an equivalent298

quality of the fit.299

The ensemble of time series for the recovered glacier mass anomaly resulting from the combi-300

nation of various GRACE solutions, substitutions of low degree terms, LSM and GIA models301

output (396 options in total) are shown in Figure A.2d. The resulting glacier mass-change rates302

are displayed in Figures 3 and 6 of the main article. The spatial distribution of the GRACE303

residual signal prior and after mascon adjustment is shown in Figures A.9 and A.10, respectively.304

7


A.6 Uncertainty estimates305

The recovered glacier mass-change rates are affected by a series of uncertainty sources inherited306

from both processing scheme and propagation of model errors. For computing the total error307

budget, all sources are treated as independent.308

Uncertainties for individual GRACE solutions originate mainly from errors in the measurements309

of the satellite range-rate, and errors from imperfectly reduced atmospheric and oceanic mass310

contributions. Root mean square errors (RMSE) for a given month are typically in the range of311

5 mm (10 to 50 mm, depending on latitude; about 15 mm over the Tien Shan) equivalent water312

thickness for the range-rate measurement (the atmospheric and oceanic corrections), and can be313

estimated empirically from residual variations over ocean surfaces [e.g. 68, 69]. Here, GRACE314

TMC uncertainties are estimated as the RMSE over oceans in the same latitude-band as the Tien315

Shan, but excluding ocean regions within 1000 km of continental coast lines to avoid leakage from316

changes in terrestrial water storage [14]. Averaged over the various solutions, GRACE-observed317

TMC for the Tien Shan and the period 2003-2009 are estimated to be −13.3± 3.8 Gt a−1. The318

uncertainty introduced by the GRACE observation (i.e. ±3.8 Gt a−1), thus, induces roughly319

1/2 of the total uncertainty when recovering glacier mass changes (cf. Tab. A.4). The spread320

between individual solutions is slightly larger (±4.6 Gt a−1). This might be linked to the impact321

of the different filtering options, and the destriping filter in particular, which largely affects the322

GRACE signal (Figures A.3). The difference between destriped CSR and GFZ solutions (solu-323

tions G1.p1 and G2.p1, respectively) for example, is 1.3 Gt a−1, while unconstrained GRACE324

solutions filtered with DDK4 yield TMCs that are consistent within 0.5 Gt a−1.325

The variability between individual LSM outputs approximately accounts for the other half of326

the total uncertainty budget (Tab. A.4). The uncertainty introduced in the recovered mass327

change rate, calculated as the mean standard deviation for monthly values of individual model328

outputs, is in the order of 5 Gt a−1. Dispersion among models is clearly scale dependent (cf.329

Fig. A.6 and Section A.3), which hampers any interpretation of trends at the sub-regional scale.330

Moreover, some LSMs clearly depart form the ensemble mean: CLM v2.0 (m01) for example,331

yields negligible hydrological contribution to TMC, whereas the W3RA model (m10), explains332

the totality of the observed TMC trends over the region of interest, thus yielding very small333

glacier change contributions. This clearly highlights the importance of considering an ensemble334

of LSMs driven by different forcing datasets rather than an individual LSM.335

Estimating the uncertainty from estimated SWS changes is difficult. The main uncertainties336

during the period 2003-2009 (period with direct SWS observations; cf. Section A.3) arise from337

(a) the constant-area hypothesis when converting lake level changes to volume changes, and (b)338

the extrapolation of lake levels from nearby lakes. Here, we consider a conservative estimate of339

20%, i.e. an uncertainty of about 0.4 Gt a−1. Note that this estimate would need adjustment340

for the period after 2010.341

The uncertainty in GIA contributions is taken from [15], and estimated to be about 1 Gt a−1.342

According to the results of the GIA models used in the present study (cf. Section A.4) this is343

a very conservative estimate. As described in Section A.4, and in line with [15], uncertainties344

deriving from tectonic and erosion processes are assumed to be negligible.345

All uncertainty sources and their contributions to the estimated glacier mass changes are sum-346

marized in Table A.4. Following the rules of Gaussian error propagation for independent errors347

(cf. Section C.6), the total uncertainty for the glacier mass change rate recovered for the period348

2003-2009 is estimated to be ±6.4 Gt a−1 (95% confidence level).349

A.7 Comparison with previous studies350

So far, only four studies [15, 16, 17, 62] have computed glacier mass change rates for the entire351

Tien Shan based on GRACE data.352

8


[15] used CSR RL04 data truncated at degree 60 and filtered with a Gaussian smoother of353

150 km half-width (T60 G150), addressed the period 2003-2010, and used LSM outputs from354

NOAH v2.7.1 (our m05) and CLM v4.0 (m02). Using the same GIA correction as these authors355

and the same methodological settings, our estimated average glacier mass change over the stated356

period yields −4.9 ± 3.0 Gt a−1. This is in good agreement with the −5 ± 6 Gt a−1 estimate in357

the original study, and increases the confidence in the developed methodology. The stated358

confidence intervals, however, differ largely. This seems mainly due to the fact that [15] used359

LSMs outputs at full resolution, which, as shown in Figure A.6, is prone to cause a larger spread360

in the estimated trends.361

Focusing on the 2003-2009 time period and using the same methods as above, [16] found glacier362

mass change rates of −7±4 Gt a−1 (pers. comm. A. Gardner, October 2013; results for the Tien363

Shan are not shown explicitly in the original publication but included in the estimates for High364

Mountain Asia as a whole). Also in this case, the results can be reproduced: Our estimate for365

the particular setting yields −7.0± 3.1 Gt a−1, with again, a slightly smaller confidence interval366

probably arising from LSM filtering.367

In a recent study using CSR RL05 solutions, [17] calculated glacier mass change rates for the368

period 2003-2012 by using truncation at degree 60, and a Gaussian smoother with 300 km half-369

width (T60 G300). After the removal of a 5-year cycle that the authors suggested to be linked370

to the Arctic Oscillation and the El Nino-Southern Oscillation, the glacier mass change rate for371

the Tien Shan was estimated to be −8.41 ± 4.82 Gt a−1. Following the same methodology, our372

estimate yields a significantly less negative trend, i.e. −1.4± 0.6 Gt a−1. We suspect this large373

difference to be associated to a combination of three reasons: (i) the use of a destriping filter,374

whose data-adaptive nature makes the filter output hardly predictable, (ii) the low effective375

resolution of the GRACE solutions used by [17] when compared to their mascon size, and (iii)376

the difficulty in exactly reproducing the removal of the mentioned cycle. Concerning point (i)377

Figure A.3a and A.3d show for example, how the spatial distribution of two solutions having378

very similar mean temporal evolution (c.f. solutions G1.p1 and G2.p1 in Fig. A.2) can differ379

substantially when processed with a destriping filter (note for example the movement of about 3◦380

longitude in the centre of the positive trend in the north west corner, or the concentration towards381

the west for the negative trend in the Chinese Tien Shan). The application of more predictable382

decorrelation filters such as DDK (c.f. Figures A.3c, A.3f, and A.3i for example) is therefore383

encouraged. Glacier mass-changes derived from DDK filter are not only more consistent among384

different unconstrained GRACE solutions, but also closer to the estimates by using regularized385

and stabilized GRACE solutions (Fig. A.9).386

[62] is currently the most recent study including our region of interest. In it, a global-scale387

mascon strategy was proposed to infer global ice cap and glacier mass changes for the period388

2003-2013. The glacier mass-change rate for the Tien Shan and the period 2003-2009 was389

estimated to be −10 ± 1.7 Gt a−1 (pers. comm. E.J.O. Schrama, February 2015; similarly as390

in [16], explicit results included in the original publication refer to High Mountain Asia as a391

whole). This is more negative than our estimates (−6.6± 4.0 Gt a−1 when including all options,392

−7.5 ± 4.3 Gt a−1 when excluding Gx.p2-options), but within the stated confidence intervals.393

The discrepancy is explained to a minor extend by the different mascon adjustment approach,394

and mainly by the use of a single LSM (GLDAS NOAH, our model m05a in Tab. A.2) in their395

study. Indeed, for the region of interest, the particular model predicts a less negative trend396

in SMS and SPP as compared to alternate models (Fig. 2c of the main article). When using397

LSM-options m05a only, our estimates reach −7.9±2.3 Gt a−1 (including all remaining options)398

and −8.5 ± 1.9 Gt a−1 (when excluding remaining Gx.p2-options), respectively, thus being in399

satisfactory agreement.400

9


FReal world: TMC = SWS + SMS + GWS + SSP + GIA + ICE

GRACE resolution: TMCF = SWSF + SMSF + GWSF + SSPF + GIAF + ICEF

Spatial �ltering (straightforward mathematical process)

Mascon approach (includes a -priori information)

Green = Constrained from measurementsBlue = Constrained from model results

Black = Non-observed quantitiesRed = Target quantity

②

③①

Processing �ow

Figure A.1: Schematic representation of the approach used for the GRACE-derived estimates. Observedmass change contribution from surface water storage (SWS), and modelled contributions from soil mois-ture storage (SMS), groundwater storage (GWS), and the seasonal snow pack (SSP) are filtered in orderto achieve the same spatial resolution as the total mass change (TMC) observed by GRACE (¬). Allfiltered mass contributions (subscript F ), including the effect of glacial isostatic adjustment (GIA), areremoved from the observed TMC (). The obtained residual is interpreted as contribution from glaciers(ICE) and back-transformed to real-world resolution by using a mascon approach (®).

10


-60

-40

-20

0

20

40

60O

bser

ved

TM

C a

nom

aly

( Gt )

G1.p1G2.p1

G3.p1G4.p1

G5.p0G6.p0

G7.p0GRACE solutions

a

-60

-40

-20

0

20

40

60

Mod

elle

d T

WS

ano

mal

y ( G

t )

m01m02

m03m04

m05m05a

m06m07

m08m09

m10LSMs

c

-8

-6

-4

-2

0

2

4

6

Filt

ered

SW

S a

nom

aly

( Gt )

noneT120

T60T50

T60 G150T60 G300

T60 DDK4Applied filters

b

2004 2006 2008 2010 2012

-60

-40

-20

0

20

40

60

Gla

cier

mas

s an

omal

y ( G

t ) d

Figure A.2: Anomalies in (a) total mass storage (TMC) as observed by GRACE, (b) surface waterstorage (SWS) contributions to TMC, (c) total water storage (TWS) as modelled with the suite of landsurface models (LSMs) given in Table A.2, and (d) recovered total glacier mass over the Tien Shanfor all used processing options. Anomalies are computed with respect to the average over the period2003-2009 and refer to the region defined in Figure A.8 (437 000 km2). For the nomenclature of thedifferent GRACE solutions refer to Table A.1. SWS data are available for the period 2003-2010 only, anda constant anomaly is assumed outside that period. For the filtering methods, Tn denotes the truncationat degree and order n, Gw a Gaussian smoother with half-width w (km), and DDK4 a decorrelation filterafter [29]. The red line in panel (d) is the 2003-2009 mass-change trend. Note that in (b) the scale differsfrom the other panels.

11


ihg

fed

cba

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

72°E

76°E

80°E

84°E

88°E

72°E

76°E

80°E

84°E

88°E

Mea

n TM

C tr

end

(Gt a

-1)

10-2

020

-10

0

G 4 . p 0 G 5 . p 0 G 6 . p 0

72°E

76°E

80°E

84°E

88°E

72°E

76°E

80°E

84°E

88°E

G1

.pX

G2

.pX

G3

.pX

G x . p 1 G x . p 2 G x . p 3

lkj

Figure A.3: Mean trend of total mass change (TMC) for (a-i) unconstrained, (j-k) stabilized, and (l)regularized GRACE solutions. The nomenclature on the right-hand-side and figure top is according toTable A.1. X, and x stand for an arbitrary processing method or centre, respectively. Trends refer tothe period 2003-2009.

12


fT60 G300

dT60 DDK4

bT60 G150

eT50

cT60

aT120

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

72°E 76°E 80°E 84°E 88°E72°E 76°E 80°E 84°E 88°E

Mean SWS trend (Gt a-1)

10-20 20-10 0

Figure A.4: Spatial distribution of the surface water storage (SWS) contribution to the total mass-changetrend during the period 2003-2009 as seen at GRACE resolution. Individual panels refer to individualfiltering options. The filter notation (upper-left corner) is according to Fig. A.2b. Outlines of lakes (givenin red) that are (not) accounted for are (not) filled.

13


ic46°N

44°N

40°N

38°N

42°N

h

g

b46°N

44°N

40°N

38°N

42°N

a46°N

44°N

40°N

38°N

42°N

Mean TWS trend (Gt a-1)

10-20 20-10 0

Standard deviation (Gt a-1)

0 105

T120T60

T50

l

72°E 76°E 80°E 84°E 88°E

f46°N

44°N

40°N

38°N

42°N

72°E 76°E 80°E 84°E 88°E

k

j

e46°N

44°N

40°N

38°N

42°N

d46°N

44°N

40°N

38°N

42°N

T60 G150

T60 DD

K4

T60 G300

Figure A.5: Spatial distribution of the (a-f) mean trend and (g-l) according standard deviation for thetotal water storage (TWS) changes predicted by the ensemble of land surface models given in Table A.2.Individual panels refer to individual filtering options (filter notation on the right-hand side according toFig. A.2b). Values refer to the period 2003-2009.

14


-8

-6

-4

-2

0

TWS

tren

d (G

t a-1)

Full resolution T120 T60 T50 T60G150 T60G300DDK4T60

Figure A.6: Effect of various filtering options (notation according to Fig. A.2c) applied to the ensembleof land surface models (LSMs) given in Table A.2. The boxplots show the spread between minimum andmaximum values (whiskers), the interquartile range (box), and the average value (horizontal line insidethe box) for the 2003-2009 trend in total water storage (TWS) as calculated by the various LSMs. Thedegree of filtering increases from left to right. Note the reduction in spread for increasing filtering degree.

0

5

10

15

20

Tota

l unc

erta

inty

(%

)

T120 T60 T50 T60G150 DDK4 T60G300

1 mascon, 6.0°3 mascons, 3.4°7 mascons, 1.8°

16 mascons, 1.2°

T60

Figure A.7: Total uncertainty introduced during the mascon inversion (step ® in Figure A.1) as a func-tion of mascon size and filtering option. The notation for the filtering options is according to Fig. A.2b.

15


ba

0 0.40.2 0.6 0.8

Synthetic mass (Gt)

46°N

44°N

40°N

38°N

42°N

d

72°E 76°E 80°E 84°E 88°E

0 5 10 15%

Glacierization

c

Alay Range and Pamirs

central part

northern part

western partBogda Shan

72°E 76°E 80°E 84°E 88°E

46°N

44°N

40°N

38°N

42°N

Figure A.8: (a) Synthetic mass distribution used for the assessment described in Section A.5, and (b-d)various options assumed for sub-mascon mass change distribution: (b) uniform mass change over theindividual mascons, (c) uniform mass change concentrated in the highlighted pixels, (d) mass changedistribution proportional to the glacierized area within individual pixels. In all panels, grey outlinesshow glacierized areas according to the RGI v3.2. Panel (c) gives the names of the individual mascons asused in Section A.5.

16


ihg

fed

cba

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

72°E

76°E

80°E

84°E

88°E

72°E

76°E

80°E

84°E

88°E

Mea

n tre

nd (G

t a-1)

10-2

020

-10

0

72°E

76°E

80°E

84°E

88°E

72°E

76°E

80°E

84°E

88°E

G1

.pX

G2

.pX

G3

.pX

G x . p 1 G x . p 2 G x . p 3

lkj

G 4 . p 0 G 5 . p 0 G 6 . p 0

Figure A.9: Mean trend of recovered glacier mass-change rates prior to mascon adjustment for (a-i)unconstrained, (j-k) stabilized, and (l) regularized GRACE solutions. The nomenclature on the right-hand-side and figure top is according to Table A.1. X, and x stand for an arbitrary processing methodor centre, respectively. The mean refers to the ensemble of different land surface models (cf. Table A.2)and the period 2003-2009.

17


ihg

fed

cba

lkj

Mea

n tre

nd (G

t a-1)

10-2

020

-10

0

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

46°N

44°N

40°N

38°N

42°N

72°E

76°E

80°E

84°E

88°E

72°E

76°E

80°E

84°E

88°E

72°E

76°E

80°E

84°E

88°E

72°E

76°E

80°E

84°E

88°E

G1

.pX

G2

.pX

G3

.pX

G x . p 1 G x . p 2 G x . p 3

G 4 . p 0 G 5 . p 0 G 6 . p 0

RM

SE

9.3

mm

E.V

ar.

72

%

RM

SE

3.9

mm

E.V

ar.

98

%

RM

SE

4.3

mm

E.V

ar.

87

%

RM

SE

9.5

mm

E.V

ar.

61

%

RM

SE

3.5

mm

E.V

ar.

98

%

RM

SE

4.5

mm

E.V

ar.

86

%

RM

SE

8.6

mm

E.V

ar.

76

%

RM

SE

3.9

mm

E.V

ar.

95

%

RM

SE

4.1

mm

E.V

ar.

87

%

RM

SE

4.5

mm

E.V

ar.

95

%

RM

SE

7.6

mm

E.V

ar.

67

%

RM

SE

6.4

mm

E.V

ar.

88

%

Figure A.10: Residual signal after mascon adjustment (post-fit residuals) for (a-i) unconstrained, (j-k)stabilized, and (l) regularized GRACE solutions. The root mean square error (RMSE) of the fit and theportion of explained variance (E.Var) are provided. The nomenclature on the right-hand-side and figuretop is according to Table A.1. X, and x stand for an arbitrary processing method or centre, respectively.The mean refers to the ensemble of different land surface models (cf. Table A.2) and the period 2003-2009.

18


Table A.1: Overview of the different GRACE solutions and processing strategies used in this study.Option is a code which, combined with the codes in Table A.2, is used for distinguishing the variousestimates. The first (second) part of the code defines the GRACE solution (processing method), whereX is either 1, 2, or 3. RL is the product release, dmax is the maximal degree and order provided inthe Level-2 data, TI is the time integration of the solution, and Ref. a reference for the data source.In the column Processing, T dn indicates truncation at a particular degree n, and D, Gw, and DDK4indicate the application of a decorrelation filter after [27], a Gaussian filter with half-width w (km), or adecorrelation filter after [29], respectively.

Option Solution RL Type dmax TI Processing Ref.

G1.pX CSR 5 Unconstrained 60 30 d either X=1: T dmax + D + G150 [70]G2.pX GFZ 5a Unconstrained 90 30 d or X=2: T dmax + D + G300 [71]G3.pX JPL 5 Unconstrained 90 30 d or X=3: T dmax + DDK4 [72]

G4.p0 GRGS 2 Stabilized 50 10 d T dmax [32]G5.p0 GRGS 3 Stabilized 80 30 d T d60 [33]

G6.p0 CSR reg. 3 Regularized 120 30 d T dmax [25]

Table A.2: Overview of the different land surface models used in this study. Option is the code usedin combination with the codes in Table A.1 for distinguishing various estimates. Ver. indicates themodel version, Res. is the spatial resolution of the model output (irr. stands for irregular), and Ref. isa reference for the given model. The column Represented compartments indicates which water storagecompartments are represented in the models; SWS, SMS, GWS, and SSP are the storages in surface water,soil moisture, groundwater, and the seasonal snow pack, respectively; ant. indicates that anthropogenicwater use is represented as well. Forcing indicates which climatic forcing is used as model driver.

Option Model Ver. Res. Represented compartments Forcing Ref.

m01 CLM (GLDAS) 2 1◦ SMS, SSP CMAP + NOAA/GDAS [73]m02 CLM 4 irr. SWS, SMS, GWS, SSP GPCP + CRUNCEP [74]m03 CLM 4.5 irr. SWS, SMS, GWS, SSP, ant. GPCP + CRUNCEP [75]m04 MOSAIC (GLDAS) - 1◦ SMS, SSP CMAP + NOAA/GDAS [73]m05 NOAH (GLDAS) 2.7.1 0.25◦ SMS, SSP CMAP + NOAA/GDAS [73]m05a NOAH (GLDAS) 2.7.1 1◦ SMS, SSP CMAP + NOAA/GDAS [73]m06 NOAH (GLDAS-2) 3.3 1◦ SMS, SSP Princeton University [76] [73]m07 VIC (GLDAS) - 1◦ SMS, SSP CMAP + NOAA/GDAS [73]m08 WGHM 2.1 0.5◦ SWS, SMS, GWS, SSP, ant. GPCC + ECMWF [77]m09 WGHM 2.2 0.5◦ SWS, SMS, GWS, SSP, ant. GPCC + ECMWF [78]m10 W3RA - 1◦ SMS, GWS, SSP Princeton University [76] [79]

19


Table A.3: Mass changes for major lakes and reservoirs close to the study area. The stated trendsand average seasonal variations (SV) refer to the period 2003-2009, and are given in Gt a−1 and Gt,respectively. Meth. indicates the method used for estimating the change (V = from reported lake volume;LL = from reported lake level; E = estimated from nearby records; see Section A.3 for details), and Ref.is a reference for the data source. Given coordinates are approximate. Lakes and reservoirs are listedaccording to the trend magnitude.

Name Type Coordinates Obs. SV Trend Ref.

Zaysan Reservoir 48.00 N 84.00 E LL 2.123 -1.415 Hydroweb1

Toktogul Reservoir 41.78 N 72.83 E V 1.317 -1.105 HydrowebBalkhash Lake 46.10 N 74.10 E LL 3.583 -0.825 HydrowebBosten Lake 41.98 N 87.00 E V 0.259 -0.454 HydrowebKayrakkum Reservoir 40.30 N 70.10 E E 1.164 -0.109 -Tchardarin Reservoir 41.13 N 68.13 E LL 2.243 -0.094 HydrowebKapchagay Reservoir 43.80 N 77.50 E LL 0.234 -0.072 HydrowebUlungur Lake 47.25 N 87.20 E LL 0.097 -0.057 HydrowebAlakol Lake 46.15 N 81.65 E E 0.530 -0.041 -Jili Lake 46.91 N 87.45 E E 0.011 -0.012 -Sasykkol Lake 46.55 N 80.95 E LL 0.139 -0.011 HydrowebEbinur Lake 44.88 N 82.92 E E 0.134 -0.010 -Sayram Lake 44.60 N 81.20 E E 0.086 -0.007 -Uyaly Lake 46.44 N 81.28 E E 0.021 -0.002 -Sarez Lake 38.20 N 72.78 E E 0.049 0.002 -Karakul Lake 39.03 N 73.40 E E 0.187 0.006 -Charvak Reservoir 41.65 N 70.03 E V 0.295 0.014 SIC-ICWC2

Issyk Kul Lake 42.40 N 77.30 E LL 0.622 0.050 HydrowebAydarkul Reservoir 40.95 N 66.50 E LL 1.009 0.102 Hydroweb

1 LEGOS Hydroweb (www.legos.obs-mip.fr/soa/hydrologie/hydroweb/) [40]2 Scientific-Information Center of the Interstate Coordination Water Commission

of the Central Asia (www.sic.icwc-aral.uz)

Table A.4: Summary of the contributions to total mass changes (TMC) observed by GRACE andcorresponding uncertainty sources. Values (Gt a−1) and uncertainties (Uncert.; 95% confidence level) areaverages and refer to the period 2003-2009. TWS = total water storage; SWS = surface water storage;neglig. = negligible.

Source Value Uncert. Notes

GRACE TMC rate −13.3 3.8Substitution of degree 1 and 2 terms < 0.1 0.1

Unknown actual spatial distribution of TMC 0 ∼ 0.7 (1)(2)

TWS correction (excluding SWS) +3.6 5.0 (1)

SWS correction +2.1 0.4 (1)(3)

Correction for tectonic uplift and erosion neglig. neglig.

GIA correction +1 1 (4)

LIA correction 0 0 (4)

Recovered glacier mass change -6.6 4.0 (5)(6)

(1) Depending on filtering option(2) 4-16% of the recovered glacier mass change (see Figure A.7)(3) 20% of the correction (4) Based on [15](5) −7.5 ± 4.3 Gt a−1 when excluding Gx.p2 options(6) Confidece interval corresponds to 2 times the standard deviation of all ensemble members

20


B Estimates based on ICESat data401

As part of NASA’s Earth Observing System of satellites, the Ice, Cloud and Land Elevation402

Satellite (ICESat) mission was operative between February 2003 and October 2009 for a total of403

18 observation campaigns lasting between 12 and 55 days [80]. During the individual campaigns,404

the onboard Geoscience Laser Altimeter System (GLAS) measured time delays between 1064 nm405

laser pulse transmissions and surface echo returns, thus deriving time series of surface elevation406

along its repeat-track orbits [81]. GLAS ground footprints were separated by about 170 m407

along-track, and had a varying elliptical shape with an average diameter of about 70 m [82, 83].408

Although originally designed for measuring elevation changes of the Greenland and Antarctic409

ice sheets, GLAS measurements have successfully been applied for deriving mass changes of410

glaciers outside the polar regions, such as in the Himalayas [84], High Mountain Asia [16], or411

the Tibetan Plateau [85]. Here, GLAS/ICESat L1B Global Elevation Data (GLA06) altimetry412

product release 33 [86] is used. For calculating glacier volume changes, three different approaches413

presented by [16] are reproduced and extended. In particular, the elevation dependency that414

can be detected in the elevation change signal for the glaciers in the Tien Shan (see also the415

supplementary material by [16]) is explicitly accounted for in the spatial extrapolation.416

B.1 Basic pre-processing and auxiliary data417

Because of the relatively large cross-track separation distances of ICESat orbits at lower latitudes418

(distances up to a few kilometres are common), pure repeat-track methods that are commonly419

used in polar regions [e.g 87, 88]) are not suitable for the region of interest. To overcome420

the problem and targeting the Hindu Kush-Karakoram-Himalaya area, [84] proposed to use421

an external DEM to correct for topographic differences between the altimetry measurements,422

and to analyse elevation trends within the so-corrected ICESat data for deriving mass budgets.423

The same method was used for entire High Mountain Asia by [16], who additionally analysed424

elevation differences between nearest-neighbour points in a slightly modified version of the DEM425

projection-method of [89]. The here presented study, relies on and extends the methods described426

in [16].427

All analyses are performed by using orthometric elevations in the Universal Transverse Mer-428

cator (UTM) projection of WGS84. These are obtained by subtracting the geoid of the Earth429

Gravity Model 2008 [90] from the ellipsoidal elevations of the GLA06 product, and converting430

the default TOPEX/Poseidon datum [91] into WGS84. Saturated return waveforms, induced431

by detector overload from return energy of near-specular reflectors [92], are corrected by adding432

the correction product provided jointly to the data set.433

The void-filled version 4 of the Shuttle Radar Topography Mission (SRTM) DEM provided by434

the Consultative Group on International Agricultural Research [93] was used as the reference435

DEM. [16] showed that for retrieving surface elevation changes with the proposed methods, the436

SRTM DEM is better suited than the potentially competing Global DEM obtained from the437

Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER GDEM). Part of438

the reason is that the SRTM DEM refers to a single point in time (February 2000), whereas the439

ASTER GDEM is constructed by stacking and averaging stereoscopic imagery acquired between440

the years 2000 and 2011.441

Following [16], DEM elevation and slope for each ICESat footprint is extracted from the reference442

DEM through bi-linear interpolation of the DEM grid cells. Glacier surfaces are discerned by443

using the glacier outlines provided by the RGI (see Section C.1). ICESat footprints showing444

a difference larger than ±100 m from the reference DEM, as well as footprints over void-filled445

SRTM grid cells are removed from further analysis. This results in the removal of 10% of the446

data, and a remaining sample of about 15,000 ICESat footprints over glaciers (Fig. 4a of the447

main article).448

Histogram analysis reveals that the so-reduced sample is representative for the glacierized sur-449

21


faces in the region of interest in terms of both spatial distribution and morphological characteris-450

tics (Fig. B.1). A tendency in over-representing flat and steep slopes can be detected (Fig. B.1f).451

Note, however, that in this case local values from the ICESat footprints (grey line) are compared452

to glacier-averaged values (red line), and that assigning the corresponding glacier-averaged value453

to the individual footprints (dashed line) eliminates the difference.454

The temporal consistency of the elevations retrieved by ICESat in the region of interest is455

assessed over non-glacierized terrain. Following [16] and [84], footprints over land areas within456

a 5 km buffer from glaciers are considered, and the data are decimated in order to achieve457

agreement between the slope histograms for glacierized and non-glacierized terrain. Robust458

trend fitting through the so obtained data sample of about 14,400 data points reveals a non-459

significant trend of 0.03± 0.07 m a−1 (dark grey line in Fig. 4b of the main article), which is in460

good agreement with the values found for the entire region of High Mountain Asia [84, 16]. The461

analysis also reveals a systematic elevation difference of about 1.4 m between ICESat and SRTM462

DEM (Fig. 4b of the main article). This has previously been explained with the low-frequency463

biases in the SRTM elevations [94], and the amplitude of the bias is in line with the analyses by464

[84] (see their supplementary Table S2 for example). Note that since all methods described in465

the following consider either elevation differences (method I1) or elevation trends (methods I2466

and I3), the detected bias has no influence on the derived elevation change rates.467

B.2 Method I1 : Elevation difference between nearby footprints468

Method I1 corresponds to method “A” in the analysis of High Mountain Asia by [16]. Basically,469

the method estimates local elevation change rates by dividing the difference in elevation between470

two nearby ICESat footprints with the time span between the two acquisition dates. Since the471

footprints are not at the same location, the ICESat elevations are first corrected for topographic472

differences by subtracting the elevation of the reference DEM at the particular location. Ele-473

vation differences are only computed between footprints stemming from the same season and474

separated by 3 or more integer years (i.e. autumn-to-autumn or winter-to-winter comparisons).475

The comparison between the same season allows to minimize the effects of the temporally vary-476

ing snow cover, whereas a separation by 3 or more years is necessary for achieving a sufficiently477

large signal-to-noise ratio [16]. The obtained elevation change rates are then averaged within478

clusters of 5 km radius in order to reduce the potential bias due to uneven spatial sampling479

and the large spacing between ICESat tracks. Following [16], an iterative 3-standard-deviation480

outlier removal (5% convergence) was applied to the data prior to averaging in order to re-481

duce the sensitivity to gross errors. For the analyses, all autumn and winter ICESat data from482

campaign L2a onwards (autumn 2003 and later) were used, i.e. only data from the calibration483

campaign (L1) and the three summer campaigns (L2c, L3c, L3f) were discarded (Fig. 4a of the484

main article). This resulted in a total of about 180 clusters, each composed of approximately485

80 footprints.486

B.3 Method I2 and I3 : Elevation trends within ICESat data487

Methods I2 and I3 correspond to methods “B” and “C” of [16], respectively, which are in488

turn based on the ideas by [84]. Both methods estimate the elevation change rate within a re-489

gion by computing the temporal trend in the difference between all ICESat footprints available490

for that region and the reference elevation extracted from the reference DEM. The difference491

between method I2 and I3 is given by the considered ICESat campaigns: Method I2 (I3) con-492

siders only data collected during autumn (winter) campaigns (Fig. 4b of the main article). As493

in [16], glacierized surfaces are not subdivided further into debris-free and debris-covered ice,494

since the differences have been shown to be not significant [84, 95]. Trend fitting is performed495

through (a) ordinary least squares fitting, after a 3-standard-deviation edit for outlier removal496

(methods I2.a and I3.a), or (b) robust linear regression [e.g. 96] with iterative weighting based on497

22


Tukey’s biweight function (e.g. [97]) (methods I2.b and I3.b). In both cases, constant campaign-498

wise weights were additionally assigned in order to account for the unequal number of ICESat499

footprints within individual campaigns. The analyses include ICESat data collected between500

campaigns L2a (autumn 2003) and L2e (winter 2009). Data from the calibration campaign L1501

(winter 2003), the incomplete campaign L2f (autumn 2009), and the three summer campaigns502

(L2c, L3c, L3f) were discarded (Fig. 4a-b of the main article), as discussed by [84].503

B.4 Regional extrapolation and volume to mass conversion504

The sparse ICESat footprint coverage and the relatively high level of noise in the calculated505

elevation change rates hampers a robust spatial interpretation of the results. Compared to506

other regions in High Mountain Asia, a pronounced correlation between elevation change rate and507

altitude can be found for the glacierized surfaces in the Tien Shan (see Supplementary Figure S8508

in [16]). Here, two different options (options e2 and e3) are proposed for utilizing this relation509

in the spatial extrapolation. These options are compared to the “benchmark solution” (option510

e1) which simply applies the average elevation change rate to all glacierized surfaces [84, 16].511

The altitudinal dependence of the elevation change rate is determined as follows (Fig. 4d of the512

main article): Methods I1, I2, and I3 (including the options I2.a, I2.b and I3.a, I3.b) are applied513

individually to subsamples of ICESat footprints selected according to the local surface elevation514

given by the reference DEM. The subsamples are chosen to contain all footprints within ±100 m515

of a given altitude z, and the procedure is repeated by systematically varying z in uniform steps516

of 1 m within the altitude range of the study region. For methods of the group I1 (I2 and I3),517

the altitude-specific elevation change rate and the according standard error is estimated if at518

least 5 ICESat clusters (50 ICESat footprints) are available in the considered elevation band519

(Fig. 4c of the main article). The so obtained function is then either approximated through a520

linear relation obtained by robust regression (option e2) or through a non-parametric relation521

obtained by smoothing the function with a running median of 200 m elevation width (option522

e3). In both cases, the extrapolation outside the domain within which a change rate could523

be estimated is performed by assuming a constant value. As an example, Figure 4d of the524

main article visualizes the various altitude-dependent functions obtained when using methods525

I2.b. The interval of 200 m used for selecting subsamples of ICESat footprints and smoothing526

the altitude-dependent function was determined empirically, and is a trade-off between a high527

resolution of elevation and a sufficiently large sample for meaningful parameter estimation.528

When determining the elevation change rate of a given glacier within the study region, the529

median elevation of the glacier is computed by intersecting the glacier outlines provided by530

the RGI with the reference DEM, and the elevation change rate determined for that altitude531

is assigned. The intersection of the three options (e1, e2, and e3) with the different methods532

described in the previous section (methods I1, I2.a, I2.b, I3.a, and I3.b) give rise to a total of533

15 combinations for the performed extrapolations (see Tab. B.1).534

No reliable information exist about firn compaction rates in the study area. A recent study by535

[98], however, was able to show that “assuming a value of 850±60 kg m−3 to convert volume536

change to mass change is appropriate for a wide range of conditions”. The proposed value is537

adopted. For a more detailed discussion on the topic, refer to [98].538

The mass change rates resulting for the entire study region from the 15 options are shown in539

Figure 3b of the main article and given in the last column of Table B.1.540

B.5 Uncertainty estimates541

Several sources of uncertainty affect the total error budget for the mass change estimates based542

on ICESat data. Following former works [e.g. 99, 84, 16] and the notation introduced by [99],543

the total uncertainty is estimated as544

σMB = (σ2STDE + σ2

BIAS + σ2SPAT + σ2

TEMP + σ2AREA + σ2

DENS)1/2, (2)

23


where σMB is the standard deviation of the estimated total mass change of the region of interest;545

σSTDE is the standard error of the coefficients of the relations fitted with the various options546

given in Table B.1 and is an expression of (a) random observational errors in the ICESat data547

[84] and (b) the capability of the fitted functions in reproducing the altitudinal dependency548

of the elevation change rates; σBIAS accounts for the uncertainty introduced by not correcting549

for unknown systematic offsets due to inter-campaign biases [100] or crustal uplift [101]; σSPAT550

takes into consideration potential systematic spatial biases that can occur because of uneven551

sampling of different terrain characteristics (e.g. over-representation of flat slopes, Fig. B.1f);552

σTEMP accounts for potential biases related to uneven temporal sampling (e.g. campaigns with553

less data because of particularly cloudy conditions); σAREA is the uncertainty introduced by the554

imprecisely known glacier area; and σDENS is the standard error associated with the density555

assumed for converting volume changes into mass changes. σSTDE is option specific, and has a556

value ranging between 0.06 and 0.19 m a−1 for options I2.b.e3 and I1.a.e1, respectively. σBIAS,557

σSPAT, and σTEMP are all three set to 0.06 m a−1, following [16]. σAREA is assumed to be 20%558

(a more conservative estimate than assumed in [84, 16] for example), and σDENS is computed559

from the standard error of the density given by [98].560

Note that (1) since the distinction between footprints on glacierized and on non-glacierized561

terrain is performed trough the glacier outlines provided by the RGI (which generally refers to562

the pre-ICESat era; see Section C.1), ice thickness change rates at very low elevations (i.e. at563

elevations where glacier retreat is most pronounced) can potentially be underestimated (since564

footprints erroneously classified as “on glacier” are expected to show change rates close to zero),565

and (2) the misclassification described in (1) has a negligible effect on the overall mass balance566

estimate since the regional extrapolation is performed with the same glacier inventory.567

B.6 Comparison with previous studies568

To date, the only study computing glacier elevation changes from ICESat data in the Tien569

Shan is the one by [16]. The methodologically similar work by [84] excluded the mountain570

range and focused on the Hindu Kush-Karakoram-Himalaya region only. The here presented571

options I1.a.e1, I2.b.e1, and I3.b.e1 are identical with the methods “A”, “B”, and “C” of [16],572

respectively, thus allowing to cross validate the implementation of the methods. As expected, the573

results agree well. The deviations in the mean values (−1.3 Gt a−1, −0.4 Gt a−1, and −0.7 Gt a−1574

for methods “A”,”B”,”C”, respectively; negative values indicating that less negative mass change575

rates are calculated in the here presented study) reflect the differences in (a) assumed density576

for the volume to mass change conversion [850 kg m−3 in this study, and 900 kg m−3 in 16], and577

(b) slight differences in the study region (here, the Bodga Shan range, located north east of578

Urumqui Glacier No.1, was not included) and glacier inventory (RGI v3.2, vs RGI v2.0), which579

jointly result in a difference in glacierized area of about 800 km2 [13,700 km2 in this study, and580

14,500 km2 in the analyses by 16].581

24


Table B.1: Overview of the 15 different model options for estimates based on ICESat data. The accordingmass change rate dM/dt for the entire study area is given in Gt a−1. Confidence intervals refer to the 95%level. For the average, the stated confidence interval corresponds to two times the standard deviationof all ensemble members. Abbreviations: Elev. = Elevation; diff. btw. = difference between; LS = LeastSquares; regr. = regression.

Code Method Fitting Elev. dependence Period dM/dt(Gt a−1)

I1.a.e1 None 2003-2009 −8.97 ± 3.13I1.a.e2 Elev. diff. btw. nearby footprints Linear 2003-2009 −6.33 ± 2.65I1.a.e3 Non-parametric 2003-2009 −5.88 ± 1.95

I2.a.e1 None 2003-2008 −4.60 ± 2.29I2.a.e2 Ordinary LS Linear 2003-2008 −3.97 ± 1.92I2.a.e3 Non-parametric 2003-2008 −3.93 ± 1.77

Elev. trends within autumn dataI2.b.e1 None 2003-2008 −4.54 ± 2.30I2.b.e2 Robust regr. Linear 2003-2008 −3.89 ± 1.88I2.b.e3 Non-parametric 2003-2008 −3.85 ± 1.70

I3.a.e1 None 2003-2009 −6.59 ± 2.28I3.a.e2 Ordinary LS Linear 2003-2009 −4.49 ± 1.83I3.a.e3 Non-parametric 2003-2009 −5.73 ± 1.83

Elev. trends within winter dataI3.b.e1 None 2003-2009 −6.84 ± 2.28I3.b.e2 Robust regr. Linear 2003-2009 −4.87 ± 1.94I3.b.e3 Non-parametric 2003-2009 −5.82 ± 1.98

AVERAGE 2003-2009 −5.35 ± 2.88

25


75 80 850

1

2

3

4

5 longitude adegrees east

40 41 42 43 44 45

0

1

2

3

4

5latitude bdegrees north

-2 -1 0 1 20

1

2

3

4

5 log(area) clog(km2)

1.5 2.0 2.5 3.0 3.5

0

1

2

3

4

5log(elev. range) dlog(m)

3000 4000 5000 60000

1

2

3

4

5 mean elev. em a.s.l.

0.8 1.0 1.2 1.4 1.6

0

1

2

3

4

5log(mean slope) flog(degrees)

100 200 3000

1

2

3

4

5 mean aspect fdegrees from north

-2 -1 0 1 2

0

1

2

3

4

5log(pot. radiation) hlog(W m-2)

RGI outlines

Monitored glaciers

ICESat data

Figure B.1: Smoothed histograms of various morphological characteristics for the glacierized areas inthe study region. Characteristics for all glacierized surfaces included in the RGI (red) and for consideredICESat footprints (grey) are shown. Black dots represent the seven glaciers for which mass balance timeseries are available (see Tab. C.1). Units of the abscissa are given below the panel description (upper leftcorner), whilst the ordinate is histogram density given in % (the area under each curve sums up to 100%).Apart from panels (c) and (d), values for glaciers are averaged over the according glacier area, whilstvalues for ICESat footprints are averaged over the footprint extent. In (c) and (d) the value referring tothe entire glacier is assigned to each ICESat footprint individually. In panel (f) the dashed histogram isobtained by assigning the mean glacier slope to the according ICESat footprint. Note that the variablesin panels (c), (d), (f), and (h) are logarithmically transformed. Potential solar radiation (h) is computedas described in Section C.3.

26


C Estimates based on glaciological modelling582

Similarly as for the estimates based on GRACE and ICESat data, the estimates based on583

glaciological modelling explore a range of different possibilities. This range comprehends a total584

of 30 model options, and can mainly be subdivided into two groups: The first group (M1) relies585

on actual field measurements only, whilst the second (M2) makes additional use of mass balance586

modelling. The two groups are described separately in the next sections.587

C.1 Available glaciological measurements and glacier outlines588

For Central Asia, in-situ mass balance observations (i.e. observations derived from repeated589

stake readings) with a length of ≥ 5 years are available for seven glaciers (Table C.1, Fig. 1 of590

the main article). Out of these series, only two (the series for Tuyuksu Glacier and Urumqi591

Glacier No.1) are still maintained at present. All time series comprehend measurements of both,592

annual mass balance and accumulation. Geodetic glacier ice volume changes are available for593

three selected regions (see Fig. 1 of the main article) and different time periods (Table C.1).594

Sparse additional information on glacier mass balance exists for 13 other glaciers. These time595

series, however, cover either a very short period (< 4 years), or stem from very small glaciers596

(area <1.5 km2) that are adjacent to Tuyuksu Glacier, and are thus not further considered.597

For characterizing the glaciers in the study region individually, the glacier outlines provided by598

the Randolph Glacier Inventory (RGI) version 3.2 [67, 102] are used. In the region of interest,599

large parts of the RGI are taken from the database of the Global Land Ice Measurements from600

Space (GLIMS) initiative [103]. For the Chinese part of the region, RGI data were obtained601

from the first Chinese glacier inventory [104] representing the 1970s and 1980s. For most of the602

Kyrgyz and Kazakh part of the Tien Shan, RGI outlines were mapped semi-automatically from603

ASTER and Landsat TM/ETM+ scenes referring to the period 1999-2003 [105, 106, 107, 108].604

Minor missing areas in western Kyrgyzstan were filled by the outlines compiled by [109] from the605

Digital Chart of the World [110], or the World Glacier Inventory [111]. The uncertainty deriving606

from the imprecise temporal attribution and the uneven quality of the inventory is included into607

the final uncertainty estimate (section C.6). The outlines for Abramov and Shumskiy Glacier608

(Fig. 1 of the main article), known to be inaccurate in RGI v3.2, are replaced with outlines609

digitized manually from 2007 satellite imagery. Basic characteristics of the glacierized surfaces610

(e.g. distributions of size, elevation, aspect, slope, etc.) are shown in Figures B.1 and C.2.611

A number of studies have addressed glacier area changes in the region of interest. These studies612

are summarized in Table C.2 and the information is used for prescribing glacier area changes613

within all of the considered model options (section C.5).614

C.2 M1 : Estimates based on measurements only615

Estimates of the group M1 are exclusively based on in-situ measurements. The general idea is616

to first generate a continuous time series covering the period 1961-2012 for all seven glaciers617

with observations ≥ 5 years, and then to extrapolate those measurements in space. Four dif-618

ferent methods are explored. The first two methods (M1.a and M1.b) are taken from [112];619

the remaining two methods (M1.c, M1.d) follow the same principle but additionally use the620

information that is available from the two glaciers monitored continuously. All estimates refer621

to annual balances. Accumulation measurements are not considered.622

Let bi(t) be the annual balance of glacier i for year t, and let ty (tn) denote years in which the623

mass balance was (not) measured. The different options can be described as follows:624

M1.a: Constant rate625

For each glacier with an incomplete time series, the annual mass balance in years without626

measurements is set to the average balance of the period in which measurements were available627

27


for this glacier [112]:628

bi(t) = bi(ty), (3)

where t ∈ tn and X is the arithmetic average of X.629

M1.b: Constant trend630

For each glacier with an incomplete time series, a linear trend is fitted to the available mass631

balance data and extrapolated to the unmeasured period [112]:632

bi(t) = a0,i + a1,i · t, (4)

where a0 and a1 are two coefficients to be estimated for glacier i, and t ∈ tn. The coefficients633

are estimated using least squares fit.634

M1.c: Constant ratio635

For each glacier with an incomplete time series, the ratio between its average mass balance636

and the average mass balance of the two continuously measured glaciers is computed. The637

annual mass balance during the unmeasured period is then computed by multiplying the average638

measured balance of the two measured glaciers with that ratio:639

bi(t) =1

2· (bj(t) + bk(t)) · bi(ty)

1/2 · (bj(ty) + bk(ty)), (5)

where j and k indicate the two glaciers for which a measured mass balance is available contin-640

uously between 1961 and 2012, and t ∈ tn.641

M1.d : Constant relation642

For each glacier with an incomplete time series, a relation to the mass balance of the two contin-643

uously measured glaciers is established through a multiple linear regression. The annual mass644

balance during the unmeasured period is then computed by using the continuously measured645

time series as input:646

bi(t) = c0,i + c1,i · bj(t) + c2,i · bk(t), (6)

where c0,i, c1,i, and c2,i, are the coefficients of the linear regression, j and k are the indices of647

the two glaciers with a continuously measured mass balance, and t ∈ tn. As for model M1.b,648

the coefficients are estimated using least squares fit.649

C.3 M2 : Estimates based on mass balance modelling650

Estimates of the group M2 are based on mass balance modelling. The glaciological in-situ mea-651

surements are used to calibrate two different models. The first one (M2.a) is based on a degree-652

day approach whilst the second (M2.b) relies on an energy-balance formulation. Both models are653

spatially distributed and are forced by meteorological reanalysis data. Additional local temper-654

ature and precipitation observations are used to constrain model parameters (see below). Three655

reanalysis products, ERA-40 [113], ERA-Interim [114] and NCEP/NCAR Reanalysis 1 [115], are656

considered in order to account for uncertainties in the meteorological input fields (Tab. C.3). The657

models are forced with the three time series individually, providing an ERA-40 driven run for658

the period 1961-2001, an ERA-Interim driven run for 1980-2012, and an NCEP/NCAR driven659

run for 1961-2012. In Table C.4, the three drivers are denoted with E4, EI, and NN, respec-660

tively. ERA-40 and ERA-Interim reanalysis data are retrieved from the portal of the European661

Centre for Medium-Range Weather Forecasts (http://apps.ecmwf.int/datasets/), whilst662

NCEP/NCAR data are provided by the Earth System Research Laboratory of the National663

Oceanic & Atmospheric Administration (NOAA, ftp.cdc.noaa.gov/Projects/Datasets/).664

Table C.3 gives an overview of the data used, whilst Figure C.1 illustrates the spatial distribu-665

tion and temporal evolution of the temperature and precipitation forcing fields for the addressed666

28


region. Monthly values for individual sub-regions are shown in Figure C.2. Additional local tem-667

perature and precipitation data with daily resolution and a time series length of more than 5668

years are obtained for a total of 72 and 183 stations, respectively, from the Global Historical669

Climatology Network [116] maintained at NOAA’s National Climatic Data Center, the national670

hydro-meteorological services of Kyrgyzstan, Uzbekistan, and Tajikistan, and the Central-Asian671

Institute of Applied Geosciences. The location of the stations is displayed in Figure C.1.672

For any grid cell i within a given glacier, the models of group M2 compute daily mass balance673

bi (kg m−2 d−1) by subtracting daily ablation ci from accumulation ai, i.e. bi = ai − ci. The674

difference between the models M2.a and M2.b is given by the computation of ci, whilst ai is675

computed for both models as676

ai = Pref · (1 + Cprec) · [1 + (zi − zref) · dP/dz] ·Dsnow,i · rs, (7)

[117, 118]. In the equation, Pref (kg m−2 d−1) is the daily precipitation obtained from the reanal-677

ysis data and the reference altitude zref (see below); Cprec is a dimensionless calibration factor678

used to accommodate the local, measured annual accumulation; zi (m a.s.l.) is the elevation679

of the considered grid cell; dP/dz (m−1) is a precipitation lapse rate describing the relative680

increases in precipitation with altitude [119]; Dsnow,i is a dimensionless, spatially distributed681

factor which accounts for snow redistribution processes [e.g. 120, 121]; and rs (dimensionless)682

is the fraction of solid precipitation. The daily precipitation amount Pref is calculated through683

inverse-distance weighting of the precipitation given in the four reanalysis grid cells closest to684

the glacier centrepoint. The corresponding geopotentials of the four considered grid cells are685

weighted in the same way and define the reference altitude zref . Dsnow,i is determined from char-686

acteristics of the surface topography [117], dP/dz is estimated from the station data through687

linear regression of the annual precipitation sums and the station elevation, and rs is defined688

to decrease linearly from 1 to 0 in the temperature range Tthr − 1 ◦C to Tthr + 1 ◦C, where689

Tthr = 1.5 ◦C is a threshold temperature that distinguishes snow from rainfall [122].690

M2.a: Degree-day approach691

In the degree-day approach, ci is computed as692

ci =(fM + rsnow/ice · Ipot,i

)· T i if T i > 0 ◦C (8)

[122], where fM (kg m−2 d−1 ◦C−1) is a melt factor, rsnow/ice (kg W−1 d−1 ◦C−1) are two distinct693

radiation factors for snow and ice, Ipot,i (W m−2) is the potential direct clear-sky solar radiation694

for grid cell i, and T i (◦C) is the mean daily air temperature for the same grid cell. For days695

with T i ≤ 0 ◦C, no ablation occurs. The spatial distribution of T i is obtained by first computing696

a representative temperature for the reference elevation zref as described for precipitation, and697

then extrapolating the temperature over the glacier domain by means of a vertical temperature698

lapse rate dT/dz (◦C m−1). The lapse rate has a yearly cycle (one value for each day of the699

year) and is obtained through linear regression of the temperature observations at the local meteo700

stations. The spatial distribution of Ipot,i is first computed at hourly time steps according to the701

methods presented in [122], and then averaged to daily values. Thus, the averaging is performed702

over the temporal domain, whilst the spatial distribution is maintained.703

Following [123] for example, the parameters fM, rsnow, and rice are calibrated for each glacier704

individually by imposing a constant ratio of 0.015:0.75:1.0 between them, and minimizing the705

discrepancy between measured and observed annual balances. The assumption is required for706

reducing the degrees of freedom of the model. The ratio rsnow:rice of 0.75:1.0 is meant to reflect707

the difference between the broadband albedo of snow and ice, whilst the ratio fM:rice of 0.015:1.0708

was found to be appropriate in previous analyses [e.g. 124, 125, 118].709

Calibration is performed in an automated, iterative procedure. The model is initialized with710

an initial guess for Cprec and rice, and run forward in time. In a first step, Cprec is adjusted in711

29


order to match the mean of the available annual accumulation measurements. In a second step,712

rice (and thus rsnow and fM) is adjusted in order to minimize the sum of the absolute deviations713

between modelled and measured annual mass balances. Since this re-introduces a mismatch714

in the accumulation measurements, Cprec is re-calibrated again, and so on. The procedure715

converges within 10 iteration steps in all cases.716

Through the chosen calibration procedure, the model parameters incorporate the effect of down-717

scaling the driving reanalysis data (which by design represent the larger-scale meteorological718

boundary conditions rather than the actual local meteorology) to the local conditions. Our719

model approach is, thus, an effective method for quantifying mass budgets, but does not allow720

us to study the full spectrum (e.g. mountain-induced mesoscale flow processes) of the large-721

to local-scale interactions. The latter would require a physically-based downscaling, which has722

only been established for individual glaciers so far [e.g. 126].723

In this respect some uncertainty remains in the calibrated values of Cprec since, in the region724

of interest, the highest rates of both accumulation and ablation occur during summer. In fact,725

although the available measurements are declared to be annual (i.e. total) accumulation values726

by the relevant data sources, some doubt remains on whether these measurements were not727

actually collected within a stratigraphic framework and thus rather represent net accumulation.728

In this latter case, total modelled accumulation would likely be underestimated. Note, however,729

than even in this case the presented results, which all refer to annual mass budgets only, would730

remain unaffected. This is because through the calibration to the annual mass balances, any731

underestimation of accumulation would be compensated by an overestimation of ablation, thus732

leaving the annual budgets unaltered.733

M2.b: Energy balance formulation734

In the energy balance model, the simplified formulation by [127] is adopted, according to which735

ci can be computed as:736 {ci = −ϕd,i/L if ϕd,i > 0

ϕd,i = τ(1− α) ·QE + C0 + C1 · T i, (9)

where ϕd,i (J m−2 d−1) is the daily mean surface energy flux at location i, L = 334 103 J kg−1737

is the latent heat of fusion of ice, τ (dimensionless) is the total atmospheric transmissivity, α738

(dimensionless) is the broadband surface albedo, QE (W m−2) is the extra-terrestrial irradiation,739

and C0 (W m−2) and C1 (W m−2 ◦C−1) are two empirical parameters to be calibrated. The740

term C0 +C1T i parametrizes the sum of the long-wave radiation balance and the turbulent heat741

exchange [127]. T i is obtained the same way as described for model M2.a, whilst the product742

τQE is approximated by scaling Ipot,i calculated for model M2.a with the ratio between actual743

and clear-sky surface solar radiation derived from the reanalysis data.744

Following [127], we (1) fix C1 at a value of 10 W m−2 ◦C−1, (2) use C0 as a calibration parameter745

for maximizing the agreement between calculated and observed annual mass balances, and (3)746

assign two different values to α depending on the presence of a snow cover. For snow and ice747

covered surfaces we use α = 0.7 and α = 0.4, respectively [e.g. 128]. Calibration is performed748

analogously to the degree-day approach.749

As for the estimates based on ICESat, debris-free and debris-covered surfaces are not treated750

separately (this is true for both model options M1.a and M2.b). This choice is motivated by751

the fact that (a) the majority of the glaciers in Tien Shan are clean-ice glaciers, i.e. not covered752

by debris (according to [129], the debris-covered area fraction for the central part of the Tien753

Shan is less than 5 %), (b) the comparison with geodetic mass balances derived for the selected754

sub-regions that include some large glaciers with a significant debris coverage [130, 129], does755

not indicates the models yielding too negative mass balances for these areas (see Section C.7 and756

Fig. 5a-d of the main article), as would be expected by postulating an insulating effect of the757

debris cover, and (c) a sensitivity experiment conducted with model M2.a.e1.NN for the region758

30


analysed in [129] (i.e. the region of the Tien Shan including the largest debris-covered glaciers),759

shows that even the postulation of an overall melt-rate reduction by 75 % under debris covered760

areas (a very substantial reduction), would change the mass budget for the entire Tien Shan761

by 0.3 Gt a−1 only (not shown). The fact that debris-covered glaciers can lose mass similar to762

debris-free glaciers has, moreover, recently been highlighted by a series of studies focussing on763

the Himalayas [e.g. 131, 95, 84, 132].764

The mass balance time series resulting for the individual glaciers for which direct measurements765

are available are shown in Figure C.3.766

C.4 Regional extrapolation767

The approaches described above (M1.a-d and M2.a-b) only provide an estimate of the mass768

balance time series for the seven glaciers that have available long-term measurements. In order769

to extrapolate these results over the entire study region, three options (e1, e2, and e3) are770

explored: Option e1 simply assigns the average value to all remaining glaciers in the region;771

option e2 assigns a glacier specific value following the nearest neighbour principle; and option772

e3 uses an inverse distance interpolation. For the estimates of group M1, the extrapolated773

quantity is the annual glacier mass balance, whilst for group M2 we spatially extrapolate the774

model parameters and use the corresponding model for explicitly calculating a glacier-specific775

mass balance for every glacier in the region. More sophisticated extrapolation approaches,776

that could include an elevation dependency for example, were not considered in light of the777

small sample of glaciers that would be available for establishing such a relation. The choice is778

additionally motivated by the findings of [133] who concluded that “simple arithmetic averaging779

that completely neglects glacier characteristics is a robust alternative particularly if only few780

(< 10) mass balance series [...] are available”. The combination of the different models with781

the different extrapolation schemes and, for models of group M2, the different meteorological782

drivers, provides an ensemble with a total of 30 model options (Tab. C.4).783

For the methods of group M1, only the surface area is required, whilst for M2, a DEM of the784

surface of each individual glacier is derived by intersecting the according RGI outline with the785

ASTER GDEM version 2. In this case, the ASTER GDEM is preferred upon the SRTM DEM786

because of the higher spatial resolution, and because for the modelling, exact knowledge of the787

acquisition date is less important than for the ICESat derived estimates (cf. section B.1). In788

order to save computational time, the glacier specific DEMs extracted from the ASTER GDEM789

are resampled according to the glacier size. The resampling is chosen such that the computational790

domain remains below 4 × 104 grid cells for every glacier. This results in a resolution between791

30 and 190 m. The potential direct clear-sky solar radiation is calculated from the so obtained792

DEMs, as described in section C.3. Together with the aforementioned meteorological fields, this793

provides all necessary inputs for both models (M2.a and M2.b) in group M2.794

The modelling procedure as described so far yields so called “reference-surface balances” [134],795

i.e. mass balances that refer to a constant glacier hypsometry. The concept was introduced796

by [135] and has been suggested as to be “more useful for climate interpretation” [136, 137].797

When adopted in modelling studies, the concept has the convenient advantage that it does798

not require any update of the considered glacier surfaces. For hydrological applications and799

questions related to water resources management, however, the relevant quantity is given by the800

so called “conventional balance” (i.e. the mass balance that refers to the actual glacier geometry801

at any point in time), since it directly reflects the amount of water that is stored or released802

by the considered glaciers. In general, the link between conventional and reference-surface803

balances is not straightforward, since the effects of the evolving glacier surface can be complex.804

An analysis carried out by [138] over a sample of 36 Alpine glaciers and a period of about805

80 years, however, suggests that the difference between the two quantities can be reasonably806

approximated by a linear function. Here, the hypothesis of a linear relation is tested for the Ak-807

31


Shiirak mountain range (region “A” in Fig. 1 of the main article), for which the data provided808

by [139] allow an assessment. To this end, all 12 models of group M2 that have a meteorological809

driver covering the period 1977-2000 (see Tab. C.4) are re-initialized three times: The first and810

second time, reference-surface balances are computed by using the surface DEMs of the year811

1977 and 2000 provided by [139], respectively; whilst the third time, the glacier surface of all812

the glaciers located in the mountain range is updated on a yearly basis. In this third case, the813

updating is performed by linearly interpolating the elevations of individual grid cells between814

the two years 1977 and 2000 [e.g. 140, 117]. The mass change rates resulting from the three815

model runs are shown in Figure C.4a and C.4b for the example of model option M2.a.e2.E4. The816

difference between the results obtained by computing conventional and reference-surface balances817

for the individual model options (Fig. C.4c), confirms that the magnitude of the difference818

grows approximately linearly with time to/from the reference year. This observation is used for819

converting the reference-surface balances computed for the entire study region into conventional820

mass balances: A linear function is fitted through ordinary least squares to the differences found821

in the case of the Ak-Shiirak region (solid line in Fig. C.4c), and the function is assumed to822

be applicable to all remaining areas of interest as well. Although the procedure has a clear823

advantage in terms of computational cost, the choice is mainly motivated by data availability.824

The considered glacier inventory and DEM (i.e. the RGI and the ASTER GDEM, respectively)825

are in fact the only data with a (nearly) time-consistent, region-wide coverage. Since both826

data sets refer to the end of the reconstructed period, a transient updating of the individual827

glacier surfaces would require a backward-in-time integration, which is not straightforward. The828

uncertainty introduced in the regional mass budget by converting the reference surface mass829

balances into conventional ones with the described procedure, is accounted for in the overall830

error budget (section C.6).831

C.5 Estimation of regional mass budgets832

For obtaining time series of mass budgets, the specific mass change rates calculated above need833

to be multiplied by the according glacier area at every time step. Since none of the models is834

able of updating the glacier area explicitly, glacier area changes are prescribed directly. This835

is done by compiling sub-regional area changes from the literature (Tab. C.2), and assuming a836

constant change rate during the period 1961-2012.837

It follows from simple geometrical considerations that for the same climatic forcing, small glaciers838

generally exhibit higher relative area changes than larger ones. Despite large variability, the839

results of various studies carried out in the region [e.g. 141, 142, 108] suggest that this size840

dependency can be roughly approximated through an empirical relation of the form841

r = a (1/A)b, (10)

where r is the relative area change of a glacier with area A, and a and b are two coefficients to be842

estimated. Here, the relation is used for distributing the total area change inferred for a given843

sub-region over the individual glaciers contained in the RGI. This is done by fixing parameter844

b in equation 10 to a constant value of 0.1 (the value is estimated from the results by [141],845

cf. their Figure 9) and adjusting parameter a until the total area change in the sub-region is846

matched. For the sample of glaciers that is not contained in any of the sub-regions for which an847

area change is available, the average rate of all other sub-regions is imposed.848

The resulting spatial distribution of the area changes for the period 1961-2012 is given in Fig-849

ure C.5. Numerical values for the area changes and additional information on the individual850

data sources are given in Table C.2. Resulting time series of actual mass change rates for the851

entire study region and the individual model options are shown in Figure 6 of the main article.852

For the period in which results derived from GRACE and ICESat data are available simulta-853

neously, the average mass change rate for the individual model options is reported in the last854

32


column of Table C.4, and visualized in Figure 3c of the main article. The spatial distribution of855

the average mass change rate for the periods 1961-2012 and 2003-2009 are shown in Figures 1856

and 5e of the main article.857

C.6 Uncertainty estimates858

All confidence intervals stated for the estimates based on glaciological modelling are constructed859

according to the theory of Gaussian error propagation [e.g. 143]. All uncertainties are considered860

to be potentially correlated. In general, the variance var(f) of a function f with n variables861

x = (x1, x2, ..., xn)T, is given by862

var(f) = gTV g (11)

where g is the vector of size n whose ith element is ∂f∂xi

, and V is the variance-covariance matrix863

of x, with elements Vij = cov(xi, xj). In the notation, xi is the ith element of a vector x, xT864

denotes the transpose of x, ∂f∂xi

is the partial derivative of f with respect to xi, and cov(xi, xj)865

is the covariance between xi and xj . Note that cov(xi, xi) corresponds to the variance of xi,866

denoted with σ2xi

.867

When computing the total mass change ∆M of a region with n glaciers during a period of m868

years, the function f becomes:869

f = ∆M =

m∑t=1

n∑i=1

bi(t) ·Ai(t) (12)

where bi(t) is the estimated annual balance of glacier i for year t, and Ai(t) the corresponding870

glacier area. For this case, it can be shown that the evaluation of Equation 11 requires knowledge871

of (1) σ2bi(t)

, which is the variance of the estimated mass balance for glacier i and time t, (2)872

cov(bi(t), bj(t)), which is the covariance of the estimated mass balance of glaciers i and j at873

time t, (3) ρbAi(t), which is the correlation between estimated mass balance and glacier area874

for glacier i and time t, and (4) σ2Ai(t)

, which is the variance of the glacier area for glacier i875

and time t. For the analyses, σ2bi(t)

, cov(bi(t), bj(t)), and ρbAi(t) are estimated in a leave-one-876

out cross-validation scheme [144], and by using the seven measured mass balance time series877

available. For all 30 considered model options (Tab. C.4), the model set-up and calibration878

is performed seven times. At each time, six glaciers are used for calibration, whilst for the879

seventh, non-considered glacier, a mass balance time series is calculated and compared to the880

actual measurements. The so obtained differences are then used to estimate both an option-881

specific variance-covariance matrix, providing σ2bi(t)

and cov(bi(t), bj(t)) for the seven glaciers882

with measurements, and the correlation between estimated mass balance and glacier area. For883

the generalization to the whole region and supported by the analysis of the model residuals, we884

assume that time and glacier dependencies can be ignored, i.e. σ2bi(t)

= σ2b , with σ2

b being the885

average of σ2bi(t)

for the seven glaciers with measurements, and analogously for cov(bi, bj) and886

ρbAi. This is equivalent to the assumption that on average, the model performs equally well for887

any given glacier as it performs for a glacier with available measurements, when the latter is888

NOT used for calibration. For σ2Ai(t)

, which corresponds to the accuracy with which the area889

of glacier i is known at time t, it is conservatively assumed that the glacier area is known with890

a relative accuracy of ±50% at the 95 % confidence level at any given time. In the adopted891

notation, this means σ2Ai(t)

/A2i (t) = (0.5/2)2. The conservative estimate is chosen in order to892

accommodate the uncertainties deriving from both the RGI glacier outlines and the approach893

used for updating the glacier area (Section C.5).894

For the models of group M2, additional uncertainty is introduced by the procedure used for895

converting reference-surface balances to conventional ones. The uncertainty is included in the896

formulation used above by augmenting the standard error associated to the estimated mass bal-897

ance by σref.surf(t). The time dependency can not be neglected in this case, since the uncertainty898

33


of the correction increases with increasing time distance from the reference year (cf. the size of899

the bars in Fig. C.4c). The results of the analysis carried out for the Ak-Shiirak mountain range900

indicate that the spread between the correction computed for different model options can be in901

the same order of magnitude of the correction signal itself. For any time t, σref.surf(t) is thus902

set to the magnitude of the applied correction.903

When presenting glacier changes as a fractional change in total glacier mass (the estimates for904

total mass is retrieved from [145]), the uncertainty in the latter needs to be accounted for. This905

is done by assuming (1) independence between estimated mass budgets and estimated total906

glacier mass, (2) stationarity in the uncertainty of the modelled mass budgets, and (3) a 10 %907

relative uncertainty (one-sigma level) in the estimated total glacier mass (cf. entry “Central908

Asia” in Table 2 of ref. [145]).909

C.7 Model validation910

The results of the different models of both groups M1 and M2 are validated against geodetic911

volume changes available from the literature. To date, only three regional assessments are912

available: [139] computed geodetic volume changes for the Ak-Shiirak mountain range (“Ak-913

Shiirak” in Fig. 1 of the main article; ∼370 km2 of glacierized area as of 2009) during the914

periods 1943-1977 and 1977-2000, [130] conducted a similar analysis for a selected sub-region915

south of Tomur Feng (Kyrgyz name: Jengish Chokusu; Russian name: Pik Pobedy) in the916

Aksu-Tarim catchment (“Tomur region” in Fig. 1 of the main article; ∼370 km2 of glaciers in917

2003) and the time periods 1976-1999 and 1999-2009, and this latter work was recently extended918

to the Aksu basin (“Aksu basin” in Fig. 1 of the main article; ∼5000 km2 of glaciers in 1999)919

and the period 1977-1999 by [129]. The comparison is not possible for every model option,920

since the meteorological forcing fields do not necessarily cover the entire time period (the period921

1943-1977, for example, is not covered entirely by any of the forcing fields). The results of922

the comparison are shown in Figure 5a-d of the main article. In general, the bulk of the model923

options is capable of reproducing the observed mass change rates. This is particularly true when924

considering the Aksu basin (Fig. 5a of the main article), which is the largest region for which925

a geodetic estimate of glacier mass changes is available. For the other regions, the picture is926

slightly more heterogeneous: For the sub-region south of Tomur Feng (“Tomur region” from now927

on) and the period 1999-2009, models of the group M2 reasonably agree with the results from the928

geodetic surveys, but one model M2.a.e2.EI (i.e. the degree-day model forced with ERA-Interim929

data and parameters assigned through a nearest-neighbour procedure) overestimates the mass930

loss rate. A similar overestimation is found for several models of the group M1, in particular931

for options relying on the temporal extrapolation of the observed trend (models of the category932

M1.b) or options based on a a nearest-neighbour procedure (models with ending .e3). This can933

be explained by the fact that for the period 1999-2009, the closest glacier with a measured time934

series (Tuyuksu Glacier, see Fig. 1 of the main article for location) lies about 300 km away from935

the Tomur region, and is thus not particularly representative. For the same region and the936

period 1976-1999, all models of the group M1 perform well. Models of the group M2, however,937

generally underestimate the mass change loss. The underestimation is very prominent in model938

runs driven by ERA-40 data, and can be attributed to a significant precipitation anomaly in939

the dataset for the particular region and the considered period. This points at the fact that940

the results of individual model options must be interpreted with caution, especially at the sub-941

regional scale. The mass change rates of the Ak-Shiirak mountain range is well reproduced by942

models of the group M1. Although consistent within the assessed confidence intervals, models943

of the group M2 indicate a less negative mass change rate than M1. This difference reflects944

the fact that Sary-Tor Glacier (the closest glacier with in-situ measurements, see Fig. 1 of the945

main article) is located within the considered mountain range, but has an altitude that is below946

average compared to the region. This results in a generally more negative mass balance for the947

34


particular glacier, and has a large effect in the models of group M1 which rely on the measured948

time series only. On the other hand, models of group M2 are capable of accounting for this949

elevation difference and thus result in a less negative mass change rate. The fact that even950

models of group M1 yield a mass change rate that is less negative than reported by [139] seems951

to suggest that the assessed value might have been too negative.952

The obtained spatial distribution of the modelled mass budgets is additionally compared to sub-953

regional estimates derived from ICESat. To this end, the analyses described in Section B are954

repeated individually for each sub-region defined in Figure 5e of the main article. The number of955

ICESat footprints available within the individual sub-regions is limited, which is reflected in the956

comparatively large confidence intervals of the derived estimates (Table C.5). For sub-regions in957

which a sufficient number of footprints (about 2000) are available, the agreement is satisfactory958

(Fig. 5f of the main article). This supports the capability of the model ensemble in capturing the959

large-scale spatial variability of the mass change signal. An exception seems to be the Borohoro960

range (region “R3”) for which the ICESat estimates indicate a more negative mass change than961

the glaciological models do. A partial explanation could be the relative under-sampling of very962

high elevations in the ICESat footprints for the particular region (not shown).963

C.8 Multiple linear regression analysis964

In general, a multiple linear regression (MLR) model aims at reproducing the n values observed965

for a target variable y through a linear combination of a series of m explanatory variables X,966

i.e.967

y = Xβ + ε. (13)

In the notation, y = (y1, y2, ..., yn)T is the vector of n values observed for the target variable;968

X is a (n × (m + 1)) matrix with elements Xi1 = 1 for i ∈ [1, n] and elements Xi(j+1) = x(j)i969

for i ∈ [1, n], j ∈ [1,m], with x(j)i being the ith observed value for the jth explanatory variable;970

β = (β0, β1, β2, ..., βm)T is a set of m+ 1 coefficients to be estimated; and ε = (ε1, ε2, ..., εn)T is971

a vector of residuals for which a normal distribution with zero mean and standard deviation σ972

is assumed. The estimation of β is performed through ordinary least squares fit, i.e. through973

the minimization of∑

y −Xβ, where β is the vector of estimated coefficients. The fraction of974

variance in the target variable that is explained by the combination of a given set of explanatory975

variables, can be expressed through the adjusted coefficient of determination R2 [e.g. 146].976

For detecting which topographical parameters have the largest influence on the results provided977

by the models of group M2, a first MLR model that includes all possible explanatory variables978

is set up. This first set of explanatory variables includes longitude, latitude, elevation, elevation979

range, glacier area, slope, and orientation, calculated as the mean value for every individual980

glacier. The target variable is defined as the average glacier-specific mass change rate over the981

period 1961-2012. A common backwards selection procedure [e.g. 147], i.e. a one-at-the-time982

removal of non-significant variables, is not suitable for model reduction since the large sample983

of glaciers (about 13700) yields significant coefficients for all variables (all p-values < 10−16).984

An “all possible subsets regression procedure” [e.g. 148] is therefore preferred. To this end, all985

26 = 64 possible MLR models that can be obtained from the combinations of the 6 explanatory986

variables are set up, and evaluated in terms of R2. Plotting this set of R2 coefficients in a Pareto987

chart [e.g. 149] reveals a clear break-point when elevation, orientation, and latitude are included988

in the MLR model (Fig. C.6a). Together, the three variables explain about 75% of the total989

variance of the target variable. Elevation alone explains 41% of the variance.990

The analogous procedure is repeated for detecting the variables having the strongest influence in991

the temporal variability. To this end, standardized yearly anomalies in temperature, precipita-992

tion, downscaled net solar radiation, and positive degree days are computed for each individual993

glacier, and averaged over the entire mountain range. The standardized annual glacier mass994

35


change anomaly is chosen as target variable. In this case, the break point in the Pareto chart995

is found for MLR models that include precipitation and positive degree days (Fig. C.6b). Com-996

bined, the two variables explain 93% of the total variance. The sum of positive degree days997

alone explains 83% of the variance.998

36


ER

A-4

0

-20 0 20

Temperature ( oC)

ER

A-I

nte

rim

NC

AR

/NC

EP

72o E 74o E 76o E 78o E 80o E 82o E 84o E 86o E

40o N

42o N

44o N

0 1000 2000

Precipitation ( mm a-1 )

40o N

42o N

44o N


40o N

42o N

44o N

1960 1970 1980 1990 2000 2010

-2

-1

0

1

2

An

om

aly

w.r

.t. r

efer

ence

reference

1960 1970 1980 1990 2000 2010

-200

-100

0

100

200

300

referenceERA-40

ERA-Interim

NCAR/NCEP

Figure C.1: Overview of the used meteorological forcing fields. The left column refers to air temperature,the right column to precipitation. Starting from the top, the first three panels of each column show thespatial distribution of the mean value during the reference period 1979-2001 at the resolution of theparticular reanalysis product (either ERA-40, ERA-Interim, or NCEP/NCAR). The reference period ischosen as the period in which all three reanalysis data sets have values. The lowermost panel in eachcolumn is a time series of yearly anomalies with respect to the reference period. In this case, values referto the average of the displayed domain. The yellow (red) dots in the uppermost three panels indicate thelocation of the available temperature (precipitation) stations.

37


50

100

150

200

Pre

cipi

tatio

n (m

m)

0

455 mm

-10

0

10

20 Temperature (

oC)

-0.6 oC

J F M A M J J A S O N D

R1

0

400

800

Are

a (k

m2 ) 5194 km2

4428 m

N

50%

25

Aspect

50

100

150

200

Pre

cipi

tatio

n (m

m)

0

403 mm

-10

0

10

20 Temperature (

oC)

-0.7 oC

J F M A M J J A S O N D

R2

0

400

800

Are

a (k

m2 ) 2007 km2

3920 m

N

50%

25

50

100

150

200

Pre

cipi

tatio

n (m

m)

0

373 mm

-10

0

10

20 Temperature (

oC)

1.5 oC R3

0

400

800

Are

a (k

m2 ) 2734 km2

3938 m

N

50%

25

50

100

150

200

Pre

cipi

tatio

n (m

m)

0

547 mm

-10

0

10

20 Temperature (

oC)

-0.3 oC R3a

0

400

800

Are

a (k

m2 ) 1474 km2

4084 m

N

50%

25

50

100

150

200

Pre

cipi

tatio

n (m

m)

0

491 mm

-10

0

10

20 Temperature (

oC)

4.1 oC R4

0

400

800

Are

a (k

m2 ) 649 km2

3600 m

N

50%

25

50

100

150

200

Pre

cipi

tatio

n (m

m)

0

483 mm

-10

0

10

20 Temperature (

oC)

2.9 oC R5

0

400

800

Are

a (k

m2 ) 640 km2

3966 m

N

50%

2550

100

150

200

Pre

cipi

tatio

n (m

m)

0

516 mm

-10

0

10

20 Temperature (

oC)

-1.3 oC R6

3000 4000 5000 6000Elevation (m a.s.l.)

0

400

800

Are

a (k

m2 ) 1768 km2

4185 m

N

50%

25

50

100

150

200

Pre

cipi

tatio

n (m

m)

0

620 mm (B)

-10

0

10

20 Temperature (

oC)

1.9 oC (A) All other

3000 4000 5000 6000Elevation (m a.s.l.)

0

400

800

Are

a (k

m2 ) 718 km2

3883 m (C)(D)

N

50%

25

Aspect

Aspect

Aspect

Aspect

Aspect

Aspect

Aspect

Figure C.2: Seasonal distribution of the meteorological forcing fields and topographic characteristics forindividual sub-regions. For each sub-region “R1” to “R6” (see Fig. 5e of the main article for location)three panels are displayed. The top panel shows monthly means for air temperature (solid red line) andprecipitation (blue bars). Mean values are obtained by averaging over the three reanalysis products (ERA-40, ERA-Interim, NCEP/NCAR) and the reference period 1979-2001. Vertical confidence intervals showthe range spanned by the individual reanalysis products. The bottom left panel shows the hypsometry(i.e. the distribution of area with elevation) of the glacierized surfaces. The hypsometry is obtained byconsidering mean glacier elevations and 100 m elevation bins. The radar chart in the bottom right panelshows the aspect of the glacierized surfaces. The aspect is expressed as the share of the total glacierizedarea, and is displayed for the eight sectors N, NE, E, SE, S, SW, W, and NW. The last set of panels(labelled with “All others”) refers to glacierized surfaces that are not included in any of the sub-regionsshown previously. The set includes the key for the numbers displayed in the panel corners: (A) = Averageannual temperature at mean glacier elevation; (B) = Mean annual precipitation; (C) = Total glacierizedarea; (D) = Mean glacier elevation.

38


1960 1970 1980 1990 2000 2010

-3

-2

-1

0

1

MB

(m w

.e. a

-1 )

Urumqi Gl. No.1 (URU)

-3

-2

-1

0

1

MB

(m w

.e. a

-1 )

Shumskiy (SHM)

-3

-2

-1

0

1

MB

(m w

.e. a

-1 )

Ts. Tuyuksu (TYK)

-3

-2

-1

0

1

MB

(m w

.e. a

-1 )

Golubin (GLB)

-3

-2

-1

0

1

MB

(m w

.e. a

-1 )

Sary-Tor (SRT)

-3

-2

-1

0

1

MB

(m w

.e. a

-1 )

Kara-Batkak (KRB)

-3

-2

-1

0

1

MB

(m w

.e. a

-1 )

Abramov (ABR)

MeasuredModelled

Figure C.3: Mass balance time series for glaciers with available measurements. For each glacier, theobserved (black) and modelled (red) mass balance (MB) is shown. The modelled mass balance is given asthe mean of all model options listed in Table C.4. The grey band is the envelope of all model realizationsof group M2. The location of the individual glaciers is shown in Figure 1 of the main article. The key forthe three-letter code on the top right corner is given in Table C.1. For SRT, the solid grey line indicatesthe reconstruction by [150].

39


1980 1985 1990 1995 2000year

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

Gla

cier

mas

s ch

ange

rat

e(1

03 kg

m-2 a

-1 )

ConventionalRef. surface 1977Ref. surface 2000

Ak-Shiirak

Option M2.a.e2.E4

a

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

Ave

rage

mas

s ch

ange

rat

e(1

03 kg

m-2 a

-1 )

conv

.r.1

977

r.200

0

b

-30 -20 -10 0 10 20 30Time from reference year (a)

-0.1

0.0

0.1

Diff

eren

ce (

103 k

g m

-2 a

-1 )

conv

entio

nal v

s re

f. surf

ace

All available options c

Figure C.4: Difference between mass change rates computed by considering conventional and reference-surface mass balances. (a) Time series of the specific mass change rate dm/dt computed for the glaciersin the Ak-Shiirak mountain range (see Fig. 1 of the main article) during the period 1977-2000. The black(blue and red) line shows the dm/dt resulting from the computation of conventional (reference-surface)mass balances. (b) Mass change rates averaged over the considered region and the considered periodaccording to the three methods. Confidence intervals refer to the 95% level. (c) Difference between masschange rates computed according to the conventional and the reference-surface method as function of thetime from the reference year. Blue (red) bars refer to the case in which the reference-surface correspondsto the year 1977 (2000), and span over the range given by the 12 considered model options (the minimalspan is fixed to 2.5 103 kg m−2 a−1 for visibility). The solid black line is a linear function fitted to all datapoints through ordinary least squares. Panels (a) and (b) refer to the model option M2.a.e2.E4, whilstpanel (c) comprehends all 12 options for which meteorological drivers are available for the consideredtime period (see Tab. C.4 for details).

40


200 kmSurface elevation (m a.s.l.)

0 3000 6000


40o N

42o N

44o N

A01

A02b

A02a

A02c

A07a

A03

A02e

A02dA04

A05

A06A07

A08

A09

A10

A11

A12aA12bA17 A16

A14

A12dA12c

A15

A13

Glacier area change 1961-2012 (%)

0 -10 -20 -30 -40 -50

Figure C.5: Spatially distributed glacier area changes for the period 1961-2012, relative to the glacierarea in 1961. Each coloured dot represents one glacier within the RGI v3.2. Data sources and detailedinformation for individual sub-regions are given in Table C.2. For additional details on the symbology,refer to Figure 1 of the main article.

0.0

0.2

0.4

0.6

0.8

1.0

Por

tion

of e

xpla

ined

var

ianc

e

elevationaspectlatitude

areaslope

longitude

000000

001000

000001

000010

001010

000100

000011

001100

001011

001101

001001

000101

000110

001110

010000

011000

000111

001111

010001

011001

010010

011010

011011

010011

010100

011100

010101

011101

010110

011110

011111

010111

100010

100000

100001

100011

100100

100110

100101

100111

110000

110010

101000

101010

110100

110110

110001

101100

101110

110011

110101

110111

101001

101011

101101

101111

111000

111100

111010

111001

111110

111011

111101

111111

rad.110010100110101

a b

Included variables

elevationaspect or latitude

aspect and latitude

temp.000111110010011prec.011001100001111PDD000000011111111

Figure C.6: Pareto charts for the detection of variables strongly influencing the results. The portionof explained variance is shown for all possible regression models that relate (a) topographic variablesto the long-term (1961-2012) specific mass change rate of each glacier, and (b) meteorological variablesto the standardized annual mass budget anomaly of the region. The lower part of the figure indicateswhether a particular variable is included (1) or not included (0) in a particular regression model. In (b),the variables are standardized yearly anomalies of positive degree days (PDD), precipitation sum (prec.),average temperature (temp.), and net solar radiation (rad.).

41


MonthJ F M A M J J A S O N D

Pre

ssur

e (h

Pa) 200

300

500-0.2

-0.1

0

0.1

0.2

0.3

0.4

Cor

rela

tion

coef

ficie

nt

Figure C.7: Linkage between glacier mass budgets and atmospheric circulation. The plot displaysthe correlation between the annual regional glacier mass-budget (ensemble mean of all model optionsin Table C.4) and the monthly meridional wind speed over the Tien Shan (averaged over the domain72◦-86◦ E, 40◦-45◦ N, data from NCEP/NCAR Reanalysis 1) at different atmospheric pressure levels.The analysis refers to the period 1961-2012. Both variables are linearly detrended. Black dots indicatesignificance at the 95 % confidence level.

42


Table C.1: Overview of glaciological mass balance measurements used in this study, and period of dataavailability. For glaciers, TLC is a three letter code used for abbreviation. Location coordinates, given indecimal degrees, are approximate and refer to the centrepoint of the according glacier or region. “Meth.”indicates the method of data collection: stake readings (st. r.) or geodetic mass balance (geod.). “Ref.”is a reference for the data source. Individual glaciers are sorted according to glacier area.

TLC Glacier/Region Name Location Meth. Period Ref.

ABR Abramov 39.623 N 71.557 E st. r. 1968-1998 [151]KRB Kara-Batkak 42.100 N 78.300 E st. r. 1957-1998 [151]GLB Golubin 42.452 N 74.497 E st. r. 1969-1994 [151]SRT Sary-Tor 41.825 N 78.177 E st. r. 1985-19891 [151]TYK Ts. Tuyuksu 43.045 N 77.079 E st. r. 1957-2010 [151]SHM Shumskiy 45.083 N 80.233 E st. r. 1967-1991 [152]URU Urumqi Gl. No.1 43.116 N 86.809 E st. r. 1959-2010 [151]

– Ak-Shiirak 41.850 N 78.330 E geod. 1943-20002 [139]– Tomur region 41.900 N 80.100 E geod. 1976-20093 [130]– Aksu basin4 41.900 N 80.100 E geod. 1977-1999 [129]

1 A reconstructed glacier mass balance for the period 1930-1988 is available from [150]

and was included in the model calibration.2 [139] report two separate values for the periods 1943-1977 and 1977-2000, respectively.3 [130] report two separate values for the periods 1976-1999 and 1999-2009, respectively.4 The region is named Central Tien Shan in the original publication [129]

43


Tab

leC

.2:

Ove

rvie

wof

the

dat

au

sed

for

qu

anti

fyin

ggl

acie

rar

each

ange

s.T

he

ind

ivid

ual

sub

-reg

ion

sar

ed

efin

edin

Fig

ure

C.5

.nRGI,A

RGI

=to

tal

gla

cier

nu

mb

eran

dar

ea,

resp

ecti

vely

,acc

ord

ing

toth

eR

GI

v3.

2;ndA

=nu

mb

erof

anal

yse

dgl

acie

rs;A

yr1

,A

yr2

,A

yr3

=gl

acie

rize

dar

eafo

rth

eyea

rsst

ate

din

the

colu

mn

syr 1

,yr 2

,yr 3

,re

spec

tive

ly;dA/dt

=an

nu

alp

erce

ntu

algl

acie

rar

each

ange

refe

ren

ced

toth

eye

aryr 1

;dA

ref

=p

erce

ntu

algl

acie

rar

each

an

ge

du

rin

gth

ep

erio

d19

61-2

012,

calc

ula

ted

asd

escr

ibed

inse

ctio

nC

.5.

Ifn

otst

ated

oth

erw

ise

abov

e,th

enu

mb

ers

are

retr

ieve

dfr

omth

eso

urc

egi

ven

inth

eco

lum

nR

ef..n.a.

ind

icat

esth

at

the

info

rmat

ion

isn

otav

ailab

le.

Con

fid

ence

inte

rval

sst

ated

for

the

resu

lts

ofth

isst

ud

yre

fer

toth

e95

%co

nfi

den

cele

vel.

Note

that

the

spel

lin

gu

sed

for

the

nam

esof

the

ind

ivid

ual

regi

ons

foll

ows

the

dat

aso

urc

egi

ven

inth

eco

lum

nR

ef.

(t.s

.st

and

sfo

r“t

his

stu

dy”)

,an

dm

ight

diff

erfr

omw

hat

state

din

Fig

ure

5eof

the

main

arti

cle

an

dT

able

C.5

.

Sub-r

egio

nnRGI

ARGI

ndA

yr 1

yr 2

yr 3

Ayr1

Ayr2

Ayr3

dA/dt

dA

ref

Ref

.-

km

2-

--

-km

2km

2km

2%

a−1

%

A01

Pask

emare

a28

34.0

525

1968

2000

2007

219.8

177.0

168.7

n.a

.-2

9.4

[141]

A02a

Low

erN

ary

nare

a199

88.4

n.a

.1977

1999

2007

83.0

77.0

75.0

n.a

.-1

5.7

[107]

A02b

At-

Bash

iK

irka

siare

a345

214.0

n.a

.1977

1999

2007

151.0

130.0

128.0

n.a

.-2

5.2

[107]

A02c

Bork

old

oyT

oo

are

a433

185.9

n.a

.1977

1999

2007

234.0

218.0

190.0

n.a

.-2

5.9

[107]

A02d

Big

Nary

nbasi

n626

468.7

462

1956

2007

n.a

.403.6

289.4

n.a

.n.a

.-2

9.1

[153]

A02e

Dzh

etim

are

a629

384.7

n.a

.1977

1999

2007

532.0

410.0

351.0

n.a

.-4

8.1

[107]

A03

SE

-Fer

gana

are

a119

94.6

306

1968

2001

2007

190.1

172.6

171.7

n.a

.-1

3.0

[141]

A04

At-

Bash

yare

a199

122.6

192

1968

2000

2007

113.6

99.9

95.7

n.a

.-1

9.6

[141]

A05

Aksu

Riv

erbasi

n907

1611.4

247

1963

1999

n.a

.1760.7

1702.1

n.a

.-0

.16

-8.2

[154]

A06

Ogan

Riv

erbasi

n847

1771.5

n.a

.1970

2002

n.a

.n.a

.n.a

.n.a

.-0

.31

-15.8

[142]

A07

Kaid

uR

iver

basi

n853

576.6

462

1963

2000

n.a

.331.1

292.6

n.a

.-0

.31

-15.9

[154]

A07a

Alb

inm

ounta

ins

71

66.4

70

1963

2000

n.a

.55.0

48.0

n.a

.n.a

.-1

7.4

[155]

A08

Aydin

gkol

Lake

basi

n79

40.1

203

1962

2006

n.a

.144.1

112.9

n.a

.-0

.56

-25.0

[156]

A09

Manas

Riv

erbasi

n1689

1427.0

n.a

.1962

1993

n.a

.n.a

.n.a

.n.a

.-0

.54

-27.5

[142]

A10

Ebin

ur

Lake

basi

n967

865.4

446

1964

2004

n.a

.366.3

312.5

n.a

.-0

.38

-18.5

[157]

A11

Ili

Riv

erbasi

n2002

1968.8

n.a

.1960

2009

n.a

.n.a

.n.a

.n.a

.-0

.46

-23.5

[142]

A12a

Sary

-Jaz

East

ern

regio

n390

809.5

318

1990

2010

n.a

.926.8

912.8

n.a

.n.a

.-3

.8[1

08]

A12b

Sary

-Jaz

Nort

her

nre

gio

n468

522.3

384

1990

2010

n.a

.487.4

455.8

n.a

.n.a

.-1

5.1

[108]

A12c

Sary

-Jaz

Wes

tern

regio

n478

443.4

498

1990

2010

n.a

.510.7

485.2

n.a

.n.a

.-1

1.9

[108]

A12d

Sary

-Jaz

South

ern

regio

n234

242.7

146

1990

2010

n.a

.130.1

124.1

n.a

.n.a

.-1

1.0

[108]

A13

Ak-S

hiira

kare

a222

302.2

178

1943

1977

2003

424.7

406.8

371.6

n.a

.-1

0.7

[139]

A14

Tes

key

are

a357

298.3

269

1971

2002

n.a

.245.0

226.0

n.a

.n.a

.-1

2.4

[158]

A15

Ili-

Kungoy

are

a831

616.9

735

1972

2000

2007

672.2

590.3

564.2

n.a

.-2

2.0

[141]

A16

Ala

-Arc

ha

are

a68

41.1

48

1963

1981

2003

42.8

40.6

36.3

n.a

.-1

9.3

[139]

A17

Sokolu

kR

iver

basi

n26

61.6

77

1963

1986

2000

31.7

27.5

22.8

n.a

.-3

6.8

[159]

–A

ll”re

main

ing”

gla

cier

s1809

1370.8

1809

1961

2001

2012

1690±

90

1370±

70

1300±

70

-0.4

5±

0.1

2-2

3.1±

6.6

t.s.

Tien

Shan

mounta

inra

nge

13696

13714.4

13696

1961

2001

2012

16150±

750

13710±

690

13190±

680

-0.3

6±

0.1

2-1

8.3±

6.4

t.s.

44


Table C.3: Overview of the used reanalysis data. The name of the variable is stated as listed in theplatform from which the data were retrieved.

Data set Resolution Variable

ERA-40 1◦ × 1◦ 2 m air temperatureERA-40 1◦ × 1◦ Large-scale precipitationERA-40 1◦ × 1◦ Convective precipitationERA-40 1◦ × 1◦ Surface net solar radiationERA-40 1◦ × 1◦ Surface net solar radiation, clear sky

ERA-Interim 0.5◦ × 0.5◦ 2 m air temperatureERA-Interim 0.5◦ × 0.5◦ Total precipitationERA-Interim 1◦ × 1◦ Surface net solar radiationERA-Interim 1◦ × 1◦ Surface net solar radiation, clear sky

NCEP/NCAR 1.9◦ × 1.9◦ Mean daily air temperature at 2 mNCEP/NCAR 1.9◦ × 1.9◦ Mean daily precipitation rate at surfaceNCEP/NCAR 1.9◦ × 1.9◦ Mean daily clear sky downward solar flux at surfaceNCEP/NCAR 1.9◦ × 1.9◦ Mean daily downward solar radiation flux at surface

45


Table C.4: Overview of the 30 different model options for estimates based on glaciological observationsand modelling. Glacio. meas. indicates that the model is driven by glaciological observations only.Other model drivers are defined in Table C.3. dM/dt (Gt a−1) is the mass change rate during the period2003-2009 in which both GRACE and ICESat data are available simultaneously. N.A. indicates that themodel driver is not available for the whole period. Confidence intervals refer to the 95% level. For theaverage, the stated confidence interval corresponds to two times the standard deviation of all ensemblemembers.

Code Group Model Extrapolation Driver Period dM/dt

M1.a.e1 Average Glacio. meas. 1961-2012 −4.91 ± 3.36M1.a.e2 Constant rate Nearest neighbour Glacio. meas. 1961-2012 −5.19 ± 3.44M1.a.e3 Inverse distance Glacio. meas. 1961-2012 −4.59 ± 3.34

M1.b.e1 Average Glacio. meas. 1961-2012 −8.27 ± 3.37M1.b.e2 Constant trend Nearest neighbour Glacio. meas. 1961-2012 −8.93 ± 4.13M1.b.e3 Inverse distance Glacio. meas. 1961-2012 −8.33 ± 3.37

M1M1.c.e1 Average Glacio. meas. 1961-2010 −6.54 ± 2.66M1.c.e2 Constant ratio Nearest neighbour Glacio. meas. 1961-2010 −7.47 ± 3.16M1.c.e3 Inverse distance Glacio. meas. 1961-2010 −6.29 ± 2.65

M1.d.e1 Average Glacio. meas. 1961-2010 −4.51 ± 2.55M1.d.e2 Const. relation Nearest neighbour Glacio. meas. 1961-2010 −5.34 ± 2.85M1.d.e3 Inverse distance Glacio. meas. 1961-2010 −4.45 ± 2.54

M2.a.e1.E4 ERA-40 1961-2001 N.A.M2.a.e1.EI Average ERA-Interim 1979-2012 −7.23 ± 2.56M2.a.e1.NN NCEP/NCAR 1961-2012 −7.31 ± 2.62

M2.a.e2.E4 ERA-40 1961-2001 N.A.M2.a.e2.EI Degree-day Nearest neighbour ERA-Interim 1979-2012 −8.17 ± 3.42M2.a.e2.NN NCEP/NCAR 1961-2012 −6.81 ± 2.55

M2.a.e3.E4 ERA-40 1961-2001 N.A.M2.a.e3.EI Inverse distance ERA-Interim 1979-2012 −5.53 ± 2.53M2.a.e3.NN NCEP/NCAR 1961-2012 −5.66 ± 2.47

M2M2.b.e1.E4 ERA-40 1961-2001 N.A.M2.b.e1.EI Average ERA-Interim 1979-2012 −5.41 ± 1.94M2.b.e1.NN NCEP/NCAR 1961-2012 −6.71 ± 2.51

M2.b.e2.E4 ERA-40 1961-2001 N.A.M2.b.e2.EI Energy balance Nearest neighbour ERA-Interim 1979-2012 −5.08 ± 2.47M2.b.e2.NN NCEP/NCAR 1961-2012 −6.28 ± 2.47

M2.b.e3.E4 ERA-40 1961-2001 N.A.M2.b.e3.EI Inverse distance ERA-Interim 1979-2012 −3.77 ± 2.09M2.b.e3.NN NCEP/NCAR 1961-2012 −5.08 ± 2.39

AVERAGE 2003-2009 −6.16 ± 2.84

46


Table C.5: Average mass change rates for sub-regions defined in Figure 5 of the main article. dm/dtICESat

and dm/dtmodelling are the average specific mass change rate calculated from ICESat data and the modeloptions listed in Table C.4, respectively. The superscript indicate the period to which the estimaterefers to. The number of glaciers (ngl), the total glacier area (ARGI), and the number of retrieved ICESatfootprints over glaciers (nICESat) is given for each sub-region. ngl and ARGI are according to the RGI v3.2.Confidence intervals refer to the 95% level. The ICESat estimate for the remaining areas is not available(N.A.) since too few ICESat footprints can be retrieved. The estimates for the period 2003-2009 areplotted against each other in Figure 5 of the main article.

ngl ARGI dm/dt1961−2012modelling dm/dt2003−2009

modelling nICESat dm/dt2003−2009ICESat

Sub-region- km2 103 kg m−2 a−1 103 kg m−2 a−1 - 103 kg m−2 a−1

R1 Central Tien Shan 3087 5197.8 −0.21 ± 0.26 −0.31 ± 0.32 7157 −0.06 ± 0.31R2 Halik Shan 2429 2005.8 −0.63 ± 0.31 −0.69 ± 0.28 2945 −0.68 ± 0.43R3 Borohoro 3208 2734.9 −0.32 ± 0.30 −0.41 ± 0.28 2941 −0.63 ± 0.50R3a Central Borohoro 1449 1474.7 −0.17 ± 0.24 −0.29 ± 0.24 1432 −0.46 ± 0.76R4 Djungar Alatau 984 649.3 −0.44 ± 0.24 −0.49 ± 0.22 628 −0.75 ± 0.52R5 Ile and Kungoy Alatau 876 640.1 −0.31 ± 0.16 −0.33 ± 0.16 887 −0.68 ± 0.44R6 Inner Ranges 2303 1768.9 −0.36 ± 0.21 −0.41 ± 0.22 2336 −0.39 ± 0.37– Remaining areas 812 718.4 −0.60 ± 0.47 −0.72 ± 0.49 248 N.A.

47


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