High-Asia glaciers have been observed to be retreating the fastest
in the southeastern Tibet Plateau (SETP), where vast numbers of glaciers and amounts of
snow feed the streamflow of the Brahmaputra, a transboundary river
linking the world's two most populous countries, China and India. However,
the low temporal resolutions in previous observations of glacier and snow (GS) mass balance
obscured the seasonal accumulation–ablation variations, and their modelling
estimates were divergent. Here we use monthly satellite gravimetry
observations from August 2002 to June 2017 to estimate GS mass variation in
the SETP. We find that the “spring-accumulation-type” glaciers and snow in
the SETP reach their maximum in May. This is in stark contrast to seasonal
variations in terrestrial water storage, which is controlled by summer
precipitation and reaches the maximum in August. These two seasonal
variations are mutually orthogonal and can be easily separated in
time-variable gravity observations. Our GS mass balance results show a
long-term trend of
The Tibetan Plateau, considered the Asian water tower, is the source of
several major river systems. The upper streams of these rivers are fed by rainfall, base
flow, and widespread glacier and snow (GS) melt (Barnett et al., 2005;
Immerzeel et al., 2010; Jansson et al., 2003; Lutz et al., 2014). The GS
melt is susceptible to climate change, while its sustainable supply is
critical to the local freshwater security, flood prevention and control, and
hydroelectric development (Bolch et al., 2012; Kaser et al., 2010; Yao et
al., 2012). The southeastern Tibetan Plateau (SETP), including the Nyenchen
Tanglha Mountains (NTM) and eastern Himalayas, holds 10 439 glaciers with a
total area of 9679 km
Geographic environment of the upper Brahmaputra basin. The
boundary of the basin is outlined by the dashed black line. The violet areas
in the plateau represent mountain glaciers, but only the darker ones (9679 km
Due to the lack of observational data, most of the previous estimates on the
contribution of seasonal meltwater to the upstream flow of the Brahmaputra
river were based on modelling approaches that were only calibrated by
employing streamflow data. As a result, the previous estimates disagree
widely from 19 % to 35 % (Table 1) due to different forcing data and
approaches without direct constraints on GS mass balance (Bookhagen and
Burbank, 2010; Chen et al., 2017; Huss et al., 2017; Immerzeel et al., 2010;
Lutz et al., 2014; Zhang et al., 2013). The amount of meltwater could be
even more divergent. For example, Huss et al. (2017) estimated that the amount of annual GS melt to the Brahmaputra river
was 138 km
Previous model-based estimates of meltwater contribution to the Brahmaputra discharge.
Spaceborne sensors can be helpful in this desolate mountain region. Remote sensing techniques for regionwide GS mass balance measurements can be divided into three categories: laser altimetry (e.g. Ice, Cloud and land Elevation Satellite – ICESat – Kääb et al., 2012), multi-temporal digital elevation models (e.g. SPOT, Gardelle et al., 2013; ASTER, Brun et al., 2017), and space gravimetry (Gravity Recovery and Climate Experiment – GRACE – Matsuo and Heki, 2010; Yi and Sun, 2014). The first two geodetic approaches require the average ice density to convert volume changes into mass changes. The ICESat observation suffers from a short operation period (2003–2009) and sparse spatial sampling, both of which can be overcome by the stereo-imagery approach, which has become popular for the whole HMA study recently (Brun et al., 2017; Dehecq et al., 2018). Brun et al. (2017) provided an estimate of the detailed glacier mass balance trends over HMA between 2000 and 2016 and highlighted the regional dissimilarity. Despite recent improvements in spatial resolution in HMA glacier mass change studies, there has been little advance in their temporal resolution.
Observations at a monthly temporal resolution are necessary to separately
quantify summer and winter mass balances, two processes dominating the
annual glacier mass balance (Cogley et al., 2011, pp. 61–62) and thus crucial for
the calibration and validation of glaciological models. The amplitude of
seasonal variation in the glaciers in the SETP is up to
Precipitation in the SETP is controlled by various atmospheric circulation systems in different seasons, with westerly winds and the Bay of Bengal vortex in winter and spring and the Indian monsoon in summer (Wu et al., 2011; Yang et al., 2013; Yao et al., 2012). The first two systems were found to drive the spring precipitation in the SETP along the Brahmaputra river, thus forming a “spring-accumulation” type of glacier (Yang et al., 2013). The Indian monsoon prevails from June to September and brings intense precipitation to the southern side of the Himalayas, where terrestrial water storage shows tremendous seasonal changes and peaks in late summer. Therefore, according to the climate stations near NTM, we can observe bimodal precipitation variations throughout the year (Yang et al., 2013).
In this work, we will first introduce the precipitation characteristics in
this region by both meteorological stations and global precipitation
products. We will then use empirical orthogonal function (EOF) analysis
to decompose hydrological and GS signals in our study region, which does not
exactly coincide with the range of the glacierized zone in the Brahmaputra
basin. Our study region covers only 83 % of the basin glaciers (the
undetected 17 % are in the western part) and 15 % of non-Brahmaputra
glaciers. We will scale our results by a ratio of
We adopt the monthly GRACE spherical harmonics Release 06 products from
August 2002 to June 2017. The three datasets are solved respectively by
three organizations: the Center for Space Research (CSR) at the University of
Texas, the GeoForschungsZentrum (GFZ) in Potsdam and the Jet Propulsion
Laboratory (JPL). These datasets are available at
Two different filtering strategies, a combination of a P4M6 decorrelation
(Swenson and Wahr, 2006) and 300 km Gaussian filter (hereafter G300
We adopt different uncertainty estimation strategies for the seasonal variation and the trend due to their intrinsically different error sources. The error in seasonal variation consists of the standard deviations among these six datasets (i.e. errors from the data solution and smoothing methods) and the leakage error, while that in the long-term trend also includes other potentially uncorrected signals. We assume that the majority of the hydrological signal is captured by the first EOF mode. The leakage error is then determined by how effectively the hydrological and GS signals are separated by the EOF technique. Based on the modelled and recovered glacier mass changes, their residuals are estimated to have a seasonal variation of up to 11 % of the modelled glacier mass change (refer to Sect. 3.2 in the Supplement), which is used to calculate the seasonal leakage error. We do not quantify or account for potential hydrological (non-GS) signals in EOF mode 2.
For the long-term trend error, the three different solutions and two
smoothing techniques have a total effect of 0.44 Gt yr
GRACE error sources for the long-term trend (Gt yr
Version 34 of the ICESat Global Land Surface Altimetry Data is used to
derive glacier height changes. The data span is from 2003 to 2009, with two
or three observation campaigns per year (Fig. S1 in the Supplement). The processing of
ICESat data includes the following steps. (1) Orthometric heights are
obtained from original elevation data based on the Earth's gravity model
2008. (2) Footprints of glaciers are identified based on Randolph Glacier Inventory (RGI) 6.0 glacier
outlines. (3) For each ICESat footprint, Shuttle Radar Topography Mission (SRTM; Farr et al., 2007)
elevations and slopes are extracted by bilinear interpolation of the digital-elevation-model grid cells. Glacier height variation is defined as the elevation differences
between the footprints and the SRTM data. (4) We exclude footprints over
SRTM voids, footprints with slopes higher than 30
ICESat has shown good ability to estimate snow variation in flat regions
(Treichler and Kääb, 2017), but applying the same technique in
mountainous areas with high terrain heterogeneity is cumbersome. Therefore,
here ICESat is only used to estimate changes in glacier mass. Although our
GRACE estimate includes both glaciers and snow, the estimates by GRACE and
ICESat are comparable in the late ablation season (i.e. the
October–November campaign of ICESat), when the contribution of seasonal snow
meltwater is negligible (Sect. 5.1). To convert the glacier thickness
changes into mass changes, two parameters are required, i.e. glacier
density and total glacier area. We assume an average glacier density of
To analyse the impact of temperature and precipitation on GS and water mass
balance here, we adopt two types of datasets, gridded reanalysis
products and in situ measurements from four meteorological stations (their
locations are labelled in Fig. 1, and coordinates are listed in Table S1 in the Supplement).
Precipitation and temperature records for each site from 2003 to 2016
(Fig. S4) are available from the China Meteorological Data Service Center
(
Global gridded precipitation data of the Tropical Rainfall Measuring Mission (TRMM; Huffman et al., 2014) are used to examine the
influence of precipitation on water storage. The data are available at
Moderate Resolution Imaging Spectroradiometer (MODIS) data MOD10 (Hall
et al., 2006) are used to investigate snow coverage here. The MOD10CM product
has a temporal resolution of 1 month and spatial resolution of 0.05
The method of this study is based on the fact that the change in GS mass
driven by spring precipitation precedes the change in hydrological signals.
Therefore, before introducing the method, we want to demonstrate that GRACE
can detect mass changes caused by spring precipitation. At two out of four
stations (Bomi and Chayu), spring precipitation is noticeable, even
surpassing the summer–autumn precipitation brought by the Indian monsoon
(Fig. S4). Yang et al. (2013) provided precipitation records at 22
sites in a broader area and outlined the boundary of the impact zone of the
spring precipitation, which roughly covers the glacierized area studied
here. Summer precipitation and its associated hydrological mass change are
enormous and well recognized, while the spring equivalents are not. Therefore, here
we only use the TRMM and ERA5 results from January to March in
Fig. 2 to show the initiation of spring
precipitation. The precipitation begins to spread south and west starting in
April, when the monsoon gradually increases (not shown here). The TRMM
results show a boundary along the latitude 29
Monthly precipitation from January to March by TRMM and ERA5 and mass anomalies from March to May by GRACE. The Brahmaputra and its basin boundary are marked. The white shaded areas in the bottom plots represent glacier distribution.
The performance of TRMM and ERA5 is compared with our station measurements
in Fig. S5. According to the in situ records, the spring precipitation, as
a part of the bimodal variation, is obvious at the Bomi and Chayu stations.
TRMM is capable of revealing the conditions at Chayu at 28.65
These results show that spring precipitation can be captured to a limited extent by various reanalysis products and the spring-accumulation pattern of GS mass change in the SETP is recognizable in GRACE observations. The amplitude and phase of the seasonal mass variation from the equivalent water height (EWH) of GRACE are compared in the background of Fig. 1. The seasonal amplitude has a spatial distribution similar to that of the Indian-monsoon-affected area. This pattern reflects the predominance of the monsoon-controlled hydrological process and the weaker glacial signals in this region. However, the peak month of seasonal changes (the contours in Fig. 1) divergently appears earliest in June in the NTM and is gradually delayed to August in the southern Himalayas, where the annual amplitude reaches its maximum. The shift in peak months reflects the increasing–decreasing contribution from the sinusoid of the hydrological and GS seasonal variation. A key point to point out is that the peaks of hydrological and GS seasonal variations have a 3-month time window offset (Sect. 4.4), which is a quarter of the annual oscillation cycle and means that the two signals are mathematically orthogonal.
GS and hydrological mass changes dominate the seasonal gravity signals observed by GRACE in this region, and they are mathematically orthogonal due to different phases. Therefore, we employ the EOF technique (see the Supplement for mathematic expressions; Björnsson and Venegas, 1997) to decompose hydrological and glacial signals in the GRACE datasets (Fig. 3). We thus extract two modes with significantly higher explained variances than the other modes (i.e. two significant modes are obtained). Results of different datasets and filters show good consistency, indicating that the first two modes are robust.
Each mode consists of one EOF (the spatial pattern) and one principal component (PC; the temporal
evolution). Only the first two modes, accounting for
The trends of the GRACE observation and its decomposed modes are shown in
Fig. 4. The GRACE observation shows a significant
mass loss, which is divided into the first two modes. In the glacierized
zone, approximately two-thirds of the negative trend comes from the second mode
and approximately one-third comes from the first mode. The trend of higher
modes (
EOF decomposition of GRACE observations in the form of EWH in the
study region. Six combinations are averaged to generate these plots, and
uncertainties are estimated based on the dispersions.
According to the spatial coverages (EOF
GRACE results only show smooth mass patterns, and we need a strategy to
recover the original amount of mass change. If we adopt the second mode to
estimate GS mass change, this step is necessary. Therefore, a forward-modelling method (Yi et al., 2016) is chosen to recover the mass in a
predefined region iteratively. This method has been widely used (Chen et
al., 2015; Wouters et al., 2008), especially in the study of polar ice
sheets. In the first step, we divide the glacier mask based on the glacier
distribution recorded in RGI 6.0 (RGI Consortium, 2017; Fig. 4e). The lattices have a resolution of
0.5
Trend of GRACE signals and the GS mass estimation. The CSR product
with the DDK4 filter is used here.
To validate the hypothesis that the first mode represents hydrological
signals, we compare it with EOF decomposition results of two other datasets,
soil moisture from GLDAS Noah and precipitation data from TRMM
(Fig. 5). To make them comparable to GRACE in terms
of spatial resolution, they are expanded into spherical harmonics, truncated
at degree 60, and smoothed by the same filter. Their results are shown in
Fig. 5. Different from GRACE, which has two
significant modes, they each only have one due to the lack of a glacial signal.
The EOF
EOF analysis of soil moisture using GLDAS Noah
Notably, mass contributions from the Brahmaputra river and groundwater are
absent (and they are troublesome to obtain) and precipitation is assumed as
the dominant driver of water storage change without considering the
influence of runoff and evaporation (Humphrey et al., 2016), so we
do not expect that we can reach a thorough agreement between different
datasets. This is acceptable if their temporal consistency is targeted.
However, long-term trends in runoff, evaporation and groundwater cannot be
ignored and they are differently reflected in these three products, so their
trends have been removed before the comparison. The exclusion of unavailable
surface water and groundwater in the GLDAS result also causes a weaker
strength of its EOF
The phase difference of 3 months is a prerequisite for this method and can be verified retrospectively. We tested different phase differences between hydrological and GS signals and decomposed them by the EOF method (refer to Sect. 3.1 in the Supplement). Only when the GS mass change peaks in May (3 months before the peak month of the hydrological signal) does our simulated result show similarities to the GRACE observation.
Only hydrological and GS signals can explain the first two modes considering their spatial and temporal patterns. The atmosphere contribution has already been removed in GRACE observations (Dobslaw et al., 2017), and mass transports of solid earth are unlikely to have such strong seasonal variations. We cannot quantify the contribution of groundwater in the second mode, but groundwater is apt to be modulated by stronger rainfall in summer (Andermann et al., 2012), rather than by snowfall in winter–spring, and groundwater activity will be reduced in winter–spring when the ground is frozen. Therefore, the groundwater component is inclined to be captured by the first mode. We attribute the negative trend in the first mode to decreasing precipitation in recent years (Fig. S10) and intense groundwater pumping (Shamsudduha et al., 2012). The negative trend in the second mode is supposed to represent GS melting and can be used for estimating GS mass balance.
The glacier surface elevation changes measured by ICESat are compared
with the result estimated from the second mode of GRACE. We interpolate the
series of GRACE estimates (2002–2017) into the observation epochs of ICESat
(2003–2009) and plot mass changes by GRACE as a function of elevation
changes by ICESat (Fig. 6a). After dividing by the
glacier density, the slope of the elevation–mass regression line represents
the inventorial glacierized area by RGI 6.0. The observations in
October–November (blue squares) approximate with the line, indicating the
good consistency between ICESat and GRACE in the late ablation season
between 2003 and 2009. The MODIS result indicates that the snow coverage
increases rapidly from September (Fig. 6b), while
the GRACE PC
GS mass balance in the SETP.
The difference between GRACE and ICESat-based estimates of mass change
indicates that the snowpack outside the glaciers is a non-negligible
contributor to the seasonal mass variation. This is quite different from
previous glacier trend estimates, where non-glacier snow was neglected.
Based on MODIS observations, the snow coverage area in this region varies
from approximately 80 000 km
Figure 6c compares the time series of glacial mass in
the SETP from GRACE (August 2002–June 2017) and ICESat (2003–2009). The
times series from two sensors are consistent in seasonal and interannual
variations, despite the absence of the snow component in the ICESat result.
Monthly mass change shows that the ablation season is generally between June
and October with slightly varied initiation and duration from year to year.
The maximum mass increase (10–20 Gt) usually occurs in April, when the
spring precipitation peaks, and the severest mass loss (
We calculate annual mass increase and decrease by the difference in mass
anomalies between November and May and between June and October
respectively. From 2002 to 2017, the annual mass decrease ranged from
Temperature is a dominant factor influencing the melting of glaciers
(Cogley et al., 2011, pp. 68). Here, the monthly temperature records from the
ERA5 product are compared with month-to-month mass changes by GRACE to
investigate the sensitivity of the GS mass balance in response to
temperature change (Fig. 7). Mass changes are
negatively correlated with the temperature anomalies by a factor of
Regression between mass change and temperature.
To investigate the impact of climatic variables on the interannual
variations in GS mass, we compare annual mass losses (from May to October)
with summer temperatures (from June to August; Fig. 7b). The annual mass loss is significantly correlated with the summer
temperature, with a slope of
We could not find a significant relationship between the mass and precipitation changes, probably because our data fail to reflect the strong orographic effect in precipitation and/or because the GS mass gain process is too complex to be attributed to precipitation alone.
The trend of glacier elevation change by ICESat in this study is
A recent result on changes in interannual glacier flow in this region (Dehecq et al., 2018) indicates a strong correlation between ice flow rate and changes in glacial thickness. The interannual variation in GRACE-based mass changes (the 1-year smoothed sequence in Fig. 6c) notably shows equilibrium during the periods of 2003–2005 and 2011–2014. According to the aforementioned study (Dehecq et al., 2018), thinning glaciers reduce their flow rate by weakening gravitational driving stress; therefore, this balanced mass state may slow down the decreasing flow rate. Coincidentally, we can identify such decelerating phases in the decline in glacier flow rate during 2004–2006 and 2012–2015 (Fig. 1 in Dehecq et al., 2018).
GS mass loss is caused by flow, melting, and evaporation processes, and
the last one does not contribute to the river flow. Evaporation is important
for continental-type glaciers where the climate is usually cold and dry.
For example, it accounts for 12 % of the glacier ablation in Tianshan (Ohno et
al., 1992). However, the importance of evaporation is greatly reduced in our
maritime glaciers due to the extremely humid air and rapid melting.
Therefore, we assume that the mass loss is completely turned into meltwater
and can be compared with analogous outputs from models. In our study region,
85 % of its meltwater (estimated according to the area proportion) runs
into the Brahmaputra, and this area accounts for 83 % of total glaciers in
this basin (9912 km
Monthly mass change from GS in the upper Brahmaputra basin
estimated by GRACE and by the model of Lutz et al. (2014).
Negative values mean a net increase in meltwater (i.e. more GS melt than accumulation). Note that Lutz's model only estimated the melt
component, while GRACE detects the net change including both melt and
accumulation. The estimates of summer melt are annotated. A schematic
diagram of seasonal mass balance is shown in the inset (blue text represents
mass accumulation, red represents ablation, and the black curve represents
the net change). Note 85 % of the meltwater in our study region runs into
the Brahmaputra, and this amount comes from 83 % of the glacierized area in
this basin; we scale our result by
Our annual mass decrease (average 49.0 Gt) is still much smaller than the
137 Gt of annual meltwater given by Huss et al. (2017). However, this larger value even exceeds the annual streamflow of
130.7 km
In this study, we use GRACE gravimetry to estimate the GS mass balance in the SETP from August 2002 to June 2017. The second EOF mode of GRACE observations is attributed to changes in GS mass, which can be validated in the following three steps. First, a simulation experiment shows that two signals with peaks in August and May can be decomposed unbiasedly by EOF. Second, the first decomposed mode shows consistent spatio-temporal patterns with the soil moisture and precipitation variations from the GLDAS and TRMM data and thus can be reasonably attributed to hydrological processes. Thirdly, the second mode of the GRACE signal with a peak in May temporally corresponds to the glacier and snow accumulation and ablation processes and spatially coincides with the glacier distribution, which is also supported by the spring precipitation pattern observed by meteorological stations. Glacier mass change measured by ICESat is further adopted to compare with our GRACE-based GS estimates, and good agreement is reached in the ablation season when the snow contribution is negligible. The ICESat measurements also show that the seasonal glacier mass variation is large, which is consistent with our finding that GS mass change in this region peaks in May.
The GRACE-based GS mass balance not only shows a long-term decreasing trend
of
The data that support this study are mostly publicly open, and their sources are indicated in the “Data” section. The meteorological data and the series of glacier mass balance estimates are available upon request to the corresponding author.
The supplement related to this article is available online at:
SY conceived the study and conducted the calculations. SY and CS analysed the results and wrote the manuscript. KH discussed and revised the manuscript. SK discussed and suggested the experiment. QW processed the ICESat data. LC processed the MODIS data.
The authors declare that they have no conflict of interest.
Shuang Yi is supported by JSPS and the Alexander von Humboldt Foundation. Chunqiao Song is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences and the National Key R&D Program of China.
This research has been supported by the JSPS KAKENHI grant (grant no. JP16F16328), the Alexander von Humboldt Foundation, the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDA23100102) and the National Key R&D Program of China (grant no. 2018YFD1100101, 2018YFD0900804).This open-access publication was funded by the University of Stuttgart.
This paper was edited by Bert Wouters and reviewed by Enrico Ciracì and four anonymous referees.