Endorheic (hydrologically landlocked) basins spatially concur with arid/semiarid climates.
Given limited precipitation but high potential evaporation, their water storage is
vulnerable to subtle flux perturbations, which are exacerbated by global warming and
human activities. Increasing regional evidence suggests a likely recent net decline
in endorheic water storage, but this remains unquantified at a global scale. By integrating
satellite observations and hydrological modeling, we reveal that during 2002–2016,
the global endorheic system experienced a widespread water loss of about 106.3 Gt
yr−1, attributed to comparative losses in surface water, soil moisture, and groundwater.
This decadal decline, disparate from water storage fluctuations in exorheic basins,
appears less sensitive to El Niño–Southern Oscillation-driven climate variability,
implying possible responses to longer-term climate conditions and human water management.
In the mass-conserved hydrosphere, such an endorheic water loss not only exacerbates
local water stress, it also imposes excess water on exorheic basins, leading to a
maximal sea level rise that matches the contribution of nearly half of the land glacier
retreat (excluding Greenland/Antarctica). Given these dual ramifications, we suggest
the necessity of long-term monitoring of water storage variation in the global endorheic
system and inclusion of its net contribution to future sea level budgeting.
Global endorheic basins (Fig. 1a), where surface flow is landlocked from the ocean,
cover a fifth of the Earth’s land surface but nearly half of its water-stressed regions
1
. Many arid and semiarid regions are inherently endorheic, where surface flow is unable
to break topographic barriers, and retained in landlocked storage that equilibrates
through evaporation
2
. Because surface flow is scarce in endorheic regions, water storage, particularly
in sizable lakes, reservoirs, and aquifers, becomes of vital ecological and social
importance. Endorheic water storage can be maintained only if the system fluxes, chiefly
through precipitation, evaporation, and groundwater exchanges, remain in a delicate
balance. However, recent climate change, notably warming and drying in many arid/semiarid
regions
3–5
, has triggered observable perturbations to the endorheic water balance, intensified
further by human water withdrawals, damming, and diversions
5–8
. Regional evidence of storage declines has been seen for decades in desiccating lakes
(e.g., Aral Sea and Great Salt Lake)
8,9
, retreating glaciers (e.g., Tibetan and Amu Darya)
10,11
, and depleting aquifers (e.g., Arabian and Persian)
12
, suggesting a likely enduring decline of the total terrestrial water storage (TWS)
within the global endorheic system.
In the mass-conserved hydrosphere, a net endorheic water deficit not only aggravates
water stress in endorheic regions, it also imposes the same amount of water surplus
on the exorheic system, where surface flow reaches the ocean. Therefore, a persistent
TWS decline in global endorheic basins signifies a potential source of sea level rise
(SLR). The rate of SLR averaged at ~1.9 mm yr−1 during the past half century
13
, and increased to ~3.4 mm yr−1 in the current millennium despite occasional hiatuses
due to El Niño-Southern Oscillation (ENSO)
14–16
. About 70–80% of the recent decadal SLR was attributed to ocean thermal expansion
(~1.2–1.4 mm yr−1) and ice-sheet mass loss in Greenland and Antarctica (~1.0–1.3 mm
yr−1). The other ~20–30% was induced by the net TWS change that integrates mountain
glacier and ice cap (GIC) loss, groundwater depletion, reservoir impoundment, and
mass changes in other stores (e.g., lakes, soil, and permafrost)
4,15
. Some of these TWS changes, however, were assessed without a discrete consideration
of endorheic and exorheic origins, which may overestimate their individual impacts
on the sea level budget. For example, glacial meltwater originating from endorheic
basins produce no direct excess discharge to the exorheic system
11
, and reservoirs in endorheic basins do not detain runoff that otherwise drains to
the ocean. Owing to observation changes, studies that explicitly assessed endorheic
contributions are limited to major terminal lakes that are often considered as basin-wide
integrators of climatic and hydrological conditions
8,17–21
. Particular emphases were given to the strikingly desiccating Aral Sea, and the world’s
largest endorheic lake, the Caspian Sea, where water level has shown cyclic fluctuations
but an overall lowering since the end of the Little Ice Age (~2 cm yr−1)
22
. Budget changes in these two lakes and their affected groundwater, if assuming a
complete loss to exorheic regions via vapor transfer, contributed a potential SLR
of ~0.1–0.2 mm yr−1 at recent decadal to centennial timescales
17–19,21,23
. Aside from regional evidence, the overall magnitude and spatial pattern of endorheic
TWS decline have not been quantified at a global scale, and its net contribution to
recent SLR remains unclear.
Here we determine the mass changes in TWS throughout the world’s endorheic basins
and the potential impact on SLR during the early twenty-first century. Our monitored
TWS is the vertical integration of all water forms on and below the continental surface
24
, where net mass changes are inverted from time-variable gravity fields observed by
NASA’s Gravity Recovery and Climate Experiment (GRACE) satellites
25
. We use the monthly mass anomalies during April 2002 through March 2016, from the
Jet Propulsion Laboratory mascon solution
26
. This solution isolated TWS signals by removing the noise from the solid earth and
improved spatial resolution over conventional spherical-harmonic solutions
27
. Monthly mascon anomalies are rescaled to 173 endorheic units (Fig. 1a), each aggregated
from refined landlocked watersheds until the size exceeds a mascon. Scaled endorheic
mass changes are partitioned into the contributions of surface water, soil moisture,
and groundwater, in order to contrast possible attributions in different regions.
We implement an ensemble of multiple hydrological models (Table S1) to derive monthly
anomalies in soil moisture and part of surface water compartments including snowpack
and plant canopies. Modeled surface water anomalies are further corrected by storage
variations in major lakes/reservoirs estimated from altimetric/optical satellite observations
(Fig. S1–S10) and mass changes in GIC derived from stereo imagery
11
(Fig. S11; Tables S2–S3). By subtracting the corrected anomalies in land water content
from net TWS changes, we then disaggregate the groundwater contribution from those
of surface water and soil moisture. Detailed data processing and uncertainty analysis
are given in Methods.
Net endorheic storage loss and potential impacts on sea level
Our results confirm a widespread TWS decline within the global endorheic system during
the studied 14 years (Fig. 1). Net water loss prevails in about three quarters of
the endorheic units in area (23.2 out of 31.8 million km2) or number (129 out of 173),
agglomerated particularly along the water-stressed Subtropical Ridge in Central Asia,
the Middle East, and northern Africa (Fig. 1a). In total, the global endorheic system
has undergone a net storage change of –106.32 (±11.70) Gt yr−1 (uncertainties in 95%
confidence intervals (CIs)). This is about twice the rate of concurrent TWS changes
from the entire exorheic region (−58.44 (±27.75) Gt yr−1 excluding Greenland/Antarctica),
although the endorheic area is only a fifth of the global landmass (Fig. 1b–c). While
the signature in exorheic TWS anomalies is closely linked to ENSO-driven climate variability
(Fig. 2, with prominent positive/negative TWS anomalies during La Niña/El Niño events),
endorheic anomalies appear less sensitive to such interannual modulations (see Fig.
S12 and Table S4 for other climate oscillations). This contrast highlights the possible
significance of longer-term climate conditions (e.g., multidecadal variability and
anthropogenic warming) and direct human water management to TWS in the arid/semiarid
hinderlands
4,5,7–9
.
The net endorheic water loss, if it completely reaches the ocean, results in an average
SLR of 0.29 (±0.03) mm yr−1, accounting for ~9% of the observed SLR (3.4 mm yr−1)
16
and ~15–20% of the barystatic (mass-induced) contribution (1.6–2.0 mm yr−1)
4,15
around the same period. Compared with other barystatic sources, the endorheic water
loss equals nearly half of the global mass decline in GIC (0.6–0.7 mm yr−1 excluding
Greenland/Antarctica)
4,15
, and matches the entire contribution of groundwater depletion (~0.27 mm yr−1)
30
. This endorheic loss also exceeds the previous estimates of the net inland water
change, e.g., in the Caspian Sea, Aral Sea, Lake Chad, Great Salt Lake, and Tibetan
lakes
8,17–19,21,31
, by a factor of ~2–4, which implies substantial but poorly understood changes in
hydrological components within the global endorheic system. However, we recognize
that our estimated SLR contribution is only the potential barystatic contribution
of the net endorheic loss or its sea level equivalent. If assuming that the surplus
of water vapor transferred from endorheic basins is evenly precipitated into the exorheic
system (including both land and ocean with a negligible net vapor change
30
) and an average precipitation-to-discharge ratio of 2.4 from land
32
, we approximate that up to ~80% of the net endorheic TWS loss might end up in the
ocean.
Regional variation and links to climate and human actions
Despite a net global decline, the change of endorheic TWS exhibits intriguing regional
variation. On one hand, our map of TWS trends for individual endorheic units (Fig.
1a) shows exacerbated water scarcity in many of the world’s drought hotspots. They
include not only drainage basins under intense human influences, such as those of
the Caspian Sea, Aral Sea, Urmia Lake, Balkhash Lake, and Great Salt Lake, but also
remote or sparsely populated deserts in Africa (e.g., Sahara), Central Asia (e.g.,
Taklamakan and Gobi), the Middle East (e.g., Arabian), South America (e.g., Atacama),
western US (e.g., Great Basin and Mojave), and western Australia (e.g., Great Sandy
and Gibson). TWS declines in these hotspots accentuate the evident impact of recent
meteorological drought on arid/semiarid regions, which is often intertwined with human-induced
evaporative loss through surface water diversion, damming, and groundwater abstraction
4,5,8,9,33
. On the other hand, water losses across most of the endorheic landmass contrast markedly
with water gains in the Inner Tibetan Plateau (ITP), eastern Australia, Sahel, Great
Rift Valley, Kalahari Desert (southern Africa), and northern Great Basin and Great
Plains (North America). However, these water gains are more spatially constrained
and are dominantly induced by natural variability
5
(Supplementary text).
To further contrast regional variation, we group global endorheic basins by continent
and climatic similarities into six primary zones (Fig. 3a), where TWS anomalies and
changing trends are compared in Fig. 3b–h and Table 1. Approximately two-thirds of
the global endorheic water loss (–73.64 (±7.74) Gt yr−1) stems from Central Eurasia,
the largest zone covering one-third of the endorheic landmass. Water loss within Central
Eurasia generally weakens along an eastward gradient, as illustrated in four secondary
zones. Over half of the total zonal loss is concentrated on the Caspian Sea Basin
alone, 10% on the Aral Sea Basin (including nearby watersheds receiving transbasin
diversions) but largely balanced out by the water gain in ITP, and the other ~40%
from across the remaining basins. Monthly TWS anomalies in Central Eurasia exhibit
a strong monotonic decline since 2005, despite an earlier increase linked to the rise
of the Caspian Sea level
21
, and a water gain in ITP that persisted for multiple decades
31
but has decelerated since ~2013
34
. The TWS in the vast desert zone of Sahara/Arabia underwent a continuous decrease
throughout 2002–2016, resulting in the other one-third of the net global loss (–33.10
(±3.57) Gt yr−1). A marked storage decline also prevailed in Dry Andes/Patagonia (–9.61
(±1.96) Gt yr−1), but has slowed down and partially reversed since 2012. Net water
losses in Australia and Western North America are less dramatic (–4.05 (±4.86) and
−2.53 (±2.00) Gt yr−1, respectively) due to spatial dipole and short-term fluctuations.
For instance, Australia’s Millennium Drought
35
was temporarily alleviated by La Niña-induced precipitation anomalies in the eastern
region (e.g., the Great Artesian Basin) during 2010–2012
36
. Water declines in the latter three zones sum up to another 15% of the net global
endorheic loss, which is, however, counteracted by the water gain in Great Rift Valley/Southern
Africa (GRVSA, 16.60 (±2.28) Gt yr−1).
Contributions of different water storage components
The net TWS changes aggregate the contributions of different hydrological components
(Fig. 4 and Table 1). During the past 14 years, the net global endorheic loss is attributed
to comparable declines in surface water (36.08% (±9.89)), soil moisture (26.36% (±7.46)),
and groundwater (37.56% (±16.57)), but such contributions result from highly unequal
partitions within zonal TWS changes. In Central Eurasia, surface water loss outweighs
that of soil moisture and is more than double that of groundwater (Fig. 4c). The prominent
surface water loss can be observed by the recent shrinkage of many large lakes across
Central Asia and the Middle East (e.g., Aydar, Aral Sea, Bosten, Caspian Sea, Khyargas,
Tengiz, and Urmia; Fig. S2). In particular, over 70% of the global endorheic surface
water loss was induced by the level drop in the Caspian Sea (–6.8 cm yr−1). Another
~11% was caused by the desiccation of the Aral Sea (–1041.7 km2 yr−1) despite the
compensation of excess discharge from warming-induced glacier melting (Fig. S5–S8
and Table S5). Surface water losses in these two basins coincided with drying climate
(deficient precipitation and rising temperature, Fig. S13o–r), along with intensive
water diversion (e.g., from the Volga River, Amu Darya, and Syr Darya) for irrigation,
which supplemented moisture supplies for evapotranspiration
17,20,37
. Diversion-based irrigation may have also increased regional return flow
38
, resulting in possible groundwater recharge despite overall soil moisture loss (Fig.
4d–e). In contrast, increasing precipitation and, to a lesser extent, warming-induced
glacier loss led to evident lake expansion in ITP
9,39
(Fig. S13s–t; Table S5), where surface water surplus explains over 80% of the net
TWS gain (Fig. 4f). As water relocation from glaciers to lakes does not alter the
endorheic system storage, increasing net precipitation (i.e., precipitation minus
evapotranspiration) is the primary contributor to the net TWS gain, which is in line
with recent literature
31,34,39
. Surface freshwater is critically limited in the remaining endorheic zone of Central
Eurasia (Fig. 4g), where groundwater withdrawal easily exceeds natural recharge
12
. Similar to river diversion, groundwater depletion might enhance evaporation by cumulatively
transferring water from aquifers to the surface, which explains 68% of the zonal TWS
loss.
Greater dominance of groundwater depletion to net TWS loss is seen in Australia (Fig.
4h) and Sahara/Arabia (Fig. 4j), where endorheic basins often remain arheic and groundwater
becomes the only permanent water source. In Sahara/Arabia, for instance, annual groundwater
depletion (–33.23 (±4.37) Gt yr−1) matches the rate of the zonal TWS loss. Our estimate
is similar to that of Richey et al.
7
(about −29 (±6) Gt yr−1 during 2003–2013) if one sums up their estimated depletions
of major aquifers including Arabian, Nubian, Northwestern Sahara, Murzuk-Djado Basin,
Taoudeni-Tanezrouft Basin, and Lake Chad Basin, although these authors did not correct
modeled surface anomalies by lake storage changes (e.g., minor increase in Lake Chad).
In addition to unsustainable human withdrawal, groundwater declines in these desert
zones may result from vadose capillary fluxes that transport water from aquifers to
compensate for soil moisture loss
40
. Such declines are in sharp contrast to the groundwater gain in GRVSA (16.54 (±2.70)
Gt yr−1; Fig. 4i), indicating persistent recharge as a result of excess precipitation
(Fig. S13i–j).
In Western North America, climate-induced soil moisture decrease (Fig. S13c–d) dominates
the net TWS loss (Fig. 4l). Meanwhile, studies
8,33,41
suggest that human activities, such as irrigation and mining, are crucial causes of
the surface water decline in Great Salt Lake (–0.20 Gt yr−1, consistent with −0.17
Gt yr−1 in Wurtsbaugh et al
8
) and Salton Sea
41
(–0.11 Gt yr−1) (Fig. S2), accounting for 12% of the zonal TWS loss. The contribution
is more evenly partitioned among surface, soil, and aquifers in Dry Andes/Patagonia
(Fig. 4k), where a quarter of the net TWS loss stems from the shrinkage of Lakes Titicaca,
Poopό, and Mar Chiquita (Fig. S2). Such concurrent losses in multiple water stores
imply an extensive impact of the recent precipitation deficit (Fig. S13e–f) and human
activities on South America’s endorheic hydrology
8,42,43
.
Implications for global water cycle
Our findings reveal the recent decadal TWS decline in global endorheic basins, which
largely outpaces the concurrent TWS change in the exorheic region. While exorheic
TWS modulates the sea level by directly affecting surface runoff to the ocean, it
is also subject to natural variability of the climate system (e.g., ENSO at multiyear
timescales) that augments/suppresses the delivery of water from the ocean
4,14
. From another perspective, we show that endorheic TWS, albeit limited in quantity,
can dominate the variation in global TWS at decadal timescales. This decadal loss
in endorheic TWS suggests that recent climate conditions, in conjunction with direct
human activities, resulted in a substantial vapor outflow from the continental interiors.
The consequential water surplus to the exorheic system might be acting as a non-negligible
source of SLR. Limited by available TWS observations, our calculated trend may not
imply a secular signal beyond the studied GRACE era. Nevertheless, this decadal endorheic
loss is in line with satellite-observed decreases in surface water extent since ~1980
9,33
, model-simulated increases in water stress over the past half century
44,45
, and reported declines in water volumes of major saline lakes over the past ~140
years
8
, all predominantly in arid/semi-arid regions. Under the latest climate change scenarios,
reversal of such a net decline in the next half/one century seems uncertain, considering
projected decreases in precipitation, soil moisture, and discharge but increases in
potential evaporation, drought duration, and water stress in many endorheic regions
3,5,46–50
.
Apart from a widespread net TWS loss, we quantify that the loss prevails comparatively
in all three primary hydrological stores (surface, soil, and aquifers). However, their
relative contributions vary among endorheic zones, resulting from strong spatial heterogeneity
in flux-storage interactions and responses to climate and water management. As detailed
in Methods and Supplementary Information, our partitioning of TWS losses relies on
a synergy of multi-model ensemble and satellite observations, and emphasizes different
components in the water cycle rather than attributions to natural variability versus
secular forces. Despite uncertainties, our analysis exemplifies a critical effort
toward the decoupling of climate-human influences on the recent TWS shift from endorheic
to exorheic systems. This analytical decoupling is essential for projecting and managing
water stress in arid/semiarid regions under future climate change. Given such dual
ramifications both to regional water sustainability and to global SLR, we thereby
suggest a continued understanding of long-term TWS variation in global endorheic basins,
and an explicit inclusion of its net contribution (such as by the Intergovernmental
Panel on Climate Change) in future sea level budgeting.
Methods
Defining endorheic regions.
Endorheic basin extents are mainly acquired from a total of 48,813 landlocked watersheds
identified in the 15-second HydroSHEDS drainage basin dataset
51
(Fig. S14a). Their spatial patterns are overall consistent with the depiction in the
Global Drainage Basin Database
52
(GDBD). Among minor discrepancies, 10 watersheds landlocked in ITP, Manchuria, Siberia,
and western US are captured only in GDBD (Fig. S14a), and thus included to supplement
HydroSHEDS. These watersheds are aggregated into three enumeration scales: (i) 173
endorheic units (Fig. 1a), each comparable to or larger than the size of a 3-degree
spherical cap mascon (~100 thousand km2), (ii) 10 endorheic zones (Fig. 3a), including
6 primary zones in the continental level and 4 secondary zones within Central Eurasia,
and (iii) the entire global endorheic system, i.e., the aggregated extent of all landlocked
basins. Each endorheic unit, as further illustrated in Fig. S14b, is a single landlocked
watershed if its size exceeds a mascon, or an agglomeration of contiguous/nearby watersheds
until their total area exceeds a mascon. These units exclude sporadic landlocked watersheds
smaller than a mascon and substantially detached from major endorheic clusters (black
areas in Fig. 1a). The secondary zones of the Caspian Sea Basin and the Aral Sea Basin
(Fig. 3a) include several surrounding endorheic watersheds to compensate for the GRACE
signal leakage from the Caspian Sea and the Aral Sea. The Aral Sea Basin also integrates
nearby endorheic watersheds receiving transbasin diversions from the Amu Darya and
the Syr Darya.
Calculating endorheic TWS changes.
GRACE-observed monthly anomalies of equivalent water thickness (EWT) from April 2002
to March 2016 in the JPL 3-degree equal-area mason solution (JPL-RL05M version 2)
26,27,53,54
are rescaled to each enumeration level (unit, zonal, and global) by an area-weighted
scaling:
M
=
Σ
a
i
m
i
/
Σ
a
i
, where M denotes a monthly anomaly for any enumeration region, m
i
the original anomaly in each mascon i that intersects with this region, and a
i
the intersection area. Deseasonalized time series M (with monthly climatology removed)
is used to calculate the TWS trend by best-fit linear regression. The RL05M solution
provides 0.5-degree gain factors simulated by the Community Land Model
27
. However, this model lacks surface water (SW) compartments (e.g., lakes and glaciers)
and human processes, and the least-squares correction in the factor derivation tends
to be dominated by the annual cycles of land water storage variations. Despite a partial
recovery of the signal variation, the gain factors may not be suitable for calculating
TWS trends at sub-mascon resolution. For these reasons, they are not applied in our
rescaling process. Instead, rescaling-induced uncertainties are accounted for in our
estimated zonal and global trends.
Specifically, uncertainties (e
M
) of monthly M in each enumeration region are propagated from the inherent errors
(e
M
) associated with original mascon data and the rescaling uncertainties (e
r
) induced by signal leakage in fringe mascons. Similar to M, a monthly e
m
is calculated as
Σ
(
a
i
e
i
)
2
/
Σ
a
i
, where e
i
denotes the provided data uncertainty for each mascon i that intersects with this
region. To infer e
r
, we compute the intersection area (a
i
) as a proportion (P) of each mascon (Fig. S15). A fringe mascon is indicated by a
value of P between 0 and 1 (hereafter “internal fringe portion”). For each month,
we first calculate the average EWT anomaly in the mascons enclosed by this region
(i.e., P = 1). This assesses the signal in the region interior exclusive of external
leakage impacts, despite a sacrifice of the signal in the internal fringe portion.
We then lower the threshold (t) of P by a step of 0.05, and calculate the average
anomaly (M
t
) in the full mascons with P ≥ t, until t = 0 (i.e., all fringe mascons included).
In this way, M
t
gradually picks up the missing signal within this endorheic region as the internal
fringe portion decreases. Meanwhile, it absorbs increasing signal leakage as the external
fringe portion expands. The variance of M
t
, therefore, reflects the uncertainty of signal scaling at sub-mascon resolution.
Given this logic, the standard deviation in the array of M
t
(Fig. S16) is used as a measure of this monthly e
r
. Time series e
M
and the variation of residuals from the trend fitting are then propagated to infer
a 95% CI of the TWS trend using a Monte Carlo method as in Wang et al
55
.
To further evaluate our estimated TWS changes, we determine how the EWT trend in each
region changes from its endorheic interior to periphery. This is done by calculating
the linear trend in monthly M
t
with a gradually lowered t, as shown in Fig. S17 (blue profiles). For a region under
a net TWS decline, a rising profile implies that the rate of water loss tends to weaken
as one moves away from the endorheic interior. If we assume that this pattern is also
true at sub-mascon scales, the magnitude of EWT decline in the internal portion of
a fringe mascon would be greater than that in the external portion. Our signal scaling
based on simple area partitioning of the fringe mascons thus underrates the actual
water loss in the peripheral endorheic areas (where signals of weaker decline leak
into the internal portions), leading to an overall conservative TWS trend for this
enumeration region. This case applies to the entire endorheic system and most zones
that experienced TWS declines. The exception in Dry Andes/Patagonia (Fig. S17c) is
likely attributed to the complex endorheic boundary (Fig. S15a) and the leakage of
stronger EWT declines from the exorheic Andes. In the Aral Sea Basin, fully enclosed
mascons are found in the Amu Darya and Syr Darya regions (Fig. S15c) but the most
significant water loss occurred in the Aral Sea. This explains the weak initial decline
(when P = 1 in Fig. S17i) in this region. As P continues to decrease, the EWT trends
are overall stable (black profile) despite increasing leakage of water loss in the
nearby Caspian Sea (blue profile). Similarly, a decreasing profile for any region
under a net TWS gain implies that our estimated TWS increase is likely underrated.
This is seen in the GRVSA (Fig. S17e) and ITP (Fig. S17j). However, since their total
water gain accounts for a marginal proportion (~17%) of the total water loss in the
other regions, our reported net TWS decline in global endorheic basins is overall
conservative (Fig. S17a).
Although our results do not apply the mascon-set of 0.5-degree gain factors, their
impact is assessed by comparing EWT trends calculated with versus without the gain
factors for each endorheic zone (black and red profiles in Fig. S17). Because the
inclusion of gain factors only affects signal rescaling at sub-mascon resolution,
the EWT trends at each t are calculated from the average anomalies within the intersected
or internal mason portions (where P ≥ t). The profiles illustrate how EWT trends between
the two solutions (with and without gain factors) increasingly differ as more incomplete
mascons are included in rescaling. The two solution profiles appear highly consistent
in each zone, and their divergence is enclosed by the 95% CIs induced by the inherent
mascon data errors (transparent shades). Therefore, including the gain factors will
make no significant difference to the estimation of global/zonal TWS trends.
Estimating lake storage changes.
We calculate storage changes in 142 large waterbodies (a total area of ~540k km2;
Figs. S1–S2) that account for ~75% of the lakes/reservoirs in area and ~98% in volume
across endorheic basins
56,57
. Level time series during our study period are collected from multi-mission altimeter
observations (e.g., Envisat, Jason, TOPEX/Poseidon, and SARAL/AltiKa), as archived
in the Database for Hydrological Time Series of Inland Water (DAHITI)
58
(https://dahiti.dgfi.tum.de/en), the Hydroweb
59
(http://hydroweb.theia-land.fr), and the USDA G-REALM (www.pecad.fas.usda.gov/cropexplorer/global_reservoir).
Hypsometry is considered for 38 (87% in area) of the 142 lakes, where level-area functions
for 8 largest lakes (79%) are calibrated in this study using time-variable inundation
areas mapped from MODIS imagery (250-m MOD09Q1) (Figs. S3–S10), and level-area functions
for the other 30 lakes (8%) are retrieved from the Hydroweb. For each of these 38
lakes, time series volume anomalies are calculated as the integrals of the hypsometric
function from the average water level, and the mean volume seasonality is further
removed for linear trend fitting. Volume anomalies in each of the remaining 104 lakes
(13%) are approximated by water level time series that are assumed to vary with a
static inundation area mapped from Landsat imagery acquired during 2008–2009 (representing
the middle-stage extent during our study period) using methods in Sheng et al
57
.
Multiple error sources are identified to propagate the uncertainties of lake volume
anomalies, which are used to infer 95% CIs for lake storage trends by the Monte Carlo
method
55
(as for TWS trends). For the 8 lakes with calibrated hypsometry, error sources include
(i) level uncertainties provided in the altimetric data, (ii) mapping errors for inundation
area, estimated from a relative bias of 5% in MODIS-based large waterbody extraction
60
, and (iii) uncertainties in calibrated hypsometry, calculated as the RMSE of fitted
level-area functions (Figs. S3–S10). For each of the remaining 134 lakes, the trend
CI is propagated from source (i), and another error term that attempts to reflect
the overall uncertainty due to unknown fitting errors in the hypsometry retrieved
from Hydroweb (for the 30 lakes), the ignored lake area variation (for the other 104
lakes), and gaps in the acquired level time series. We quantify this error term to
be 14% (95% CI) of each lake storage trend, inferred from the 8 lakes where storage
trends estimated using Hydroweb hypsometry or only water levels are validated against
the estimates using our calibrated hypsometry. For the other smaller waterbodies where
storage changes are unquantified in our study, we consider that they in total generate
a 95% uncertainty of 10 Gt yr−1. If assuming lake volume change is proportional to
lake area (akin to a simple bucket model where water budget variations reflect precipitation-evaporation
residuals multiplied by the bucket cap size), we have one third of the net annual
water loss in our studied 142 lakes to be ~10 Gt yr−1. This uncertainty is partitioned
to different endorheic zones by their total small waterbody areas.
Estimating glacier mass changes.
Changes in glacier mass balance are estimated for three secondary zones in Central
Eurasia (ITP, the Aral Sea Basin, and Others; Fig. 4a) that contain ~98% of the total
glacier extent in global endorheic basins (Fig. S11). Our estimations are based on
the 30-m gridded dataset of glacier surface elevation changes (thereafter dh/dt) from
2000 to 2016 in High Mountain Asia (HMA)
11
. The rates of dh/dt are derived by fitting a linear regression through time series
of co-registered digital elevation models (DEMs) constructed from ASTER stereo images
during 2000–2016. Details are given in Brun et al.
11
.
We obtain 132 dh/dt maps (in 1° grid with estimation uncertainties) covering the endorheic
HMA. Pixels over non-glacierized regions are masked by the Randolph Glacier Inventory
6.0
61
. Over the glacierized regions, pixels with absolute dh/dt rates above 50 m yr−1 are
excluded as noise. Similar to Brun et al.
11
, Gardelle et al.
62
and Neckel et al.
63
, glacier-hypsometry-averages are used to represent the average dh/dt for region-wide
units. To reduce the uncertainty due to spatial heterogeneity of glacier changes,
we divide the glacierized areas into several sub-regions
11,64
including northwestern ITP, southern ITP, Qilian Mountains, Kunlun Mountains within
the Tarim Basin, southern Tian Shan, northern Tian Shan, the Pamirs, and the remaining
areas. Glacierized areas in each sub-region are considered as one virtual contiguous
ice body, where glacier hypsometry is calculated using 100-m elevation bands discretized
by the ALOS World 3D-30m DEM
65
. For each elevation band, dh/dt pixel values are filtered to the level of three normalized
absolute deviations relative to the median of the elevation band
11
. Filtered dh/dt values are averaged for each elevation band, and the rate of volume
change is calculated as the sum of the mean dh/dt multiplied by the glacier area in
this band. The volume change is converted to mass change assuming a conversion factor
of 850 (±60) kg m−3 66
and a negligible difference between the rates in 2000–2016 and 2002–2016. Glacier
mass change rates for different elevation bands are then subtotaled to secondary endorheic
zones (Table S2).
Besides the above-mentioned secondary zones in Central Eurasia, small clusters of
glaciers scattered in the Caspian Sea Basin (726 km2 or 0.02% of the zonal area),
Dry Andes/Patagonia (438 km2 or 0.03%), and Western North America (17 km2 or <0.01%)
(Fig. S11; Table S3). By referring to previous studies of glacier changes around these
zones
64,67,68
, glacier mass changes may only account for miniscule portions of the zonal TWS declines
(Table S3, where glacial changes are largely under the TWS change uncertainties).
For this reason, glacier mass changes in these zones are not explicitly quantified,
and instead considered as modeled SWE variations over their glacierized regions.
Partitioning net TWS changes.
We partition GRACE-observed net TWS changes to SW, soil moisture (SM), and groundwater
contributions through a comprehensive synergy of model simulations and satellite observations.
Considering that some of the frequently used large-scale hydrological models lack
SW and groundwater compartments
69
, we rely on hydrological models only for simulating monthly anomalies in SM, snow
water equivalent (SWE), and canopy water (CW). Storage trends in major waterbodies
and GIC are derived from multi-mission satellite measurements (see previous sections),
and then combined with modeled SWE and CW trends to calculate the net SW change (Table
S5). Eventually, the groundwater contribution is separated as the residual between
GRACE-observed TWS change and the estimated SW and SM changes.
Similar to some existing studies
69,70
, we consider two widely-applied global hydrological models (WGHM
71,72
and PCR-GLOBWB
73
) and five land surface models (LSMs) from the Global Land Data Assimilation System
(GLDAS)
74
(CLM, Mosaic, Noah, VIC, and CLSM) to simulate monthly changes in SWE, CW, and SM
during 2002–2016 (see Table S1 for model descriptions). To account for model discrepancies
induced by different climate forcing and parameterizations, we follow a typical ensemble
approach, where deseasonalized multi-model time series are averaged to represent monthly
anomalies and standard deviations among the model time series as ensemble uncertainties.
Because the available modeling period for CLSM and PCR-GLOBWB discontinues after 2014,
their time series are not included in the calculation of ensemble means. Instead,
we compare their time series with the ensemble means from the other five models during
2002–2014, and use the monthly differences to further expand the ensemble uncertainties.
Several studies noticed that the amplitude of SM variation from WGHM is substantially
lower than those of other models
75,76
, which is also seen in our studied endorheic basins (Fig. S18). To avoid possible
biases in trend calculation, WGHM is excluded from the ensemble of SM anomalies, but
is used to infer additional ensemble uncertainties together with CLSM and PCR-GLOBWB.
We also assume that the during the studied GRACE era, direct irrigation impacts on
SM were regional and limited to seasonal timescales, and did not considerably alter
the interannual SM trends at zonal/global scales (also see Supplementary Information).
Our modeled SM anomalies are validated against in situ measurements from the Soil
Climate Analysis Network (SCAN; www.wcc.nrcs.usda.gov/scan) in endorheic North America
(Fig. S19). For most SCAN stations, deseasonalized SM time series from measurements
and models show significant correlations, and the discrepancies between their interannual
trends are within the 95% CIs. Detailed validations are provided in Supplementary
text, Fig. S20, and Table S6.
As previously described, our glacier mass changes are based on detected elevation
changes from stereo-correlated time series DEMs
11
. These changes include the contributions of both alpine glaciers and snowpack. To
avoid double-counting, we replace modeled SWE over glacierized endorheic HMA by satellite-observed
glacier mass changes. This replacement also minimizes the influence of modeled SWE
errors that are often amplified in alpine environments
77,78
. To further validate modeled SWE changes in other regions, we select endorheic North
America with high-quality SWE estimates from the Snow Data Assimilation (SNODAS) program
79
(Supplementary text). The time series of modeled and SNODAS anomalies show evident
differences in magnitude, but agree fairly well in interannual trend (with a discrepancy
insignificant to the CIs; Fig. S21). Although this validation is limited in North
America, the amount of water stored in snowpack and canopies in endorheic basins is
relatively small. This is reflected by the combined loss of SWE and CW (3.64 (±1.90)
Gt yr−1), contributing <4% of the global endorheic TWS loss (Table S5). Thus the influence
of their modeling uncertainties on our TWS partitioning is likely miniscule.
Assessing TWS responses to climate forcing.
Climate impacts on TWS changes are assessed by exploring (i) the correlations between
annual net TWS changes and total precipitation and (ii) the trends in monthly temperature
anomalies, for the global endorheic system and each endorheic zone (Fig. S13). We
emphasize TWS changes in response to precipitation on an annual basis, in order to
remove the influence of correlations dominated by seasonal variation. We calculate
temperature trends to assess recent warming in endorheic regions and facilitate the
discussion of warming-induced glacier retreat and possible enhancement of potential
evapotranspiration. It is worth noting that evapotranspiration responds to radiative
and aerodynamic variables in addition to temperature
80
, so we do not claim that warming alone necessarily caused the observed TWS loss.
However, since existing evapotranspiration data do not adequately account for the
impact of open surface water, the response of TWS changes to actual evapotranspiration
is not explored.
To account for uncertainties in climate variables, we retrieve the monthly means of
precipitation and temperature anomalies during 2002–2016 from multiple observation/assimilation
sources. Sources of precipitation data include the CPC Merged Analysis of Precipitation
(CMAP)
81
(www.esrl.noaa.gov/psd/data/gridded/data.cmap.html), the Global Precipitation Climatology
Center (GPCC) precipitation
82
(total full v7; www.esrl.noaa.gov/psd/data/gridded/data.gpcc.html), the Global Precipitation
Climatology Project (GPCP)
83
(www.esrl.noaa.gov/psd/data/gridded/data.gpcp.html), and the PRECipitation REConstruction
over Land (PREC/L)
84
(www.esrl.noaa.gov/psd/data/gridded/data.precl.html). As merged analysis and reanalysis
precipitation data tend to show evident uncertainties over ITP
85
, its precipitations are acquired from a 0.25° gridded observation dataset
85–87
provided by the National Climate Center of China Meteorological Administration. Sources
of temperature data include the NOAA Global Surface Temperature
88,89
(www.esrl.noaa.gov/psd/data/gridded/data.noaaglobaltemp.html), the Berkeley Earth
Surface Temperature
90
(http://berkeleyearth.org/data), and mean surface air temperature from the GLDAS LSMs.
Data availability.
Calculated water storage changes in global endorheic regions are distributed through
PANGAEA (doi: in process). Storage changes in major lakes and reservoirs are available
upon reasonable request to the corresponding author (JW). Glacier mass change data
are available through Nature Geoscience article doi:10.1038/NGEO2999.
Code availability.
All analytical codes generated in this paper are available upon request.
Supplementary Material
1