Introduction
Of all Asian basins that find their headwaters in the greater Himalayas, the
Indus basin depends most strongly on high-altitude water resources
(Immerzeel et al., 2010; Lutz et al., 2014) The largest glacier systems
outside the polar regions are found in this area and the seasonal snow cover
is the most extensive of all Asian basins (Immerzeel et al., 2009). In
combination with a semi-arid downstream climate, a high demand for water
as a result of the largest irrigation scheme in the world and a large and quickly
growing population, the importance of the upper Indus basin (UIB) is evident
(Immerzeel and Bierkens, 2012).
Overview of the UIB (Lehner et al., 2008), basin
hypsometry and three gridded precipitation products. (a) shows the
digital elevation model, the location of the major glacier systems (area
> 5 km2), the available stations in the Global Summary of
the Day (GSOD) of the World Meteorological Organization (WMO) and the
hydrological stations used for validation. Panel B shows box plots of the
elevation distribution of the basin, the large glacier systems, the GSOD
meteorological stations and the average elevation of the catchment area of
each hydrological station. (c) to (e) show the average gridded annual
precipitation between 1998 and 2007 for the APHRODITE (Yatagai et al., 2012),
TRMM (Huffman et al., 2007) and ERA-Interim (Dee et al., 2011) data sets.
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The hydrology of the UIB (4.37 × 105 km2) is,
however, poorly understood. The quantification of the water balance in space
and time is a major challenge due the lack of measurements and the
inaccessibility of the terrain. The magnitude and distribution of high-altitude precipitation, which is the driver of the hydrological cycle, is
one of its largest unknowns (Hewitt, 2005, 2007; Immerzeel et al., 2013;
Mishra, 2015; Ragettli and Pellicciotti, 2012; Winiger et al., 2005). Annual
precipitation patterns in the UIB result from the intricate interplay
between synoptic scale circulation and valley scale topography–atmosphere
interaction resulting in orographic precipitation and funnelling of air
movement (Barros et al., 2004; Hewitt, 2013). At the synoptic scale, annual
precipitation originates from two sources: the south-eastern monsoon during
the summer and moisture transported by the westerly jet stream over central
Asia (Mölg et al., 2013; Scherler et al., 2011) during winter. The
relative contribution of westerly disturbances to the total annual
precipitation increases from south-east to north-west, and the anomalous
behaviour of Karakoram glaciers is commonly attributed to changes in winter
precipitation (Scherler et al., 2011; Yao et al., 2012).
At smaller scales the complex interaction between the valley topography and
the atmosphere dictates the spatial distribution of precipitation (Bookhagen
and Burbank, 2006; Immerzeel et al., 2014b). Valley bottoms, where stations
are located, are generally dry and precipitation increases up to a certain
maximum altitude (HMAX) above which all moisture has been orographically
forced out of the air and precipitation decreases again. In westerly
dominated rainfall regimes HMAX is generally higher, which is likely related
to the higher tropospheric altitude of the westerly airflow (Harper, 2003;
Hewitt, 2005, 2007; Scherler et al., 2011; Winiger et al., 2005).
Gridded precipitation products are the de facto standard in hydrological
assessments, and they are either based on observations (e.g. APHRODITES;
Yatagai et al., 2012), remote sensing (e.g. the Tropical Rainfall
Monitoring Mission; Huffman et al., 2007) or re-analysis (e.g. ERA-Interim;
Dee et al., 2011) (Fig. 1c–e). In most cases the station data
strongly influence the distribution and magnitude of the precipitation in
those data products; however, the vast majority of the UIB is located at
elevations far beyond the average station elevation (Fig. 1a–b).
The few stations that are at elevations above 2000 m are located in dry
valleys and we hypothesise that the high-altitude precipitation is
considerably underestimated (Fig. 1c–e). Moreover, remote-sensing-based products, such as the Tropical Rainfall Measuring Mission (TRMM), are insufficiently capable of capturing
snowfall (Bookhagen and Burbank, 2006; Huffman et al., 2007) and the spatial
resolution (25–75 km2) of most rainfall products (and the underlying
models) is insufficient to capture topography–atmosphere interaction at the
valley scale (Fig. 1c–e). Thus, there is a pressing need to
improve the quantification of high-altitude precipitation, preferably at
large spatial extents and at high resolution.
A possible way to correct mountain precipitation is to inversely close the
water balance. Previous studies in Sweden and Switzerland have shown that it
is possible to derive vertical precipitation gradients using observed runoff
in a physically realistic manner (Valéry et al., 2009,
2010). Earlier work at the small scale in high mountain Asia suggested that
the glacier mass balance may be used to reconstruct precipitation in its
catchment area (Harper, 2003; Immerzeel et al., 2012a). Figure 1a and b
show that UIB glaciers are located at high elevations that are not
represented by station data. Therefore, the mass balances of the glaciers may
contain important information on high-altitude accumulation in an area that
is inaccessible and ungauged, but very important from a hydrological point
of view. In this study we further elaborate this approach by inversely
modelling average annual precipitation from the mass balance of 550 large
(> 5 km2) glacier systems located throughout the UIB. We
perform a rigorous uncertainty analysis and we validate our findings using
independent observations of river runoff.
Methods
We estimate high-altitude precipitation by using a glacier mass balance
model to simulate observed glacier mass balances. We use a gridded data set
from valley bottom stations as a basis for our precipitation estimate and we
compute a vertical precipitation gradient (PG; % m-1) until observed mass
balances match the simulated mass balance. We repeat this process for the
550 major glacier systems in the UIB, and the resulting PGs are then
spatially interpolated to generate a spatial field that represents the
altitude dependence of precipitation. We use this field to update the
APHRODITE precipitation and generate a corrected precipitation field that is
able to reproduce the observed glacier mass balance. We validate the
findings independently with a water balance approach. Estimated (annual)
runoff, based on the corrected precipitation, actual evapotranspiration
based on four gridded products and the observed glacier mass balance, is
compared with an extensive set of UIB runoff observations. We also analyse
the physical realism of our simulations by deriving a Turc–Budyko plot using
precipitation, measured runoff and potential evapotranspiration. A rigorous
uncertainty analysis is also conducted on the six most critical model
parameters including potential effects of spatial correlation.
Averages (μ) and standard deviations (σ) of
predictors for the precipitation gradient. Values and ranges are based on
literature as follows: HREF and HMAX: Hewitt (2007, 2011), Immerzeel et al. (2012b,
2014b), Putkonen (2004), Seko (1987) and Winiger et al. (2005); DDFd and
DDFdf: Azam et al (2012), Hagg et al. (2008), Immerzeel et al. (2013), Mihalcea
et al. (2006) and Nicholson and Benn (2006); MB: Kääb et al. (2012a).
Variable
Acronym
Distribution
μ
σ
Reference elevation (m)
HREF
log-Gaussian
2500
500
Maximum elevation (m)
HMAX
log-Gaussian
Himalaya
4500
500
Karakoram
5500
500
Hindu Kush
5500
500
Degree day factor debris-covered glaciers (mm ∘C-1 d-1)
DDFd
log-Gaussian
2
2
Degree day factor debris-free glaciers (mm ∘C-1 d-1)
DDFdf
log-Gaussian
7
2
Threshold slope (m m-1)
TS
log-Gaussian
0.2
0.05
Mass balance (m w.e. yr-1)
MB
Gaussian
Himalaya
-0.49
0.57
Hindu Kush
-0.21
0.76
Karakoram
-0.07
0.61
Average annual actual evapotranspiration between 2003 and 2007 for
ERA-Interim (a), MERRA (b), ET-Look (c) and PCR-GLOBWB.
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Data sets
Glacier mass balance and outlines
Glacier mass balance trends based on NASA's Ice, Cloud and land
Elevation Satellite (ICESat) (Kääb et al., 2012a) are
recomputed for the period 2003 until 2008 for the three major mountain
ranges in the UIB: the Karakoram, the Hindu Kush and the Himalaya (Fig. 1).
For each zone the mass balance is computed including a regional uncertainty
estimate (Kääb et al., 2012a). From the zonal uncertainty (σz)
we estimate the standard deviation between glaciers within a zone
(σg) as
σg=σzn,
where n is the number of glaciers within a zone. The σg values
used in the uncertainty analysis are shown in Table 1.
The glacier boundaries are based on the glacier inventory of the International
Centre for Integrated Mountain Development (Bajracharya and Shrestha, 2011).
Monthly relation between observed temperatures at meteorological
stations (OBS) and the APHRODITE temperature fields (APHRO) (Yasutomi et
al., 2011).
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Precipitation and temperature
The daily APHRODITE precipitation (Yatagai et al., 2012) and air temperature
data sets (Yasutomi et al., 2011) from 2003 until 2007 are used as reference
data sets to ensure maximum temporal overlap with the ICESat-based glacier
mass balance data set (Kääb et al., 2012a). The precipitation data set
is resampled from the nominal resolution of 25 km2 to a resolution of
1 km2 using the nearest neighbour algorithm. The air temperature data set is
then bias corrected using monthly linear regressions with independent
station data to account for altitudinal and seasonal variations in air
temperature lapse rates (Fig. 3).
Runoff and evapotranspiration
We use runoff data, potential evapotranspiration (ETp) and actual evapotranspiration (ETa) data
for the validation of our results. For runoff we compiled all available
published data, which we complemented with data made available by the
Pakistan Meteorological Department and the Pakistan Water and Power
Development Authority.
Evapotranspiration is notoriously difficult to monitor and there are few
direct measurements of ETa in the upper Indus. In earlier UIB studies, ET
was estimated using empirical formulae based on air temperature but was
only applied to the Siachen glacier (Bhutiyani, 1999; Reggiani and Rientjes,
2014). We take into account the uncertainty in ET in our streamflow
estimates and develop a blended product based on re-analysis data sets, a
global hydrological model and an energy balance model. Four gridded ETa and
three gridded ETp products were resampled to a 1 km2 resolution at which
we perform all our analyses:
ERA-Interim re-analysis (Dee et al., 2011): ERA-Interim uses the HTESSEL
land-surface scheme (Dee et al., 2011) to compute ETa. For transpiration a distinction is made between high and low
vegetation in the HTESSEL scheme and these are parameterised from the Global
Land Cover Characteristics database at a nominal resolution of 1 km2.
Modern-Era Retrospective Analysis for Research and Applications (MERRA) re-analysis (Rienecker et al., 2011): the MERRA re-analysis
product of NASA applies the state-of-the-art GEOS-5 data assimilation system
that includes many modern observation systems in a climate framework. MERRA
uses the GEOS-5 catchment land surface model (Koster et al., 2000) to
compute actual ET. For the MERRA product ETp is not available.
ET-Look (Bastiaanssen et al., 2012): The ET-Look remote sensing
model infers information on ET from combined optical and passive microwave
sensors, which can observe the land surface even under persistent overcast
conditions. A two-layer Penman–Monteith forms the basis of quantifying soil
and canopy evaporation. The data set is available only for the year 2007, but
it was scaled to the 2003–2007 average using the ratio between the
2003–2007 average and the 2007 annual ET based on ERA-Interim.
PCR-GLOBWB (Wada et al., 2014): The global hydrological model
PCR-GLOBWB computes actual evapotranspiration using potential
evapotranspiration based on Penman–Monteith, which is further reduced based
on available soil moisture.
The average annual ETa for the period 2003–2007 for each of the four
products is shown in Fig. 2. The spatial patterns show good agreement, but
the magnitudes differ considerably. The ensemble mean ETa for the entire
upper Indus equals 359 ± 107 mm yr-1.
Model description
We use the PCRaster spatial–temporal modelling environment (Karssenberg et
al., 2001) to model the mass balance of the major glaciers in each zone and
subsequently estimate precipitation gradients required to sustain the
observed mass balance. The model operates at a daily time step from 2003
to 2007 and a spatial resolution of 1 km2. For each time step the
total accumulation and total melt are aggregated over the entire glacier
surface. Only glaciers with a surface area above 5 km2 are included in
the analysis (Karakoram is 232 glaciers, Hindu Kush is 119,
Himalaya is 204 glaciers), as the ICESat measurements do not reflect
smaller glaciers. The model is forced by the spatial precipitation and
temperature fields. The precipitation fields are corrected using a
PG (% m-1). Precipitation is positively
lapsed using a PG between a reference elevation (HREF) to an elevation of
maximum precipitation (HMAX). At elevations above HMAX, the precipitation is
negatively lapsed from its maximum at HMAX with the same PG according to
Pcor=PAPHRO⋅(1+(H-HREF))⋅PG⋅0.01)
for HREF < H ≤ HMAX, and
Pcor=PAPHRO⋅(1+(((HMAX-HREF)+(HMAX-H))⋅PG⋅0.01)
for H > HMAX.
HREF and HMAX values are derived from literature (Table 1) and uncertainty
is taken into account in the uncertainty analysis. HMAX varies per zone and
lies at a lower elevation in the Himalayas than in the other two zones
(Table 1). We spatially interpolate HMAX from the average zonal values to
cover the entire UIB.
The melt is modelled over the glacier area using the positive degree day
method (Hock, 2005), with different degree day factors (DDFs) for
debris-covered (DDFd) and debris-free (DDFdf) glaciers derived from
literature (Table 1). To account for uncertainty in DDFs, the DDFd and DDFdf
are taken into account separately in the uncertainty analysis. At
temperatures below the critical temperature of 2 ∘C (Immerzeel et al., 2013;
Singh and Bengtsson, 2004), precipitation falls in the form of snow and
contributes to the accumulation. Avalanche nourishment of glaciers is a key
contributor for UIB glaciers (Hewitt, 2005, 2011) and to take this process
into account, we extend the glacier area with steep areas directly adjacent
to the glacier with a slope over an average threshold slope (TS) of 0.2 m m-1.
This average threshold slope is derived by analysing the slopes of all
glacier pixels in the basin (Fig. 4). To account for uncertainty in
TS,
this parameter is taken into account in the uncertainty analysis.
For each glacier system, we execute transient model runs from 2003 to 2007
and we compute the average annual mass balance from the total accumulation
and melt over this period. We make two different runs for each glacier
system with two different PGs (0.3 and 0.6 % m-1) and we use the
simulated mass balances of these two runs and the observed mass balances
based on ICESat to optimise the PG per glacier, such that the simulated mass
balance matches the observed.
To interpolate the glacier-specific PG values to PG spatial fields over the
entire domain we use geostatistical conditional simulation (Goovaerts,
1997). Simulated spatial fields of PGs are thus conditioned on the PGs
determined at the glacier's centroid. The semi-variogram has the following
parameters: nugget = 0, the range = 120 km, sill is the variance of PGs.
Box plots of slopes of glacierised areas per elevation bin.
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Corrected precipitation and estimated uncertainty for the UIB for
the case with intermediate spatial correlation between model parameters.
(a) shows the average modelled precipitation field based on 10 000
simulations for the period 2003–2007, (b) shows the ratio of corrected
precipitation to the uncorrected APHRODITE precipitation for the same
period, (c) shows the standard deviation of the 10 000 simulations and
(d) shows the average precipitation gradient.
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Uncertainty analysis
A rigorous uncertainty analysis is performed to take into account the
uncertainty in parameter values and uncertainty in regional patterns. To
account for parameter uncertainty, we perform a 10 000 member Monte Carlo
simulation on the parameters given in Table 1. For each run we randomly
sample the parameter space based on the average (μ) and the standard
deviation (σ), which are all based on literature values. For the
positively valued parameters, we use a log-Gaussian distribution and a
Gaussian distribution in case parameter values can be negative. We take into
account uncertainty in the following key parameters (HREF, HMAX, DDFd,
DDFdf, TS) for the PG as well as uncertainty in the mass balance against
which the PG is optimised (mass balance, MB). We randomly vary the five parameters (HREF,
HMAX, DDFd, DDFdf, TS) 10 000 times and calculate the PG for each glacier
for each random parameter set drawn, thus resulting in 10 000 PG sets for
each glacier considered. For each of the 10 000 PG sets, we then use
conditional simulation (see above) to arrive at 10 000 equally probable
spatial PG fields, taking account of parameter's uncertainty, mass-balance
uncertainty and the interpolation error. Note that for each of the 10 000
sets, the variogram is scaled with the variance of the PGs associated with
the specific parameter combination drawn. Finally, based on the results of
the 10 000 simulations we derive the average-corrected precipitation field
and the associated uncertainty in the estimates
Using the 10 000 combinations of parameters and associated PGs, we ran a
multi-variate linear regression analysis to determine relative contribution
of each parameter to the spread in the PG to understand which parameter has
the largest influence on the PG.
It is possible that certain parameters used in the model are spatially
correlated. To account for uncertainty in this spatial correlation and the
presence of spatial patterns in the parameters, we perform a sensitivity
analysis where we consider three cases:
Fully correlated: we assume the parameters are spatially fully
correlated within a zone, e.g. for each of the 10 000
simulations a parameter has the same value within a zone.
Uncorrelated: we assume the parameters are spatially uncorrelated
and within each zone each glacier system is assigned a random value.
Intermediate case: we use geostatistical unconditional simulation
(Goovaerts, 1997) with a standardised semi-variogram (nugget = 0, sill is the variance
of parameter, range = 120 km) to simulate parameter values for each glacier system.
Validation
We estimate the average annual runoff (Q) for sub-basins in the UIB from
Q=Pcor-ET+MB,
where Pcor is the average corrected precipitation, ET the
average annual evapotranspiration based on the four products described above
and MB the glacier mass balance expressed over the sub-basin area in
mm yr-1. We then compare the estimated runoff values to the observed
time series (Table 2).
Runoff stations used for validation. Catchment areas are delineated
based on SRTM DEM (Shuttle Radar Topographic Mission – digital elevation model). a is calculated based on discharge provided by the
Pakistan Water and Power Development (WAPDA), b is based on Mukhopadhyay
and Khan (2014a), c is based on Sharif et al. (2013), d is based on
Archer (2003) and e is based on Khattak et al. (2011).
Station
Lat
Long
Area (km2)
Catchment mean elevation (m)
Observed Q (m3 s-1)
Period
Besham Qilaa
34.906
72.866
198 741
4598
2372.2
2000–2007
Tarbela inflowa
34.329
72.856
203 014
4532
2370.3
1998–2007
Mangla inflowa
33.200
73.650
29 966
2494
831.8
1998–2007
Marala inflowa
32.670
74.460
29 611
3003
956.5
1998–2007
Dainyor bridgea
35.925
74.372
14 147
4468
331.8
1998–2004
Skardu-Kachurab
35.435
75.468
146 200
4869
1074.2
1970–1997
Partab Bridgeb
35.767
74.597
177 622
4747
1787.9
1962–1996
Yogob
35.183
76.100
64 240
5048
359.4
1973–1997
Kharmongb
34.933
76.217
70 875
4795
452.3
1982–1997
Gilgitb
35.933
74.300
13 174
4039
286.7
1960–1998
Doyianb
35.550
74.700
4000
3987
135.7
1974–1997
Chitralc
35.867
71.783
12 824
4086
271.9
1964–1996
Kalamc
35.467
72.600
2151
3874
89.6
1961–1997
Naranc
34.900
73.650
1181
3881
48.1
1960–1998
Alam bridgec
35.767
74.600
28 201
4228
644.0
1966–1997
Chakdarac
34.650
72.017
5990
2701
178.9
1961–1997
Karorac
34.900
72.767
586
2260
21.2
1975–1996
Garhi Habibullahc
34.450
73.367
2493
3303
101.8
1960–1998
Muzafferabadc
34.430
73.486
7604
3245
357.0
1963–1995
Chinaric
34.158
73.831
14 248
2513
330.0
1970–1995
Kohalac
34.095
73.499
25 820
2751
828.0
1965–1995
Kotlic
33.525
73.890
2907
1901
134.0
1960–1995
Shigarb
35.422
75.732
6681
4591
202.6
1985–1997
Phulrad
34.317
73.083
1106
1613
19.2
1969–1996
Daggard
34.500
72.467
534
1085
6.9
1969–1996
Warsake
34.100
71.300
74 092
2828
593.0
1967–2005
Shatial Bridgeb
35.533
73.567
189 263
4667
2083.2
1983–1997
For the three zones (Himalaya, Karakoram and Hindu Kush) we also perform a
water balance analysis to verify whether the use of the corrected
precipitation product results in a more realistic closure of the water
balance. Finally, we test the physical realism of the corrected precipitation
product using a non-dimensional Turc–Budyko plot as described in Valéry
et al. (2010). This plot is based on two assumptions: (i) the mean annual
runoff should not exceed the mean annual precipitation and (ii) the mean
annual runoff should be larger than or equal to the difference between
precipitation and potential evapotranspiration. By plotting P / ETp versus
Q / P on a catchment basis, it is tested whether the use of corrected precipitation
results in more physically realistic values.
Results and discussion
Corrected precipitation
The average annual precipitation based on 10 000 conditionally simulated
fields reveals a striking pattern of high-altitude precipitation. The amount
of precipitation required to sustain the large glacier systems is much higher
than either the station observations or the gridded precipitation products
imply. For the entire UIB the uncorrected average annual precipitation
(Yatagai et al., 2012) for 2003–2007 is 437 mm yr-1
(191 km3 yr-1), an underestimation of more than 200 % compared
with our corrected precipitation estimate of 913 ± 323 mm yr-1
(399 ± 141 km3yr-1; Fig. 5). The greatest corrected annual
precipitation totals in the UIB (1271 mm yr-1) are observed in the
elevation belt between 3750 to 4250 m (compared to 403 mm yr-1 for
the uncorrected case). In absolute terms the main water-producing region is
located in the elevation belt between 4250 and 4750 m where approximately
78 km3 of rain and snow precipitates annually.
In the most extreme case, precipitation is underestimated by a factor 5 to 10
in the region where the Pamir, Karakorum and Hindu Kush ranges intersect
(Fig. 5). Our inverse modelling shows that the large glacier systems in the
region can only be sustained if snowfall in their accumulation areas totals
around 2000 mm yr-1 (Hewitt, 2007). This is in sharp contrast to
precipitation amounts between 200 and 300 mm yr-1 that are reported by
the gridded precipitation products (Fig. 1). Our results match well with the
few studies on high-altitude precipitation that are available. Annual
accumulation values between 1000 and 3000 mm have been reported for
accumulation pits above 4000 m in the Karakoram (The Batura Glacier
Investigation Group, 1979; Wake, 1989; Winiger et al., 2005). Our results
show that the highest precipitation amounts are found along the
monsoon-influenced southern Himalayan arc with values up to
3000 mm yr-1, while north of the Himalayan range the precipitation
decreases quickly towards a vast dry area in the north-eastern part of the
UIB (Shyok sub-basin). In the north-western part of the UIB, westerly storm
systems are expected to generate considerable amounts of precipitation at
high altitude.
Our results reveal a strong relation between elevation and precipitation with
a median PG for the entire upper Indus of 0.0989 % m-1, but with
large regional differences. Median precipitation gradients in the Hindu Kush
and Karakoram ranges (0.260 and 0.119 % m-1, respectively) are
significantly larger than those observed in the Himalayan range, e.g
0.044 % m-1 (Fig. 6). In the Hindu Kush, for example, for every
1000 m elevation rise, precipitation increases by 260 % with respect to
APHRODITE, which is based on valley floor precipitation. Higher HMAX in the Hindu Kush and the Karakoram (e.g. 5500 m versus
4500 m in the Himalayas; Hewitt, 2007; Immerzeel et al., 2014a; Putkonen,
2004; Seko, 1987; Winiger et al., 2005) suggests that westerly airflow
indeed has a higher tropospheric altitude and that the interplay between
elevation and precipitation is stronger for this type of precipitation.
Further research should thus focus on the use of high-resolution
cloud-resolving weather models (Collier et al., 2014; Mölg et al., 2013)
for this region to further resolve seasonal topography–precipitation
interaction at both synoptic and valley scales.
The estimated precipitation is considerably higher than what was reported in
previous studies. Several studies have used TRMM products to quantify UIB
precipitation (Bookhagen and Burbank, 2010; Immerzeel et al., 2009, 2010) and
they show average annual precipitation values around 300 mm. It was also
noted that the water balance was not closing and average annual river runoff
at Tarbela exceeded the TRMM precipitation (Immerzeel et al., 2009). Two
possible reasons have been suggested to explain this gap: (i) the high-altitude precipitation is underestimated and (ii) the glaciers are in a
significant negative imbalance (Immerzeel et al., 2009). Since the ICESat
study and several other geodetic mass balance studies (Gardelle et al., 2013;
Kääb et al., 2012b) it has become clear that the glaciers in this
region are not experiencing a significant ice loss and that this cannot be
the explanation for the missing water in the water balance. This supports our
conclusion that it is the high-altitude precipitation that has been
underestimated. A study based on long-term observations of Tarbela inflow
also confirm our results (Reggiani and Rientjes, 2014). In this study the
total UIB precipitation above Tarbela is estimated to be
675 ± 100 mm yr-1 and the difference remaining between our
results may stem from the fact that the UIB we consider is twice the size of
the area above the Tarbela, the different approach used to estimate actual
ET, the different period considered and their assumption that ice storage has
not changed between 1961 and 2009.
Box plots of precipitation gradients for the entire UIB and for
the three regions separately.
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Uncertainty
We estimated the uncertainty in the modelled precipitation field with the
standard deviation (σ) of the 10 000 realisations (Fig. 5c). The
signal-to-noise ratio is satisfactory in the entire domain, e.g. the σ
is always considerably smaller than the average precipitation with an average
coefficient of variation of 0.35. The largest absolute uncertainty is found
along the Himalayan arc and this coincides with the precipitation pattern
found here. Strikingly, the region where the underestimation of precipitation
is largest, at the intersection of the three mountain ranges in the northern
UIB, is also an area where the uncertainty is small even though precipitation
gradients are large.
By running a multiple regression analysis after optimising the PGs, we
quantify the contribution of each parameter to the total uncertainty. The
largest source of uncertainty in our estimate of UIB high-altitude
precipitation stems from the MB estimates, followed by the DDFdf, DDFd, TS,
HREF and HMAX, although regional differences are considerable (Fig. 7). The
MB constrains the precipitation gradients and thereby exerts a strong
control over the corrected precipitation fields, in particular because the
intra-zonal variation in MB is relatively large (Table 1). Thus, improved
spatial monitoring techniques of the MB are expected to greatly improve
precipitation estimates.
Figure 8 shows the result of uncertainty analysis associated with the spatial
correlation of the parameters, which reveals that the impact on the average-corrected precipitation is limited. Locally there are minor differences in
the corrected precipitation amounts, but overall the magnitude and spatial
patterns are similar. However, there are considerable differences in the
uncertainty. The lowest uncertainty is found for the fully uncorrelated case,
the fully correlated case has the highest uncertainty whereas the
intermediate case is in between both. For the fully correlated case all
glacier systems have the same parameter set for the specific realisation and
this results in a larger final uncertainty. In the uncorrelated case each
glacier system has a different randomly sampled parameter set and this
reduces the overall uncertainty as it spatially attenuates the variation in
precipitation gradients.
Normalised weights of multiple regression of the precipitation
gradients by the predictors slope (slope threshold for avalanching to
contribute to accumulation), HREF (base elevation from which lapsing
starts), HMAX (elevation with peak precipitation), DDFd (degree day factor
for debris-covered glaciers), DDFdf (degree day factor for debris-free
glaciers) and the MB (mass balance of the glacier).
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Impact of spatial correlation of parameters on the corrected
precipitation field and associated uncertainty. The top panels show the
corrected precipitation field (a) and uncertainty (b) for the
fully uncorrelated case. The middle panels (d, e) for the fully correlated
case and the bottom panels (e, f) for the intermediate case.
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Validation of the precipitation correction using observed discharge
(Table 2). Top panel: the box plots are based on the runoff estimate based on
10 000 corrected precipitation fields (grey: stations for which the observed
record does not coincide with the 2003–2007 period; yellow: stations for
which the 2003–2007 period is part of the observational record; green:
stations for which the observations are based precisely on the 2003–2007
period). The black dots and red diamonds (estimated runoff below 50 m3 s-1)
show the estimated runoff based on the uncorrected
precipitation. The box plots with a red outline have an average elevation
higher than 4000 m. and the box plots with a black outline have an
elevation lower than 4000 m. Bottom panels: water balance components of each
zone (Pcor is corrected precipitation, Porg is uncorrected APHRODITES
precipitation, ET is actual evapotranspiration, Mass is glacier mass
balance, Qcor is estimated runoff and Corg is water balance gap in case
the Porg is used).
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Non-dimensional graphical representation of catchments using
their mean runoff, Q, precipitation, P, and potential evapotranspiration,
PE. The grey line in the empty centre area represents the theoretical Budyko
relationship in the non-dimensional graph. The size of the dots is scaled to
the catchment area.
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Validation
The corrected precipitation is validated independently by a comparison to
published average annual runoff data of 27 stations (Table 2). Runoff
estimates based on the corrected precipitation agree well with the average
observed annual runoff (Fig. 9, top panel). It is interesting to note that
the higher catchments (r = 0.98, red outline) show a better correlation
with the observed runoff than the lower catchments (r = 0.76, black
outline). The runoff estimated for the uncorrected APHRODITE is consistently
lower than the observed runoff, and in some occasions even negative. Runoff
estimates were also made based on the ERA-Interim and TRMM precipitation
products. The TRMM results yield a similar underestimation as the uncorrected
APHRODITES product, but the runoff estimates based on the ERA-Interim
precipitation agrees reasonably well with the observations. However, the
coarse resolution (∼ 70 km2) (Fig. 1) is problematic and cannot
be used to reproduce the mass balance (Fig. 11). Averaged over large
catchments the precipitation may be applied for hydrological modelling, but at
smaller scales there are likely very large biases. As a result, the observed
glacier mass balances cannot be reproduced when the ERA-Interim data set is
used. Although the ERA-Interim data set may not be used to reproduce the
glacier mass balances, it can be used to verify the atmospheric convergence as
the product is based on a data assimilation scheme and the ECMWF IFS forecast
model that includes fully coupled components for atmosphere, land surface and
ocean waves, including closure of the atmospheric water balance. The total
precipitation sum from 1998 to 2007 of the ERA-Interim data set over the
entire UIB is 947 mm, which is very close to our corrected precipitation sum
of 913 mm. This indicates that the westerlies and monsoon circulation
transport sufficient moisture into the region to account for the
precipitation we estimate. The source of precipitation in the upper Indus is
a mixture of the Arabian Sea (westerlies), Bay of Bengal (Monsoon) and
potentially also intra-basin moisture recycling (Tuinenburg et al., 2012; Wei
et al., 2013); however, further research with atmospheric models is required
to quantify these contributions further.
The zonal water balance analysis (Fig. 9, bottom panels) reveals that the
water balance is much more realistic when the corrected precipitation is
used. Although the uncertainties are considerable, our analysis shows that
the Himalaya and Hindu Kush zones are about twice as wet as the Karakoram
zone. For all three zones the glacier mass imbalance only plays a marginal
role in the overall water balance and about 60 % of the total
precipitation runs off while 40% is lost through evapotranspiration.
Notable the values for Corg, which represents the water balance gap in
case the uncorrected precipitation is used, are approximately
500 mm yr-1 in all three zones. Our validation does not take into
account groundwater fluxes and we have assumed that over the observed period
from 2003 to 2007 there is no net loss or gain of groundwater in the upper
Indus basin. We do acknowledge that groundwater may play an important role in
the hydrology. A study in the Nepal Himalaya shows that fractured basement
aquifers fill during the monsoon and they purge in the post-monsoon thus
causing a natural delay in runoff (Andermann et al., 2012). However, this does
not imply significant net gains or losses over multiple year periods, which
is what we consider. A second component that we have not considered and that
may play a role in the high-altitude water cycle is sublimation. There are
some indications that wind redistribution and sublimation may play a
considerable role in the high-altitude water balance (Wagnon et al., 2013).
However, our PGs are constrained on the observed mass balance; hence, our
precipitation can be considered as a net precipitation and sublimation losses
are thus accounted for.
In Fig. 10 the Turc–Budyko plot is shown to confirm the physical realism of
our results. Those dots located in the hatched part of the graph are
physically less realistic. For the uncorrected case almost all dots (open
dots) are above the Q / P = 1 line. For the corrected case the Q / P values are
much more plausible; however, there many catchments that are located slightly
to the right side of the theoretical Budyko line, meaning that the Q is
smaller than the difference between P and ETp. Possible deviation can
potentially be explained by uncertainties in observed flows and ETp
estimates; the fact that in glacierised catchments the theoretical Budyko
curve may be different because of a glacier imbalance can be an additional water
balance term that is unaccounted for, a too short time period that is used to
construct the water balance and, finally, that some of the discharge
observations do not align in time with the rest of the water balance terms.
Overall we conclude though that the use of the corrected precipitation
results in physically more realistic results, where the water balance could
be closed and no significant amount of precipitation input is missing.
Figure 11 shows how the average simulated zonal glacier mass balance using the
corrected, the APHRODITES, the ERA-Interim and the TRMM precipitation
data sets. It shows that none of the precipitation products can reproduce the
observed mass balance. Mostly the mass balances are underestimated, which is
consistent with the underestimation of the precipitation. The ERA-Interim
data set overestimates the mass balance in the Himalaya, but underestimates
the mass balances in the other two zones as a result of the coarse resolution.
Conclusions
In this study we inversely model high-altitude precipitation in the upper
Indus basins from glacier mass balance trends derived by remote sensing.
Although there are significant uncertainties, our results unambiguously show
that high-altitude precipitation in this region is underestimated and that
the large glaciers here can only be sustained if high-altitude accumulation
is much higher than most commonly used gridded data products.
Our results have an important bearing on water resources management studies
in the region. The observed gap between precipitation and streamflow
(Immerzeel et al., 2009) (with streamflow being larger) cannot be
attributed to the observed glacier mass balance (Kääb et al.,
2012a), but is most likely the result of an underestimation of
precipitation, as also follows from this study. With no apparent decreasing
trends in precipitation (Archer and Fowler, 2004), the observed negative
trends in streamflow in the glacierised parts of the UIB should thus be
primarily attributed to decreased glacier and snowmelt (Sharif et al.,
2013) and increased glacier storage (Gardelle et al., 2012). In a recent
study the notion of negative trends in UIB runoff was contested and based on
a recent analysis (1985–2010) it was concluded that runoff of Karakoram
rivers is increasing (Mukhopadhyay and Khan, 2014b). The study suggests that
increase glacier melt during summer is the underlying reason, which in
combination with positive precipitation trends in summer does not contradict
the neutral glacier mass balances in the region. From all of these studies
it becomes apparent that precipitation is the key to understanding behaviour
of glacier and hydrology at large in the UIB. The precipitation we estimate
in this study differs considerably, in magnitude and spatial distribution,
from data sets that are commonly used in design of reservoirs for hydropower
and irrigation and as such it may have a significant impact and improve such
planning processes.
Reconstructed mass balances based on the corrected, APHRODITE,
ERA-Interim and TRMM data sets. The black horizontal dotted line shows the
observed mass balance for each zone.
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The water resources of the Indus River play an important geopolitical role
in the region, and our results could contribute to the provision of
independent estimates of UIB precipitation. We conclude that the water
resources in the UIB are even more important and abundant than previously
thought. Most precipitation at high altitude is now stored in the glaciers,
but when global warming persists and the runoff regime becomes more rain
dominated, the downstream impacts of our findings will become more evident.