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Monitoring of lake level changes on the Tibetan Plateau and Tian Shan
by retracking Cryosat SARIn waveforms
M. Kleinherenbrink
⇑
, R.C. Lindenbergh, P.G. Ditmar
Department of Geoscience and Remote Sensing, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
article info
Article history:
Received 16 June 2014
Received in revised form 17 November 2014
Accepted 22 November 2014
Available online 3 December 2014
This manuscript was handled by
Konstantine P. Georgakakos, Editor-in-Chief,
with the assistance of Marco Toffolon,
Associate Editor
Keywords:
Tibetan Plateau
Tian Shan
Cryosat
Altimetry
Lake levels
Retracking
summary
In this study we present, for the first time, the application of Cryosat SARIn mode data to monitor lakes in
mountainous areas and to find their water balance. By applying a novel retracker, tailored for lake level
observations, we find at least four useable passes for 125 lakes on the Tibetan Plateau and Tian Shan areas
over the period February 2012 to January 2014. From these 125 lakes, 30 are passed at least ten times, for
which we compute trends and periodic variations, and 16 lakes more then twenty times, for which we
additionally apply a water slope correction. This slope correction accounts for geoid inaccuracies or wind
effects. We compared the results over two lakes, Langa Co and Bosten, with Jason-2 measurements. Over
Langa Co we find an RMS difference of 0.55 m, while for Lake Bosten this is only 0.26 m. For Lake Bosten,
the estimated trends, annual and semi-annual variations from the Cryosat and Jason-2 datasets are com-
pared as well. The estimated amplitudes are comparable, while derived phases differ by a few days. Using
the trends of all lakes passed at least ten times, a water volume balance of natural lakes is estimated. A
loss of 1.51 ± 0.11 km
3
y
1
is observed in the lakes in the Tian Shan area. In Tibet, a positive mass balance
is estimated of 1.76 ± 0.24 km
3
y
1
.
Ó2014 Elsevier B.V. All rights reserved.
1. Introduction
The primary objective of this paper is to demonstrate the bene-
fits of a new satellite altimetry mission, Cryosat, for lake level mon-
itoring. The chosen study area is the Tibetan Plateau and Tian Shan.
The first studies to the applications of satellite altimetry to mea-
sure lake levels were performed in the 1990s (Birkett, 1994;
Morris and Gill, 1994). Since the launch of TOPEX/POSEIDON in
1992, several satellites have flown carrying altimeters which were
suitable for lake level measurements, notably ERS-1, ERS-2, GFO,
ICESat, Envisat, Jason-1 and Jason-2. Especially in remote regions
like the Central-Asian mountain ranges, altimetry is essential,
due to the absence of gauges at most lakes. Various studies already
used satellite altimetry data to study lake level changes there
(Phan et al., 2012; Kropác
ˇek et al., 2012; Hwang et al., 2005;
Zhang et al., 2011; Song et al., 2013).
One can distinguish two types of satellite altimeters: laser
altimeters and radar altimeters. A laser altimeter has the advan-
tage of a small footprint, of about 70 m (Schutz et al., 2005), and
is therefore able to measure the water level of almost any lake
on its ground track. Unfortunately, so far ICESat was the only
satellite with a laser altimeter, which limits the time line of mea-
surements to the operational period of this mission, namely
2003–2009. Furthermore, it was operated only for two to three
monthly periods per year, which strongly limits its temporal reso-
lution. Nevertheless, it was shown that water level trends could be
determined for 1~50 lakes in Tibet using ICESat (Zhang et al., 2011;
Phan et al., 2012).
For several lakes in Central-Asia, time series of radar altimetry
measurements are available for a time span of more than twenty
years (Crétaux et al., 2011). However, since the orbits of the radar
altimetry missions vary, lakes are not visited by all altimetry satel-
lites. As a consequence, time series might be shorter than 20 years
and/or gaps might be present. A disadvantage of radar altimeters
for lake level monitoring is their large footprint size, of approxi-
mately 15–20 km. Over mountainous areas this means that their
resolution is typically 5–10 km. As a result, over small lakes or in
near-shore regions, signals from surrounding land surface pollute
the received waveforms. The standard retrackers, which fit a theo-
retical waveform to the received waveforms to obtain geophysical
parameters like elevation, may in this case not estimate lake levels
accurately. Over Tibet, approximately 60 lakes are currently mon-
itored using radar altimetry (Crétaux et al., 2011) with a temporal
resolution of 10–35 days.
http://dx.doi.org/10.1016/j.jhydrol.2014.11.063
0022-1694/Ó2014 Elsevier B.V. All rights reserved.
⇑
Corresponding author. Tel.: +31 620928626.
E-mail address: m.kleinherenbrink@tudelft.nl (M. Kleinherenbrink).
Journal of Hydrology 521 (2015) 119–131
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
In April 2010, the Cryosat satellite was launched. Cryosat orbits
the Earth at 717 km altitude in a 369-day repeat orbit, with an
inclination of 92 degrees (Labroue et al., 2012). As a consequence,
Cryosat has a dense ground track spacing of approximately 7–8 km
at the Equator. Large lakes are even passed more than once per
repeat-cycle, even though the passes occur over different parts of
the lake. It carries a Synthetic aperture Interferometric Radar
ALtimeter (SIRAL), which is able to operate in three different
modes: Low Resolution (LR) mode, Synthetic Aperture Radar
(SAR) mode and SAR Interferometric (SARIn) mode. In LR mode
Cryosat operates as a conventional altimeter, which has an almost
circular footprint. This mode is operated over flat surfaces like
inner Greenland and open ocean. The SAR mode uses multiple
along-track observations and a complex processing chain to
improve the along-track resolution to about 300 m. SAR is mainly
activated over sea ice, where a better resolution is required to esti-
mate the freeboard. Over terrain with significant topography, like
the Tibetan Plateau and Tian Shan, Cryosat is operated in the SARIn
mode, which has an along-track resolution of approximately 300 m
and uses a second antenna to correct for cross-track slope
(Wingham et al., 2006).
The considered SARIn region is indicated by the polygons in
Fig. 4. Most natural lakes inside the polygon are located either on
the Tibetan Plateau or close to the Tian Shan mountain range. Addi-
tionally, there are four man-regulated reservoirs in the area: Pang
Dam, Toktogul, Kapchagay and Kayrakkum. Except for Pang Dam,
they are located in the Northern part of SARIn region, in the coun-
tries of Kyrgyzstan, Kazakhstan and Tajikistan, respectively. The
Pong Dam reservoir is located in the North of India. We distinguish
between natural lakes and man-regulated reservoirs, because the
levels of the latter ones are strongly influenced by the demand
for irrigation, electricity, etc. On the other hand, trends in lakes
are natural and can often be coupled to such phenomena as glacial
melt or precipitation. Furthermore, we show separately the water
balances of the Tibetan Plateau and Tian Shan. For Tibet we include
all lakes South of the Takla Makan desert and East of 75
E. For the
Tian Shan area we include all lakes North of the Takla Makan desert
and North of the Pamir mountain range (which is indicated in
Fig. 4). The lakes in the Tien Shan area are generally larger than
in Tibet and are located at lower altitudes. Tian Shan is known to
suffer from significant glacier surface area decreases (Sorg et al.,
2012), which might affect the discharge of water and therefore
the water levels in lakes. In Tibet retreating glaciers are observed
(Zhang et al., 2013) as well during the last decades and further-
more lake levels have increased (Zhang et al., 2011; Phan et al.,
2012).
In this paper we analyze for the first time the use of Cryosat
SARIn mode data to monitor lake levels in the SARIn region enclos-
ing Tibet and Tien Shan. Cryosat waveforms received over those
lakes are often polluted by surrounding land topography. To obtain
more accurate lake level estimates, we implement the cross-corre-
lation retracker described in (Kleinherenbrink et al., 2014). Using
this retracker an accuracy of several decimeters can be obtained
in near-shore regions. We estimate annual and semi-annual varia-
tions and trends of water levels. Ultimately, we derive water bal-
ances separately for Tibet and Tian Shan.
2. Methodology
2.1. Number of satellite passes over a lake
Due to a nearly-polar orbit Cryosat is flying almost parallel to
the meridians, except in the polar areas. The spacing between
tracks and a lake extent in the West to East direction can therefore
be used to estimate the number of passes over a lake. Since the
orbit has a repeat period of 369 days with approximately 15 revo-
lutions per day, the total number of ascending and descending
tracks N
t
is approximately 5500 per repeat period. Using this num-
ber, the spacing sðhÞof ground tracks at latitude his approximated
by the expression
sðhÞ¼2
p
R
e
cosðhÞ
N
t
;ð1Þ
with R
e
¼6371 km the radius of the Earth. Therefore the ground
track spacing at the Equator is 7.3 km, at 25 degrees latitude
6.6 km and at 40 degrees latitude 5.6 km, which is approximately
the range of latitudes for the area considered. The presence of both
ascending and descending tracks implies that for lakes with a width
smaller than 5.6 km, the maximum number of passes over the
water surface per repeat period, is two. The minimum number of
passes N
p
for a lake with width w(extent in the West to East direc-
tion) is computed as:
N
p
¼2int w
sðhÞ
:ð2Þ
Note that the actual number of passes can be even lower, since in
case of maintenance of Cryosat, some data may not be available.
Furthermore, tracks can pass close to the Eastern or Western shores
of the lake, where waveforms get strongly polluted, so that no reli-
able estimate of the lake level can be made. Additionally, for the
method to work properly, at least ten shots are required. The spac-
ing between the along-track measurements is between 300 and
350 m. Therefore the extent of a lake in the South to North direction
at the location of the track should be at least 3000 m.
2.2. Lake categorization
We consider lakes from the level 1 product of the Global lakes
and Wetlands Database (GLWD) (Lehner and Döll, 2004), which
contains lakes larger than 50 km
2
. Some of these lakes are only vis-
ited one or two times per year by Cryosat. At the moment of paper
writing, only two years (February 2012–January 2014) of continu-
ous Cryosat measurements are available. Therefore, trends and
periodic variations computed for such lakes are not reliable. At lar-
ger lakes, trends and periodic variations can be computed more
accurately. However, the number of measurements may still be
too limited to cope with slopes in the water surface. These slopes
most likely occur due to the low resolution of the geoid and/or
wind induced effects. Taking all these considerations into account,
we divide the lakes in four classes, based on the number of passes,
before outliers with respect to the model are removed by applying
a W-test, as described in Section 2.4.
2.2.1. Class 0
This class contains lakes that are passed less than four times
during the two-year period. Even after several years of operation,
the number of passes will be too low to estimate a trend accu-
rately. It furthermore even undersamples annual variations, since
it would require to have at least two measurements per year.
The only way to eventually use Cryosat data for the class 0 lakes
is as a complementary source for time series created from multiple
altimetry missions. This type of lakes is not considered further.
2.2.2. Class I
Lakes in the first class have at least four and maximally nine
passes during the two-year period. For these lakes no trends or
variations are estimated, since there is almost no redundancy,
causing the estimated parameters to be inaccurate. However, over
a period of five years (which is approximately the period Cryosat is
planned to operate, i.e. 2012–2017) it is likely that an accurate
120 M. Kleinherenbrink et al. / Journal of Hydrology 521 (2015) 119–131
trend can be obtained, since at least ten passes will be available,
allowing the outlier removal procedure to work properly.
2.2.3. Class II
The minimum number of passes required to estimate a trend,
annual and semi-annual signals is six. However, with only six
observations the redundancy is zero and the signal is undersam-
pled over the considered two-year period. Furthermore, the outlier
removal procedure (described in Section 2.4) cannot properly
remove outliers from the time series in that case. And even if the
number of passes is eight or larger, the outlier removal might
decrease this number and cause undersampling of the semi-annual
signal. Therefore, we require the minimum number of passes for
estimating trends and periodic variations to be at least ten. The
maximum number of passes over lakes in this category is nineteen.
The West to East extent of lakes in this class is still relatively small,
causing the surface slope signal in the time series to remain lim-
ited, i.e. maximally in the order of only 0.3 m. This value is below
the accuracy level of what can be estimated using Cryosat data.
The surface slope signal is therefore not estimated for class II lakes.
2.2.4. Class III
The lakes in this class have at least twenty passes of Cryosat in
the two-year period. These lakes are large, yielding plenty of mea-
surements with almost no waveform pollution. This, and the num-
ber of passes, enables us to accurately compute periodic variations
and trends. Due to a redundancy of measurements it is also possi-
ble to cope with slope errors, i.e. a spatial trend can be estimated in
the longitudinal direction. This increases the number of estimated
parameters to seven. With a ground track spacing of 5.6 km at the
TP, typical lakes for which a geoid correction is computed are at
least 28 km in width according to Eq. (2) if we assume at least
ten measurements per year. Over a distance of 28 km the slope
errors may reach several decimeters, which is detectable consider-
ing the accuracy of Cryosat.
2.3. Lake level estimates
In order to obtain water levels over a lake, the procedure
described in Kleinherenbrink et al. (2014) is applied. That proce-
dure was specifically designed to estimate lake levels in the pres-
ence of substantial waveform pollution, which is often the case
in regions with rough topography. We use Cryosat level 1b data
as input. Cryosat level 1b data essentially consist of waveforms
that still need to be retracked to estimate an elevation. As a first
step, a generic waveform of a reflected wave is simulated. At a sec-
ond step, the method cross-correlates the generic simulated wave-
form with the observed level 1b waveforms. The lags of the peaks
in the cross-correlation function correspond to elevations. In case
of unpolluted waveforms a single elevation is returned per wave-
form, while from polluted waveforms containing several peaks,
multiple elevations are returned. The elevation of the land surface
varies along-track, while the water surface does not. Therefore it is
possible within a track to distinguish signals reflected from the
water surface from those reflected from the surrounding land sur-
face. By retracking we estimate the retracker correction
D
r
r
, which
is the estimated range difference with a reference range. To esti-
mate the ellipsoidal height of the reflecting surface we furthermore
extract the satellite altitude a, the window delay r
wd
(which is a
reference range computed using an onboard tracking system)
and the geophysical corrections
D
r
gc
. The geophysical corrections
applied are the same as for the official Cryosat level 2 data over
land: ionosphere, wet troposphere, dry troposphere, ocean loading,
solid earth and pole tide. The inverted barometer correction is not
available for inland waters and the high frequency dynamic atmo-
spheric correction is negligible. Ultimately, the elevations H
referenced to the EIGEN-6C2 geoid (Shako et al., 2014) and are
computed as:
H¼aðr
wd
þr
r
þr
gc
ÞN;ð3Þ
where Nis the geoid height with respect to the ellipsoid. Using a tai-
lored outlier removal procedure, we remove outliers and elevations
corresponding to land surfaces to find the optimal lake level esti-
mate. In some cases multiple elevations several hundreds of meters
above the water level are present. These incorrect elevations occur
especially in areas with strong topography. Iterative removal of out-
liers above three Root Mean Square (RMS), does not properly elim-
inate these incorrect passes in the time series. To cope with this
problem, the outlier removal procedure continues until the RMS
of the time series with respect to a mean value is within 20 m,
which we consider to be the maximum expected variability of a lake
level. Further details on the outlier removal procedure can be found
in Kleinherenbrink et al. (2014). Per track, we compute the water
surface elevation, standard deviation, average latitude, average lon-
gitude and the time of acquisition. Ultimately, this forms a time ser-
ies of Cryosat measurements.
2.4. Estimation of trends, periodic variations, water slopes and water
balance
For classes II and III lakes (as discussed in Section 1), trends
and periodic variations are computed. The general model for this
is:
y¼Ax;ð4Þ
where yis a vector of lake levels (one per pass), Ais the design
matrix and xthe vector of parameters to estimate. The lake level
at January 1, 2012 with respect to the geoid, a trend and annual
and semi-annual variations are estimated for class II and class III
lakes. Furthermore, over various lakes, slopes are present in the
water surface. This effect might be caused by the low resolution
of the geoid model or prevailing winds pushing the water up to
one side of the lake (Kleinherenbrink et al., 2014). This effect is vis-
ible in Fig. 1, where the post-fit residuals eof the Nam Co water
level estimates with respect to the model are shown versus the lon-
gitude. In order to incorporate this effect, first we have to make sure
that the ‘mean lake levels’ in all tracks are referenced to a single lat-
itude, i.e. that they are de-trended along-track. The reference lati-
tude is taken from the GLWD database. Then, for class III lakes,
we include into the model a linear relationship between the eleva-
tion and the position. Since all tracks are referenced to the same lat-
itude, this is only a function of the average longitude k
i
of the
particular pass. We only include a linear relation in our model, to
ensure enough redundant observations are present. Therefore the
design matrix Ais ultimately designed as:
A¼
1t
1
sin
2
p
t
1
365
cos
2
p
t
1
365
sin
4
p
t
1
365
cos
4
p
t
1
365
k
1
::::::
1t
n
sin
2
p
t
n
365
cos
2
p
t
n
365
sin
4
p
t
n
365
cos
4
p
t
n
365
k
n
2
6
43
7
5;
ð5Þ
where t
i
is the day of the observation y
i
, where counting started at
January 1, 2012. In the model for class II lakes, the last column is
omitted. We fit sines and cosines to determine the phases and
amplitudes for annual and semi-annual variations. The post-fit
residuals ^
eare computed as:
^
e¼yA^
x;ð6Þ
where ^
xare the estimated parameters (trends and periodic varia-
tions). Then a Root Mean Square Error (RMSE) is computed with
M. Kleinherenbrink et al. /Journal of Hydrology 521 (2015) 119–131 121
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi
^
e
T
^
e
nm
r;ð7Þ
where nis the number of passes under consideration and mis the
number of model parameters (in our case 6 or 7) and therefore
nmis the number of degrees of freedom.
Outliers are identified using the W-test (Baarda, 1968). This
requires the computation of the residuals covariance matrix Q
^
e
,
which is done as:
Q
^
e
¼Q
y
AðA
T
Q
1
y
AÞ
1
A
T
;ð8Þ
where the matrix Q
y
is a diagonal matrix containing the variances of
the lake level measurements in the passes, based on the standard
deviations as derived in Section 2.3. The W-statistic for observation
iis then computed with:
WðiÞ¼
^
eðiÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Q
^
e
ði;iÞ
p
:ð9Þ
Outliers are iteratively removed until all W-statistics are below
three, i.e. the standard deviation of the post-fit residual is at maxi-
mum three times smaller than all the post-fit residuals.
For the computation of the volume change, ideally lake size
changes should be taken into account (Baup et al., 2014; Duan
and Bastiaanssen, 2013). We assume however that the surface
areas of the lakes remain constant. From the SOLS database, we
determined that the maximum increase of lake size per meter lake
level change of the lakes considered was approximately 5% of the
lake area. Since the maximum water level change of natural lakes
during the period considered is only 1.47 m (which will be shown
in Section 4) and in most cases even smaller than 0.50 m, this
assumption introduces an error much smaller than other errors
in the estimates. The reservoirs have larger fluctuations and their
sizes might change significantly, therefore their water volume vari-
ations are not estimated.
2.5. Model evaluation
To find out if the model properly fits the observations, an over-
all model test is applied. To this end, the reduced chi-square statis-
tic
v
2
red
is computed as:
v
2
red
¼
^
e
T
Q
1
y
^
e
nm:ð10Þ
The corresponding probability distribution function is a chi-square
function with nmdegrees of freedom. If the probability value is
lower than five percent, the model is considered as not fitting the
observations. In Sections 4.1.2 and 4.1.3 the fit is indicated with a
‘yes’ or ‘no’ depending on whether the data fit the model.
In a few cases, the overall model test is not an effective measure
for determining if the model fits the observations. For example, for
Bangong Co lake (Fig. 2), the model shows unrealistically high
amplitudes. Bangong Co is an East–West stretched lake with a sur-
face area of 343 km
2
. It is located in the Western part of Tibet and
surrounded by high mountains. It is sampled twelve times over
two years, which would be enough in case of evenly divided time
samples. In practice, however, the observations undersample
semi-annual signals because several samples are close together.
As a result the semi-annual variations are strongly overestimated.
To identify the time series in which such undersampling occurs,
we analyze the signal variability with respect to the mean level.
The idea of the method is to quantify the probability of the
observed signal variability, assuming that the observation times
are random. This method consists of five steps.
1. Compute the standard deviation of the samples,
r
y
, of the
estimated lake levels, y.
2. Create a set of random sample times t
1
...t
n
between 1 Feb-
ruary 2012 and 30 January 2014 based on a uniform proba-
bility distribution (with the same number of samples as in
step 1) and compute the corresponding modeled lake levels
^
y
1
...^
y
n
using the estimated parameters.
3. Compute the standard deviation
r
^
y
, of the modeled lake
levels.
4. Repeat steps 2 and 3 ten thousand times, while varying the
sample times, to create a set of signal standard deviations.
5. Use the distribution of
r
^
y
to find whether
r
y
is significantly
smaller, using a 5 percent significance level.
This undersampling only occurs at class II lakes. If
r
y
is signifi-
cantly smaller than
r
^
y
, the amplitudes are assumed to be overesti-
mated and the lake is moved to class I.
3. Expected accuracy of lake level estimates
Several components contribute to the total error in a lake level
measurement. They are listed in Table 1 for all three classes of
lakes. First, we have errors in the instrumental and geophysical
90.3 90.4 90.5 90.6 90.7 90.8 90.9 91
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
longitude [deg]
difference with model [m]
Fig. 1. Differences between the estimated model and the water level estimates versus the longitude at Nam Co.
122 M. Kleinherenbrink et al. / Journal of Hydrology 521 (2015) 119–131
corrections. The instrumental corrections for a satellite altimeter
add up to approximately 0.01 m error (Vignudelli, 2011). Geophys-
ical corrections comprise the removal of ionospheric and tropo-
spheric delay and tidal corrections. Typical errors in the
geophysical corrections are approximately 0.03 m for Cryosat,
caused by the absence of a radiometer and dual-frequency mea-
surements (Vignudelli, 2011). Second, precise orbits of Cryosat
have a radial error of approximately 0.02 m. Another contributor
to the error is ice coverage. Kropác
ˇek et al. (2013) showed that
most of the lakes in the study area are frozen at least partly during
winter time. Typical maximum ice thicknesses that occur at for
example Nam Co are 0.60 m (Ye et al., 2011), which would result
in a range error of 0.06 m.
However, the largest error sources are retracking and a sloping
water level. Using the retracker from Kleinherenbrink et al. (2014),
passes with hardly polluted waveforms yield retracking errors in
the order of 0.1 m over Lake Nasser. Since this retracker assumes
a zero water wave height, the quality of the observations decreases
if substantial water waves are present. In near-shore areas the
retracker shows a robust behavior, however the errors increase
there to 0.3 m in case of Lake Nasser (Kleinherenbrink et al.,
2014). Since the class I lakes have a width (typically 5–30 km) that
is comparable with the width of the SARIn footprint, most wave-
forms are to some extent polluted and therefore the retracking
errors are expected to be in the order of 0.3 m for those lakes.
The class II lakes are of medium size, this may cause some wave-
form pollution, which leads to retracking errors in the range of
0.1 to 0.3 m. Class III lakes are generally large and therefore suffer
less from waveform pollution. As a consequence, the retracking
error is expected to approach 0.1 m. However, over several large
lakes high water waves can develop, which reduces the accuracy
of the retracker (because the retracker assumes a flat surface
response) in the order of centimeters up to decimeters.
Water sloping effects are included in lake level estimation for
the class III lakes by using a linear dependence of the slope on
the longitude of the passes. Errors in the estimation of the slope
are assumed to be several centimeters maximally, as shown in
Table 1. Lake level estimates from passes in classes I and II lakes
are not corrected for slopes and therefore slopes contribute to
the error. However, these lakes are generally smaller and therefore
are less prone to this effect. Over 15–20 km distance, which is the
size of a medium class II lake, the maximum slope errors are
expected to reach at least 0.2 m as found over Lake Nasser
(Kleinherenbrink et al., 2014). This number is expected to be even
larger depending on the location of the lake, because the topogra-
phy in Tibet is stronger and less data are available to compute the
geoid, which can cause larger geoid errors. Furthermore, most large
lakes in Tibet have a convex shape (from inspection of the GLWD),
which might cause larger water sloping effects due to prevailing
winds. Class I lakes typically have diameters in the range of
10 km, which reduces the slope errors to a few centimeters.
4. Results and validation
In this chapter we show the ability of Cryosat to recover lake
level fluctuations in Tibet and Tian Shan. An overview of the tar-
geted lakes is given. Then, the estimated lake level trends and sea-
sonal signals are discussed. Furthermore, we show how the lake
level slopes are removed from the signal. And ultimately, we vali-
date the results over two lakes by comparing them to Jason-2 data.
The time series discussed will be made publicly available on the
website http://www.citg.tudelft.nl/en/about-faculty/departments/
geoscience-and-remote-sensing/research-themes/sea-level-change/
altimetry/.
4.1. Overview of considered lakes
The polygons in Fig. 4 indicate the area where the SARIn mode is
activated over Central Asia. The histogram in Fig. 3 shows the num-
ber of passes and the number of lakes. In total 167 lakes in the
SARIn region are passed at least once by Cryosat. 42 are passed less
than four times, are categorized as class 0 and are not discussed
further. So, for 125 lakes, the water level is estimated with Cryosat
data at least four times in two years. In total we have 79 lakes that
01−Feb−2012 01−Feb−2013 01−Feb−2014
4238
4240
4242
4244
4246
4248
4250
4252
4254
4256
date [−]
elevation [m]
Fig. 2. Time series and model for Bangong Co water level variations. Semi-annual variations are overestimated due to ‘undersampling’. The red dot with error bars indicates
an outlier. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1
Error sources in lake level measurements.
Error source Class I Class II Class III
Instrumental correction errors (m) 0.01 0.01 0.01
Geophysical correction errors (m) 0.03 0.03 0.03
Radial orbit error (m) 0.02 0.02 0.02
Lake ice (m) 0–0.1 0–0.1 0–0.1
Retracking error (m) 0.3 0.1–0.3 0.1–0.3
Sloping error (m) 0.0–0.1 0.2
a
0.0–0.1
a
The actual value might differ considerably from this number, depending on the
quality of the geoid model and wind conditions at the lake.
M. Kleinherenbrink et al. /Journal of Hydrology 521 (2015) 119–131 123
are categorized as class I, 30 lakes categorized as class II and six-
teen lakes categorized as class III. An overview of the locations of
the monitored lakes is shown in Fig. 4. The time series over a
few of these lakes are discussed below. For the ones indicated in
orange the results are validated by a comparison with Jason-2 data
from the GLRM database (Birkett et al., 2011). In the remainder of
this section the three classes of lakes are discussed one-by-one.
4.1.1. Class I
In this class, we categorized lakes that have at least four, but
less than ten passes. An additional six lakes are added to this class,
because semi-annual variations are overestimated (as described in
Section 2.5), so we moved them from class II to class I. At the
moment, for these lakes it is not possible to accurately com-
pute trends or annual variations, since there are not enough
measurements yet. The lakes in this category are listed in Table 2.
Their surface area varies between 51 and 373 km
2
. The number of
passes decreases when the lake size is decreasing, eventhough
there is also a dependancy on the geometry and the orientation
of the lakes. As mentioned in Section 2.1 the width of the lake is
most important. Compared to the estimated number of tracks,
the true included number of tracks is generally 2–6 tracks lower,
due to the causes mentioned in the same section. The last column
in the table shows whether the lake is in the SOLS database (Birkett
et al., 2011), which is the most extensive lake database, even-
though it is not processed up to 2014. Of the 79 lakes, 27 have been
monitored using other altimetry satellites, however many of them
are not operational anymore. Only one of these lakes is monitored
by a Ku-band radar altimeter satellite, which is operational until
now, Jason-2.
020 40 60 80 100 120 140
0
2
4
6
8
10
12
14
16
18
20
number of passes
number of lakes
Fig. 3. Histogram of the number of passes versus the number of lakes. The red lines indicate the borders of the classes (4 passes, 10 passes and 20 passes). (For interpretation
of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. The red circles indicate class I lakes, the triangles class II lakes and the squares class III lakes. The blue labeled lakes are discussed in detail below of which the
underlined ones are used for validation. The black polygon indicates the area over which the SARIn mode operating, which is extended, by the area enclosed by the black
dotted line, in the initial stages of the Cryosat mission. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this
article.)
124 M. Kleinherenbrink et al. / Journal of Hydrology 521 (2015) 119–131
4.1.2. Class II
This section considers lakes that have more than ten passes.
Therefore trends, annual and semi-annual variations are estimated.
Thirty lakes are categorized in this class as shown in Table 3. Cur-
rently, only four of these lakes are measured by Jason-2, which
illustrates the importance of Cryosat for lake level monitoring.
The smallest lake has a surface area of 110 km
2
, and is therefore
smaller than many of the lakes in the first category. This lake has
apparently a favorable orientation and geometry with respect to
the Cryosat tracks. The largest lake on the other hand has a surface
area of 828 km
2
. To demonstrate the method performance, we
show in Fig. 5 the time series of Song-Kul lake and it’s estimated
model. The bars indicate the 95 percent confidence area, computed
as twice the standard deviation of the measurements within the
pass. Song-Kul lake is an average-size class II lake, with a surface
area of 273 km
2
. It is located in Kyrgyzstan close to the large
Issyk-Kul lake. The lake has a convex shape, i.e. it does not have
any branches. As shown in the figure, the model properly fits the
observations. From Table 3 it can be seen that the Song-Kul water
level has an downward trend of 0.05 my
1
, which is not significant
based on the standard deviation given in the same column. On the
other hand the annual signal is substantial and more than twice
the standard deviation, showing significant seasonal variability.
Finally, the estimated semi-annual signal is small and therefore
neglectable.
Most water levels with a variability of several meters are inad-
equately modeled as described in Section 2.4, however some of
them are not. These are mainly man-regulated reservoirs, of which
an example in shown in Fig. 6. The figure shows the time series and
it’s model for the Toktogul reservoir in Kyrgyzstan. Eventhough
after outlier removal the number of measurements is only eight,
the numbers found for the amplitude of the annual variation are
comparable to those in the SOLS database between 2002–2010
(Crétaux et al., 2011). This is confirmed by the Database for Hydro-
logical Time Series of Inland Waters (DAHITI) (Schwatke et al.,
2010), which shows using Envisat that water level fluctuations
and trends of more than 10 m y
1
are not uncommon. Note that
the number of measurements before the W-test outlier removal
is fifteen. It is possible that a simple harmonic model is not ade-
quate for the time series of this reservoir, and higher frequency
harmonics should be included to get a better fit.
4.1.3. Class III
The class III lakes are listed along with the estimated parame-
ters in Table 4. As shown, the minimum size of a class III lake
has a surface area of 307 km
2
, while the largest one has an area
of 6259 km
2
. Only four of the sixteen lakes are monitored with
Jason-2 at this moment.
In Fig. 7, the estimated water level model before and after
removing a water surface slope for Nam Co is displayed, along with
the included observations. Nam Co is one of the largest lakes on the
Tibetan Plateau, located close to Lhasa, the capital of Tibetan
Autonomous Region. The shores are generally not steep, but at
the Southwestern shore large mountains are present. Nam Co is
Table 2
List of class I lakes. Indicated is the surface area Sand the number of measurements (Nr.). Furthermore, the J indicated whether the lake can currently be monitored with Jason-2.
The bottom six lakes are categorized as class I, because overestimation of the semi-annual variation occured.
ID Coord. (deg) S(km
2
) Nr. Database No. Coord. (deg) S(km
2
) Nr. Database
1 649 28.55N 90.40E 288 8 SOLS 38 1928 35.56N 82.72E 93 5 SOLS
2 676 30.72N 81.21E 278 7 SOLS, J. 39 1970 31.06N 89.01E 92 5
3 681 31.52N 88.74E 275 7 40 2010 34.64N 88.67E 89 8 SOLS
4 685 28.90N 85.58E 274 7 SOLS 41 2048 33.85N 88.58E 88 4
5 718 35.03N 81.08E 261 9 SOLS 42 2080 32.17N 84.73E 86 7 SOLS
6 743 34.33N 72.86E 254 4 43 2094 34.35N 74.54E 86 5
7 755 31.37N 84.03E 251 8 44 2116 31.81N 88.24E 85 5 SOLS
8 767 25.78N 100.18E 247 5 45 2138 33.89N 91.19E 84 4
9 913 30.27N 86.41E 205 6 46 2201 43.04N 70.70E 82 6
10 989 32.08N 90.84E 188 9 47 2238 43.66N 92.80E 81 5
11 1066 31.25N 90.58E 175 4 48 2304 35.42N 84.64E 79 8 SOLS
12 1079 32.02N 91.48E 174 7 49 2305 35.29N 83.11E 79 7 SOLS
13 1096 35.21N 79.85E 171 7 SOLS 50 2361 33.86N 87.00E 77 6
14 1124 33.23N 73.74E 166 8 51 2475 36.01N 88.78E 73 5
15 1323 30.87N 83.58E 141 4 52 2531 32.38N 88.04E 71 6
16 1336 31.22N 91.15E 139 9 53 2569 31.99N 88.17E 70 6 SOLS
17 1349 31.41N 76.47E 137 7 54 2611 31.30N 91.47E 69 4
18 1382 31.70N 91.16E 134 5 55 2613 34.57N 87.25E 69 6 SOLS
19 1417 36.88N 95.91E 130 9 56 2706 28.41N 88.22E 67 4
20 1432 31.52N 90.97E 128 5 SOLS 57 2720 33.67N 85.81E 67 4
21 1441 32.48N 67.92E 127 7 58 2786 35.70N 91.36E 65 5
22 1534 31.22N 84.97E 119 4 SOLS 59 2819 34.81N 92.21E 64 8
23 1557 38.12N 90.79E 117 6 60 2877 35.13N 86.75E 63 7
24 1619 34.15N 79.79E 112 7 SOLS 61 2881 34.34N 91.57E 63 5
25 1652 29.85N 85.72E 110 4 62 2890 31.85N 83.16E 63 4
26 1684 38.86N 93.88E 109 9 63 2957 34.48N 81.79E 62 4
27 1690 45.06N 82.70E 108 9 64 3045 35.97N 87.37E 60 5
28 1730 30.94N 89.68E 105 8 65 3078 32.98N 88.70E 59 4
29 1736 34.95N 81.56E 105 7 SOLS 66 3111 34.44N 81.94E 58 4 SOLS
30 1785 37.49N 93.92E 102 6 67 3147 30.75N 84.98E 58 5
31 1791 32.87N 82.15E 102 5 68 3156 35.73N 86.66E 57 4
32 1804 31.74N 89.52E 101 8 69 3192 32.75N 81.74E 57 4 SOLS
33 1812 35.93N 90.63E 100 6 SOLS 70 3201 35.41N 88.36E 57 5
34 1835 37.71N 93.38E 99 6 71 3343 32.90N 88.19E 54 4
35 1871 34.62N 80.44E 97 4 72 3353 28.77N 80.09E 54 5
36 1876 33.41N 90.06E 96 6 73 3534 33.95N 86.49E 51 4
37 1891 35.27N 89.25E 96 8 SOLS
74 489 33.38N 89.81E 373 12 SOLS 77 1213 40.64N 75.28E 154 12
75 520 33.48N 90.32E 351 11 SOLS 78 1806 34.01N 82.37E 101 10 SOLS
76 536 33.61N 79.71E 343 12 79 1917 35.80N 89.43E 94 10 SOLS
M. Kleinherenbrink et al. /Journal of Hydrology 521 (2015) 119–131 125
approximately 80 km wide, so substantial sloping errors may
occur. As shown in the figure, by applying the slope correction, a
significant decrease in the amplitude of the seasonal variations is
visible. Table 4 shows that the estimated slope is 5.44
l
rad, caus-
ing the slope over 80 km to be in the order of 0.40 m. After slope
correction the approximate amplitude of the annual variation for
Nam Co is 0.23 m and the amplitude of the semi-annual variation
equals 0.10 m, while the trend is negligible.
Another comparison between the models before and after
removing water slope is made for Lake Alakol as shown in Fig. 8.
This lake is located in the East of Kazakhstan. Only at the Southern
shores some substantial topography is present. Topography
might affect the accuracy of the local geoid. The less significant
topography at Lake Alakol compared to the situation at Nam Co,
may explain why the estimated slope is smaller at Lake Alakol,
as shown in Table 4. In the table it can be seen that Lake Alakol
has a decreasing trend of approximately 0.14 m y
1
and variations
in order of centimeters to decimeters.
Something remarkable occurs in the time series of Ayakkum
shown in Fig. 9. Ayakkum is a lake at the Northern border of the
Tibetan Plateau. The rivers entering this closed lake form quickly
changing deltas. Furthermore, the Western and Eastern shore are
flat, so the lake grows significantly when the water level is increas-
ing. The outlier removal procedure removes other passes when
slope estimation is included than without slope estimation, which
significantly influences the estimated parameters. For example,
Table 3
List of class II lakes, where ‘annual’ is the yearly variation and ‘semi’ is the semi-annual variations. Between brackets are the phases (in days) of the respective estimated
parameters, assuming a sine-function. Furthermore, the column ‘Fit’ determines if the model accurately fits the data, based on the overall model test from Eq. (10). A column for
the surface area Sis included as well as the number of measurements Nr. The J indicates again whether the lake can be monitored with Jason-2 currently.
ID Lake name Coord. (deg) S(km
2
) Nr. Trend (m/y) Annual (m) Semi (m) Fit Database
1 215 Tangra Yumco 31.05N 86.59E 828 17 0.22 ± 0.04 0.29 ± 0.07(341) 0.21 ± 0.08(83) Yes SOLS
2 300 Ngoring Co 34.93N 97.71E 598 19 0.18 ± 0.06 0.48 ± 0.08(244) 0.33 ± 0.07(119) Yes SOLS, J.
3 382 Gyaring Co 31.13N 88.32E 482 12 0.32 ± 0.15 0.22 ± 0.14(281) 0.29 ± 0.21(98) Yes
4 383 Taro Co 31.13N 84.12E 480 15 0.16 ± 0.11 0.21 ± 0.09(309) 0.10 ± 0.10(107) Yes SOLS
5 407 Sayram 44.61N 81.18E 450 19 0.11 ± 0.06 0.13 ± 0.07(240) 0.05 ± 0.08(144) Yes SOLS, J.
6 439 Mapam Yumco 30.67N 81.49E 418 10 0.44 ± 0.11 0.27 ± 0.13(260) 0.16 ± 0.19(122) Yes
7 444 Ngangze Co 31.01N 87.14E 411 17 0.36 ± 0.04 0.08 ± 0.06(361) 0.34 ± 0.07(24) Yes
8 470 Karakul 39.00N 73.49E 387 13 0.32 ± 0.06 0.18 ± 0.07(25) 0.05 ± 0.08(99) Yes
9 511 Aqqikol 37.06N 88.42E 356 16 0.86 ± 0.03 0.30 ± 0.12(24) 0.13 ± 0.26(155) No SOLS
10 543 Urru Co 31.70N 88.00E 340 17 0.09 ± 0.07 0.28 ± 0.08(192) 0.14 ± 0.08(104) Yes SOLS, J.
11 592 Lumajangdong Co 34.01N 81.64E 318 17 0.33 ± 0.02 0.12 ± 0.07(268) 0.09 ± 0.10(3) Yes SOLS
12 622 Pong Dam 32.00N 76.07E 300 10 0.82 ± 0.17 11.54 ± 0.46(283) 2.26 ± 0.51(60) Yes
13 629 Dabuxun 36.96N 95.15E 296 16 0.18 ± 0.06 0.11 ± 0.06(24) 0.04 ± 0.06(164) Yes SOLS
14 639 Xijir Ulan 35.22N 90.26E 294 19 0.17 ± 0.03 0.67 ± 0.05(342) 0.24 ± 0.04(48) No SOLS
15 688 Song-Kul 41.84N 75.17E 273 15 0.05 ± 0.07 0.15 ± 0.07(114) 0.04 ± 0.08(74) Yes
16 697 Bangong Co 33.82N 78.61E 270 10 0.25 ± 0.08 0.53 ± 0.08(44) 0.11 ± 0.11(122) Yes SOLS
17 725 Dogai Coring 34.57N 89.02E 259 15 0.05 ± 0.02 0.24 ± 0.05(342) 0.11 ± 0.04(62) Yes
18 729 Toktogul 41.76N 72.91E 258 15 9.17 ± 0.09 11.26 ± 0.11(379) 3.34 ± 0.16(22) Yes SOLS
19 732 Zhuonai 35.55N 91.94E 257 10 0.12 ± 0.09 0.18 ± 0.10(139) 0.39 ± 0.10(14) Yes
20 736 Kusai 35.73N 92.83E 256 10 0.62 ± 0.06 0.14 ± 0.07(306) 0.22 ± 0.08(163) Yes
21 744 Dagze Co 31.88N 87.43E 253 13 0.75 ± 0.07 0.04 ± 0.09(304) 0.16 ± 0.09(58) Yes SOLS, J.
22 812 Lexie Wudan 35.75N 90.18E 231 12 0.36 ± 0.06 0.34 ± 0.05(357) 0.14 ± 0.05(95) Yes SOLS
23 819 Donggei Cuona 35.30N 98.54E 229 14 0.24 ± 0.07 0.31 ± 0.08(221) 0.45 ± 0.08(124) Yes
24 924 Cuorendejia 35.21N 92.10E 203 17 0.49 ± 0.06 0.55 ± 0.09(266) 0.16 ± 0.10(88) Yes
25 1044 Jingyu 36.34N 89.42E 179 13 0.69 ± 0.06 0.19 ± 0.06(299) 0.21 ± 0.06(85) Yes
26 1130 Tuosu 37.13N 96.94E 165 11 1.47 ± 0.08 1.27 ± 1.48(92) 0.58 ± 0.75(18) Yes
27 1192 Kyebxang Co 32.46N 89.97E 157 11 0.03 ± 0.08 0.33 ± 0.45(130) 0.36 ± 0.29(54) Yes SOLS
28 1354 Memar Co 34.20N 82.33E 137 11 1.00 ± 0.09 0.15 ± 0.11(96) 0.03 ± 0.12(59) Yes SOLS
29 1445 Bairab Co 35.04N 83.12E 127 10 0.11 ± 0.06 0.13 ± 0.18(172) 0.07 ± 0.13(159) Yes
30 1644 Qinma 35.60N 90.63E 110 13 0.13 ± 0.08 0.53 ± 0.09(229) 0.03 ± 0.09(129) Yes
01−Feb−2012 01−Feb−2013 01−Feb−2014
3012.5
3013
3013.5
3014
3014.5
date [−]
elevation [m]
Fig. 5. Time series and model for Song-Kul lake water level variations. The model properly fits the observations.
126 M. Kleinherenbrink et al. / Journal of Hydrology 521 (2015) 119–131
centered around February 2013 in the figure, two outliers are
removed when the slope is estimated, while they are kept in the
absence of slope estimation. However, by visual inspection, it looks
that both passes might not be outliers. Therefore, a longer period of
01−Feb−2012 01−Feb−2013 01−Feb−2014
865
870
875
880
885
890
895
date [−]
elevation [m]
Fig. 6. Time series and model of Toktogul reservoir water level variations. The water level shows a strong harmonic signal and negative trend. In red the removed outliers.
(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 4
List of class III lakes, where ‘annual’ is the yearly variation, ‘semi’ is the semi-annual variations and ‘slope’ the correction for slope in the longitudinal direction. Between brackets
are the phases (in days) of the respective estimated parameters. A column for the surface area Sis included as well as the number of measurements Nr. The J indicates which lakes
can be measured with Jason-2 currently. Furthermore, the result of the overall model test is indicated in the column ‘Fit’.
ID Lake name Coord. (deg) S(km
2
) Nr. Trend (m/y) Annual (m) Semi (m) Slope (
l
rad) Fit Database
1 25 Issyk-kul 42.46N 77.25E 6259 115 0.18 ± 0.02 0.04 ± 0.03(334) 0.04 ± 0.03(122) 0.65 ± 0.24 No SOLS, J.
2 58 Alakol 46.11N 81.75E 2802 42 0.14 ± 0.03 0.16 ± 0.04(101) 0.07 ± 0.04(70) 1.54 ± 1.13 Yes
3 91 Nam Co 30.71N 90.66E 1934 38 0.02 ± 0.04 0.23 ± 0.04(273) 0.10 ± 0.04(105) 5.44 ± 0.88 Yes SOLS
4 105 Siling Co 31.77N 88.95E 1641 44 0.26 ± 0.02 0.17 ± 0.02(338) 0.08 ± 0.02(77) 2.08 ± 0.50 No SOLS
5 131 Kapchagay 43.82N 77.73E 1273 56 0.27 ± 0.03 0.79 ± 0.03(77) 0.37 ± 0.03(77) 1.72 ± 0.76 No SOLS, J.
6 179 Zhari Namco 30.90N 85.61E 1004 31 0.12 ± 0.04 0.12 ± 0.04(345) 0.16 ± 0.04(162) 4.32 ± 1.49 Yes SOLS, J.
7 181 Bosten 41.98N 87.07E 1000 38 0.13 ± 0.04 0.20 ± 0.04(73) 0.08 ± 0.04(84) 3.77 ± 1.66 No SOLS, J.
8 261 Yamzho Yumco 28.97N 90.76E 680 25 0.22 ± 0.07 0.27 ± 0.09(297) 0.07 ± 0.11(115) 5.73 ± 2.91 Yes SOLS
9 297 Ebinur 44.86N 82.92E 600 28 0.09 ± 0.03 0.40 ± 0.05(62) 0.08 ± 0.04(110) 12.70 ± 3.15 No
10 302 Hala 38.31N 97.59E 595 22 0.10 ± 0.03 0.07 ± 0.04(0) 0.04 ± 0.04(88) 5.85 ± 2.61 No SOLS
11 312 Ayakkum 37.55N 89.35E 575 27 0.39 ± 0.04 0.27 ± 0.04(344) 0.12 ± 0.04(61) 4.60 ± 1.30 Yes
12 336 Zhaling 34.92N 97.27E 534 22 0.22 ± 0.06 0.53 ± 0.07(251) 0.17 ± 0.06(121) 12.51 ± 3.05 No
13 354 Ngangla Ringco 31.53N 83.09E 513 22 0.08 ± 0.07 0.14 ± 0.08(324) 0.10 ± 0.08(128) 2.09 ± 4.45 Yes SOLS
14 456 Wulanwula 34.79N 90.34E 398 20 0.18 ± 0.04 0.60 ± 0.05(322) 0.26 ± 0.07(28) 4.69 ± 2.91 No SOLS
15 461 Kayrakkum 40.32N 70.06E 395 22 0.07 ± 0.07 1.82 ± 0.11(77) 0.63 ± 0.09(151) 9.44 ± 1.98 Yes
16 609 Kekexili 35.58N 91.12E 307 21 0.44 ± 0.04 0.17 ± 0.05(305) 0.18 ± 0.05(95) 20.61 ± 2.17 No SOLS
01−Feb−2012 01−Feb−2013 01−Feb−2014
4724
4724.5
4725
4725.5
4726
4726.5
date [−]
elevation [m]
Fig. 7. Comparison between time series and estimated models of Nam Co before (blue) and after (red) removing the water slope, with a significant slope in the water surface.
(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
M. Kleinherenbrink et al. /Journal of Hydrology 521 (2015) 119–131 127
Cryosat observations is required to accurately compute a model in
this case.
Finally, note that for nine lakes, the model does not fit the mea-
surements properly, as is visible in the column ‘fit’ of Table 4. This
can be explained as follows. We use the standard deviation of the
along-track measurements in a track as input for the covariance
matrix Q
y
in Section 2. However, since the along-track measure-
ments are strongly correlated (i.e. measurements are only several
kilometers and several seconds apart), the accuracy of the data is
slightly overestimated. As a consequence, the values for good-
ness-of-fit test increase. Another possibility for the improper ‘fits’
is that the lake level simply does not behave according to the
model. Some lakes might require a non-harmonic model, or a har-
monic model with higher frequencies, because extreme rainfall or
melting events might affect the lake level substantially.
4.2. Validation
To validate the estimated lake levels from Cryosat, we compare
them to lake levels obtained from Jason-2 over Langa Co (class I)
and Bosten Lake (class III). Furthermore, over Lake Bosten we
compare the estimated trend and periodic variations with those
computed from Jason-2 measurements. In order to do this, first the
Jason-2 passes are interpolated linearly to the dates where Cryosat
passes the lake (Kleinherenbrink et al., 2014). Then from
these interpolated measurements the trends and variations are
computed.
Langa Co is located in the South-West of Tibet. Due to it’s unfa-
vorable geometry with respect to the Cryosat tracks, only seven
proper passes could be extracted. A comparison between the inter-
polated observations of Jason-2 and Cryosat is shown in Fig. 10.
Most of the measurements are polluted due to the presence of
islands. In Section 3we estimated the retracker accuracy of Cryosat
to be in the order of several decimeters for class I lakes. On top of
that there are some centimeter level inaccuracies, for example due
to unresolved instrumental and geophysical errors and the slope
error. Typical Jason-2 accuracies found over small lakes are in the
order of several decimeters as well (Birkett et al., 2011). The RMS
of differences between the two time series is 0.55 m and is there-
fore in line with the expected values. Note further that some of the
observations of Jason-2 and Cryosat fall far outside each other’s 95
percent confidence interval. A possible cause is the presence of
islands inside the lake and the close vicinity of the shoreline, which
contaminate the waveform of Jason-2.
01−Feb−2012 01−Feb−2013 01−Feb−2014
348
348.5
349
349.5
350
date [−]
elevation [m]
Fig. 8. Comparison between time series and estimated models of Lake Alakol before (blue) and after (red) removing the water slope, with a negligible slope in the water
surface. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
01−Feb−2012 01−Feb−2013 01−Feb−2014
3881
3881.5
3882
3882.5
3883
3883.5
3884
date [−]
elevation [m]
Fig. 9. Comparison between time series and estimated models of Ayakkum before (blue) and after (red) removing the water slope. The difference is substantial because
different outliers are identified. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
128 M. Kleinherenbrink et al. / Journal of Hydrology 521 (2015) 119–131
By comparing the results over Lake Bosten, we validate the
measurements over a class III lake. The results are shown in
Fig. 11. The blue dots indicate the Cryosat observations and the
blue curve the model through the observations. The red dots repre-
sent the interpolated Jason-2 observations, including outliers. To
obtain the model (the red curve) these outliers are filtered out.
The RMS of differences was expected to decrease due to improved
retracking performance over large lakes. The RMS of differences
between both time series is estimated to be 0.27 m before applying
a slope correction. This number is in line with the expected accu-
racy of Cryosat over class III lakes. A slope correction should
decrease the RMS of differences further. In practice, compensating
for the slope reduces the RMS by only 1 cm to 0.26 m. A possible
reason for this limited improvement is the fact that the Jason-2
measurements are themselves rather noisy. Secondly, the slope
correction as shown in Table 4 is small and therefore improves
the model only a little.
Furthermore, the trends and periodic variations are compared.
They are listed in Table 5. As is visible in the table, the estimated
trends and the amplitudes of the annual and semi-annual varia-
tions are comparable. There is an off-set of the peak of 20 days in
the annual variation. For the semi-annual variation, this offset is
six days. At the moment of writing only a limited number of Cryo-
sat measurements is available, which may largely explain the
observed discrepancy. Longer time series will probably decrease
the discrepancy between the models.
5. Water volume changes
Based on the results obtained in Section 4, water volume
changes in lakes are estimated. As mentioned in Section 2.4,no
water volume changes are computed for the reservoirs.
To get an indication of the water loss depending on the geo-
graphical location, we show water level changes including reser-
voirs in Fig. 12. The observed natural lakes in the Tian Shan lose
1.51 ± 0.11 km
3
y
1
in total. This is mainly caused by water loss
01−Feb−2012 01−Feb−2013 01−Feb−2014
4567.5
4568
4568.5
4569
4569.5
date [−]
elevation [m]
Fig. 10. Plot of water level time series of Langa Co computed with Cryosat (blue) versus the interpolated time series of Jason-2 from the GRLM database (red). (For
interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
01−Feb−2012 01−Feb−2013 01−Feb−2014
1045
1045.5
1046
1046.5
1047
date [−]
elevation [m]
Fig. 11. Plot of water level time series of Bosten Lake computed with Cryosat and its model (blue) versus the interpolated time series of Jason-2 from the GRLM database and
its model (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 5
Comparison of amplitudes of trends and periodic variations at Lake Bosten. Between
brackets are the phases (in days).
Parameter Trend (m/y) Annual (m) Semi (m)
Cryosat 0.13 ± 0.04 0.20 ± 0.04(73) 0.08 ± 0.04(84)
Jason 0.11 ± 0.02 0.17 ± 0.02(93) 0.07 ± 0.02(90)
M. Kleinherenbrink et al. /Journal of Hydrology 521 (2015) 119–131 129
of the large Alakol and Issyk-Kul lakes. This is confirmed by the
DAHITI database over 2012–2013 at Issyk-Kul. The estimated
water level of Issyk-Kul is only dropping by several centimeters,
but it’s size is by far the largest of the lakes in the area considered.
Note that in the same geographical region, the Kapchagay and Tok-
togul reservoirs are also losing water.
The total water storage of the observed natural lakes of Tibet,
increases by 1.76 ± 0.24 km
3
y
1
. From Fig. 12 it becomes clear that
there is a clustering of lakes both for increasing and decreasing
water level. Most of the lakes with rising water levels are located
in closed basins and in few cases connected to each other. For
example, around 90
E, 37
N and 88
E, 32
N lake levels are clearly
rising. In the same area (Inner Tibetan Plateau) Zhang et al. (2013)
showed that increasing lake levels contributed to 86% of the mass
increase of 4.28 Gt y
1
during 2003–2009. They concluded that the
mass gain was primarily caused by increased precipitation and/or
decreasing evaporation; the lake levels might be further increased
by glacial melt, since glaciers are retreating in recent decades. Fur-
thermore, the lakes on the Tibetan Plateau that lose water do that
at a rate of level decline not exceeding 0.3 m y
1
. An exception is
visible around 92
E, 35
N, where lake levels are strongly decreas-
ing. This might be caused by the events in 2011, when flooding
of the Zhuonai and Kusai lakes caused breaks in the basin and
formed a new river (Yao et al., 2012).
6. Conclusions
In this research, for the first time, Cryosat SARIn mode data
were applied to monitor water levels in lakes on the Tibet and Tian
Shan. The adopted data retracking procedure uses at least ten
along-track measurements to distinguish lake signals from sur-
rounding near-shore topography. Since Cryosat passes over differ-
ent parts of the lake, possible slopes in the water surface have an
influence on the estimated time series. To counteract this problem,
we include a dependency on the longitude of the pass into the
model fitting the data.
We found 168 lakes that were passed at least once by Cryosat.
These lakes are divided in four classes depending on the number of
Cryosat passes. In total we identified 41 class 0 lakes, 79 class I
lakes, 30 class II lakes and sixteen class III lakes. Using the esti-
mated trends for the class II and class III lakes we estimated the
water volume changes in these lakes. Changes in the man-regu-
lated reservoirs were not estimated. The total water storage in
lakes in the Tian Shan area is decreasing at a rate of
1.51 ± 0.11 km
3
y
1
. This is very different from Tibet, where
observed lakes gain 1.76 ± 0.24 km
3
of water per year.
We validated the obtained water levels over two lakes, Bosten
Lake and Langa Co, by comparing them to Jason-2 derived water
levels from the GRLM database. Over Langa Co, which is a class I
lake, the RMS of differences was found to be 0.55 m. As expected
this is larger than for the class III Bosten Lake, where the RMS dif-
ference is only 0.26 m. Furthermore, the estimated trends and
annual and semi-annual variations from Cryosat and Jason data
over Lake Bosten were compared. The estimated trends and varia-
tions are all comparable in amplitude. There is an offset in phase of
the annual variation of twenty days and an offset in phase of the
semi-annual variations of six days. An even better agreement is
expected after several years of Cryosat operations.
Cryosat shows the potential to obtain water levels from many
more lakes than any other satellite radar altimetry mission, due
to it’s dense ground-track spacing and the SARIn mode. However,
since continuous Cryosat data are only avaible since 2012, the
available data time series are limited so far. Since the plan is to
operate Cryosat until 2017, time series of at least five years are
expected to be produced. We expect, considering this research,
that trends over about 125 lakes in this area can be determined
by 2017. Therefore it is strongly recommended to include Cryosat
observations in water level databases. In addition to Cryosat, the
Sentinel-3 (2015) and Jason-CS (2017) missions, who will operate
Fig. 12. Overview of water level trends of the observed lakes. Blue indicates water gain and red indicates water loss. (For interpretation of the references to colour in this
figure legend, the reader is referred to the web version of this article.)
130 M. Kleinherenbrink et al. / Journal of Hydrology 521 (2015) 119–131
in SAR mode, will start providing data soon. Since the repeat-orbits
are ten and 27 days respectively, which is at the cost of the density
of ground-tracks, it is expected that less lakes will be passed by
these two satellites, but the temporal resolution will strongly
increase.
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