1. Introduction
A large number of lakes are distributed in the Tibetan Plateau (TP) and most of them are totally enclosed and seldom interfered by human activities [
1,
2]. These high-altitude lakes are sensitive to global climate change [
3]. Tibetan lakes hence are of great significance for the hydrological and climatic studies [
3,
4]. However, due to the inaccessibility and the harsh environment of the TP, very few in situ gauge observations can be available for most lakes. Remote sensing becomes the best practicable means to monitor lake level changes of the Tibetan lakes.
Satellite altimetry has been extensively applied to retrieving surface level of inland water bodies in the past decades. There are also many studies dedicated to lake level change in the TP by altimetry. The geoscience laser altimeter system (GLAS) on the Ice, Cloud, and Land Elevation Satellite (ICESat) mission provided lake levels at decimeter accuracy [
5]. The diameter footprint of the laser altimeter is about 70 m, which enables GLAS to retrieve water levels over small alpine lakes. Zhang et al. [
6] successfully used ICESat to extract lake elevations between 2003 and 2009 for 111 Tibetan lakes. Using the same data, Phan et al. [
5] analyzed lake level variations of 154 Tibetan lakes of over a squared kilometer in size, and found an averaged rate of 0.20 m/year in lake level during the same period. Song et al. [
3] detected seasonal and abrupt changes in the water level of 105 closed lakes from GLAS data and categorized the changes for understanding their temporal evolution patterns based on cluster analysis. SAR Interferometry (SARIn), a new type of satellite altimetry (e.g., CryoSat-2), can also collect valuable data for monitoring lake level changes on the TP [
7,
8]. Nevertheless, both ICESat and CryoSat-2 employed non-repeated orbit, resulting in a sparse temporal sampling at non-uniform time intervals. This disadvantage makes them not suitable for detecting periodical lake level variations.
In contrast to laser altimetry and SARIn altimetry, traditional radar altimetry can provide uniform and denser temporal sampling of lake heights. Two satellite families with radar altimeters were launched since the early 1990s. The TOPEX/Poseidon(T/P)-family satellites including T/P and Jason-1/2/3 revisit the same place every 10 days, collecting repeated lake height observations from October 1992 to present. The European counterparts of the T/P-family satellites are the European Remote Sensing (ERS) satellites consisting of ERS-1 and ERS-2 and Envisat. The revisit time of the ERS-family satellites is 35 days, and the first data can be dated back to 1991. Hwang et al. [
9] early used T/P data to compute time series of lake level on the TP. They detected the lake level variations of two Tibetan lakes, La’nga Co and Ngangzi Co, and found the correlation between the lake levels and the El Nino southern oscillation (ENSO). Lee et al. [
10] generated a water level change time series over Lake Qinghai and Lake Ngoring in the northeastern Qinghai-Tibetan Plateau(QTP) using retracked Envisat radar altimeter data. Combining multi-altimeter data from Envisat, Cryosat-2, Jason-1 and Jason-2. Gao et al. [
11] monitored water-level changes at 51 lakes between 2002 and 2012 on the QTP. Hwang et al. [
12] obtained two decades of measurements (January 1993–December 2014) at 23 lakes in the QTP from the T/P-family altimeters. In theory, multiple decades of lake level changes can be obtained for a lake visited by the two satellite families. In practice, due to the large footprint of radar altimeters, e.g., 5 km for T/P-family altimeters, the quality and the number of lake height observations from the T/P and ERS-family satellites can be inconsistent with the nominal accuracy and the nominal data volume in the QTP, where the high surface roughness often causes loss of signal (radar) lock, resulting in losses of data. Even though observations are achieved over some lakes, they are very noisy because of contaminations from steep lakeshore or surrounding high mountains [
9]. A sophisticated data processing method like retracking is necessary for the retrieval of precise lake levels [
10,
12].
The objective of this paper is to present a robust scheme for generating long-term lake level time series in the TP from multiple altimeter missions. We study a series of problems, such as atmospheric path delay corrections, waveform retracking, outlier removal and bias between different altimeters. We will demonstrate the robust scheme over Ngangzi Co, where a new wetland nature reserve around the lake was established in 2010 [
13], probably as a result of rising lake level. Ngangzi Co is fortunately overpassed by the T/P-family satellites and the ERS-family satellites. ICESat also has footprints over this lake. We will construct the lake level time series using data from the T/P-family altimeters, spanning data from October 1992 to December 2017. As no in situ gauge data are available in Ngangzi Co, altimeter data from other missions will be used to inter-compare the different altimeter results. Our long-term altimeter result over Ngangzi Co will provide an important piece of information for managing this new wetland [
14].
3. Results
Lake level observations of Ngangzi Co from October 1992 to December 2017 were derived from the T/P-family satellite missions using Equation (1). The mean lake level for each cycle was estimated after outlier removal. Since no in situ data could be available, lake levels resulting from Envisat, ICESat and SARAL were also computed for validation. For the consistency, the ICE retracker was applied for all radar altimeter missions. To derive lake levels, EGM96 geoid heights with respect to the WGS84 ellipsoid were used. All missions except Envisat employed the T/P ellipsoid as the reference ellipsoid. Hence satellite altimeter measurements with respect to the T/P ellipsoid were reduced to the WGS84 ellipsoid by subtracting 0.7 m. In this section, lake a level time series from each satellite is presented and validated. Finally, biases between different missions were adjusted and a 25-year monthly lake level time series was generated.
3.1. Accuracy Evaluation of Lake Levels for Each Altimeter
Figure 6a shows the lake levels derived from T/P (blue dots), Jason-1 (red dots), Jason-2 (cyan dots), Jason-3 (magenta dots), Envisat (black triangles), SARAL (yellow downward-pointing triangles) and ICESat (green diamonds). A gray bar at each data point represents the SD for the estimated lake level. The statistics of the number of available cycles and the SDs for each mission is tabulated in
Table 1.
The Jason-series altimeters behave stably over Ngangzi Co with the mean SD varying from 8.8 to 11 cm. The maximum SDs for the three altimeters are less than 30 cm. Considering this, an SD of 30 cm is selected as a threshold value for other altimeters. The statistical numbers after the forward slash in
Table 1 correspond to cycles with the SD below the threshold. In contrast, their predecessor, T/P, is less accurate. The SDs for 11 cycles among 265 available cycles are larger than the threshold. The mean SD of T/P is about 17 cm.
Figure 6b–e shows the distribution of the SD for the four T/P-family altimeters. It can be found that these SDs are normally distributed. The differences between the third quantile (Q3) and the first quantile (Q1) are about 3 cm (for Jason-1 and Jason-2) and 7 cm (for T/P and Jason-3).
Among these missions, ICESat has the highest accuracy with the mean SD of 4.8 cm. In addition, the difference between Q3 and Q1 is only 1.7 cm. The high accuracy of ICESat is benefited from its small footprint. The accuracy of SARAL is relatively high because a Ka-band altimeter is used instead of the traditional Ku-band altimeters. After removing two cycles with the SD more than 30 cm, the mean SD for SARAL reaches to 6.6 cm. The Q1 of SARAL is even less than that of ICESat. The performance of Envisat is very unstable. The SDs for 60% cycles are more than 30 cm, with the largest one reaching to 137 cm. The difference between Q3 and Q1 is also very big. We can see from
Figure 6a that lake levels derived from Envisat are considerably unreliable. Therefore, only ICESat and SARAL data are used in the later validation of the results from the T/P-family altimeters.
3.2. Validation of T/P-Family Altimeter-Derived Lake Levels
The best way for validation is by comparing the altimeter-derived lake level with the gauge data. However, no in situ data over Ngangzi Co can be available for this purpose. According to the results in
Table 1, it is appropriate to validate the lake levels from the T/P-family altimeters using ICESat and SARAL data. As the T/P mission had been terminated before the launch of ICESat, the result from T/P cannot be validated. ICESat overlaps with Jason-1 and Jason-2, while SARAL overlaps with Jason-2 and Jason-3. Therefore, we can use ICESat to validate Jason-1 and Jason-2 and use SARAL to validate Jason-2 and Jason-3.
The statistics of comparison between these missions are presented in
Table 2 and differences are plotted in
Figure 7. It should be noted that interpolation is needed for comparison. In general, the data of Jason-series satellites are used for interpolation, because they have a larger number and a smaller temporal interval than ICESat or SARAL data. However, only one data point of ICESat is located in the period of Jason-2 and three points of SARAL are in the period of Jason-3. In the two cases, we used ICESat and SARAL data for interpolation.
According to the comparison, lake levels observed by Jason-1 are averagely higher than those by ICESat, with a mean difference of 11.3 cm. Whilst, Jason-2 observes lake level lower than ICESat. The SD and root mean square (RMS) errors of Jason-1 and Jason-2 with respect to ICESat are beyond 10 cm. The mean difference between Jason-2 and SARAL is
cm, which is consistent with the difference between Jason-2 and ICESat. Relatively speaking, Jason-3 has a better agreement with SARAL. The maximum absolute difference is less than 10 cm between Jason-3 and SARAL, and the SD and RMS errors are about 5 cm. Mean lake levels from each overlapping pair of missions have a high correlation coefficient (CC) more than 0.9. By comparing subplots in
Figure 7, there might be a systematic bias between lake levels observed by different altimeters.
Figure 7a shows lake levels from Jason-1 are higher than those from ICESat. Other three subplots indicate Jason-2 and Jason-3 observed lower lake levels than ICESat and SARAL.
3.3. Bias Adjustment Between the T/P-Family Altimeters
The T/P-family satellites share the same ground track and have an overlap between two successive satellites for inter-satellite calibration. For example, the Jason-1 spacecraft launched in December 2001 was kept on the same ground track as T/P until August 15, 2002. Observations in the overlapped period can be used to analyze the lake level bias between two missions. Over the lake Ngangzi Co, 8 paired-sample observations were retrieved in the overlap between T/P and Jason-1. For Jason-2 and Jason-3, 18 paired-sample observations were found. No paired-sample observation could be available for Jason-1 and Jason-2, because the first valid data of Jason-2 over Ngangzi Co is from cycle 30 in April 2009, when the Jason-1 satellite had been moved to a new interleaved orbit in January 2009.
The differences between these paired-sample observations are shown in
Figure 8. The maximum likelihood estimation is adopted to estimate the bias. In result, Jason-1 has a mean lake level bias of
cm with respect to T/P. The bias of Jason-3 with respect to Jason-2 is
cm after removing an outlier. Since there is no overlapped observation between Jason-1 and Jason-2, we have to estimate the bias between them using their mean lake level differences with respect to ICESat in
Table 2. Finally, all biases of Jason-1/2/3 with respect to T/P are determined and charted in
Table 3.
3.4. Monthly Lake Level Time Series of Ngangzi Co
In order to generate monthly lake level time series, Gaussian filtering was applied to the observations after bias adjustment. Three kinds of filter window length (3, 6 and 12 months) were tested. Outlying observations were rejected which deviation from the filtered value was more than 3-sigma. The results are shown in
Figure 9. The time series filtered with a 12-month window (magenta curve) is too smooth, with the intra-annual amplitudes dramatically attenuated. The results with a 3-month (blue curve) and a 6-month (green curve) window length are rather similar, keeping the energy very well. Relatively, the former has more small spikes than the latter. Therefore, we suggest using the 6-month-wide filter window.
According to the time series, the lake level of Ngangzi Co dropped with a negative trend of about -0.39 m/yr before 1998 and increased dramatically after 1998. The rising trend between 1998 and 2002 is even more than 1 m/yr. The change rate in 2003–2014 is 0.32 m/yr. The lake level declined by ~1 m in 2015 and raised again from 2006. The reversed trends have been observed by altimetry in previous studies [
9,
12]. For the first time, Hwang et al. [
9] derived a lake level time series of Ngangzi Co using T/P GDR data. In total, Ngangzi’s lake level rose by ~8 m from 1998 to 2017, which partially contributed to the making of a new wetland [
35]. Without retracking the waveforms, the resulting usable lake heights in Hwang et al. [
9] were much less than those from this study and showed only annual variations. An improved result was presented using retracked T/P, Jason-2 and Jason-2 data in [
12]. However, there is a big data gap between 1994 and 1995 in this updated result. Another problem is the large annual oscillations during the T/P mission which is difficult to explain. The method presented in this study acquired nearly continuous observations. Generated time series can reveal lake level variations with various periods.
Figure 10 shows the continuous wavelet transform of the lake level time series using the bump wavelet [
36]. It is demonstrated that not only annual and semi-annual variations but also interannual oscillations can be clearly observed in the time series.
4. Discussion
This study focused on the robust and accurate generation of lake level time series in Tibet. Although no in situ data could be used for validation in this case study, two independent datasets with higher accuracy from ICESat and SARAL were successfully applied to validate our results. In order to further demonstrate the advantage of our method, the comparison was performed between the presented results and other altimeter-derived time series products. There are several public global databases for inland water bodies, such as, the River and Lake database by the European Space Agency and De Montfort University (ESA-DMU) [
37], The Hydroweb database by the Laboratoire d’Etudes en Géophysique et Océanographie Spatiales (LEGOS) [
38], The Global Reservoir and Lake Monitor (G-REALM) by the Foreign Agricultural Service of the United States Department of Agriculture (USDA), and the Hydrological Time Series of Inland Waters (DAHITI) by the Deutsches Geodätisches Forschungsinstitut [
30]. We searched these databases and only found results over the lake Ngangzi Co in G-REALM (alias Ang-tzu) and Hydroweb (alias Ngangze). G-REALM provided a time series from April 2009 to the present resulting from the Jason-2 and Jason-3 data. The time series from Hydroweb covered all the T/P-family missions from September 1992 to present.
Figure 11 shows the mean lake levels in this study in comparison to those from G-REALM and Hydroweb. All data are without smoothing and shifted from product datum to EGM96 geoid. Apparently, our method retrieved much more data from T/P and Jason-1. In the Jason-1 period, there are few data in Hydroweb and no data in G-REALM. Hence we only compared different time series in the Jason-2 and Jason-3 periods.
Table 4 tabulates the statistic results. With respect to SARAL, the SDs and CCs for G-REALM and Hydroweb are inferior to our results (
Table 2). For Jason-2 and Jason-3 data, the presented results in this study have a high agreement with G-REALM. However, many anomalous values can be found in G-REALM product from the zoom-in plot in
Figure 11. After removing these anomalous values, the correlation between our results and G-REALM reaches to 0.99. Different biases can be found in Hydroweb product. A sharp drop of lake level happened in 2009, indicating that the bias between Jason-2 and Jason-3 was not properly adjusted in Hydroweb. With respect to our result and G-REALM, the lake level bias of Hydroweb is about −1.4 m during the T/P and Jason-1 missions before 2009 and about -2 m during the Jason-2 and Jason-3 missions. Two factors might explain the bias. T/P GDR data were used to construct the Hydroweb database, which is also the reason why fewer valid cycles were retrieved in Hydroweb. DTC in GDR contributes -1.06 m to the bias as shown in
Section 2.2. The remaining bias might be caused by different waveform retracking algorithms used.
The case study of Ngangzi Co suggests that the accuracy of retrieved mean lake levels of the Tibetan lakes is much lower in summer than in winter. For example, the mean SD for T/P is 22.5 cm in July and August, whilst 17.3 cm in the winter season. Complex shapes of contaminated waveforms in summer degrade the accuracy of retracking algorithms. More sophisticated retracking method is still expected to improve the PSR of summer cycles. Waveform decontamination [
39] presented for the coastal application may be potentially applicable to further refine altimeter measurements over the Tibetan lakes. It should be mentioned that the change in lake area was not considered in data processing. A static shoreline was used to extract altimeter data for all missions. This will cause some data on the shore may be extracted, especially when the lake level is low (e.g., in T/P period). The shrink of lake area will also make the lake level observation noisier. It can explain why the PSR value of T/P is so small. Modelling accurate time-varying shorelines is difficult and time-consuming work and need other data source, such as satellite imagery. Therefore, a procedure for outlier removal is often performed, instead of the consideration of dynamical lake boundary.
Figure 5 has shown that the estimation of mean lake levels would be less affected by the lack of consideration of horizontal boundary, benefitted from the good performance of the outlier detection procedure proposed in this study.
Since it is difficult for early altimeters to maintain a lock on the rough terrain, Ngangzi Co is one of few Tibetan lakes which have been continuously monitored by satellite altimeters for more than 25 years. So far, we constructed a high-precision lake level time series with the most samples over Ngangzi Co using the T/P-family altimeters. As shown in
Figure 10, our results allow monitoring lake level variations with various periods. The 25-year-long lake level time series is valuable for the hydrological and climatic studies. Combining with surface area changes detected by satellite imagery, it can be used to quantify the water volume balance of the lake basin. Previous studies [
9,
12] have shown that the lake level variation of Ngangzi Co is strongly correlative to ENSO. The long-term and uniform sampling time series generated in this study will greatly enhance the understanding of the relationship between the lake level variation and climate change.
Figure 12 shows surface temperature and precipitation in the lake basin, extracted from CPC global temperature and CMAP precipitation data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at
https://www.esrl.noaa.gov/psd/. It suggests that the rise of lake level after 1998 can be primarily attributed to enhanced precipitation. The increased precipitation in this region since the late 1990s was also recorded by the nearby rain gauge [
40]. According to field survey in this region, the lake level of Dagze Co, which is located on the northeast of Ngangzi Co with a distance of about 100 km, descended by 2 m in 1976–1999 and ascended by 8.2 m in 1999–2010 [
40]. It is consistent with the altimeter-derived lake level change of Ngangzi Co in this study. A large drop in temperature between 1999 and 2000 can be observed in
Figure 12. The descent of the surface temperature reduced evaporation, which would also contribute to the rise of lake level. Although the water flux shows good agreement with the seasonal variation of lake level, the quantitative relationship between each factor and water budget is not clear. This is a subject for future studies.
The altimeter-derived lake level change can also be confirmed by other independent satellite observations.
Figure 13a illustrates the area change of Ngangzi Co from 1992 to 2015, downloaded from the Third Pole Environment (TPE) database (
http://www.tpedatabase.cn/). The time series of lake area was constructed using Landsat images by Zhang et al. [
41]. To avoid seasonal effects, images in October were mainly used to construct the time series. For the sake of clarity, we only plotted the shorelines in five years. However, it is enough to verify the change pattern of lake level. It can be seen that the lake area reached the minimum in 1997 and then continuously expanded, which is in accord with the lake level change observed by altimetry.
Figure 13b is the equivalent water height (EWH) time series from August 2002 to June 2016, which is right at the center of Ngangzi Co. This EWH time series is derived using the CNES/GRGS RL04-v1 monthly gravity field solutions from the Gravity Recovery and Climate Experiment (GRACE) mission. It reflects the water storage around the lake has increased since 2002 and this trend is consistent with the trend of lake level change. However, it is unknown how the GRACE-detected water storage increase is related to the rise of lake levels. A detailed analysis combining multisource satellite observations and hydrological model is expected in the future.
5. Conclusions
Tibetan lakes are located in the high-altitude and rough-terrain region. Surface environment varies with seasons. Monitoring of lake level variation by altimetry is more difficult in Tibet than elsewhere. In this paper, a robust method was presented for generating lake level time series of Tibetan lakes using multi-altimeter data. In order to merge various altimeter data products issued in different ages, the consistency of geophysical corrections should be carefully checked. For the DTC, a large bias of about 1 m is found in T/P GDR data due to the high altitude with respect to the sea level. There is a DTC bias occurred from 2006 in Jason-1 and Envisat data. Hence, the DTCs should be updated using the same surface pressure model. Retracking correction is necessary for the accurate retrieval of lake level because the leading edges of waveforms over Tibetan lakes are seriously migrated from the theoretical tracking point. Three retrackers were evaluated in term of a presented parameter PSR, the ratio of the percentage of valid measurements to the SD of lake levels for each cycle. The ICE retracker relatively performs better than TR20 and TR50 in the case study. A two-step method was proposed for outlier removal, which has good performance without requiring any a priori information. Bias adjustment is also indispensable for the combination of altimeter data from multiple missions. The bias can be directly estimated using paired-sample measurements for two successive missions with an overlap, such as T/P and Jason-1, Jason-2 and Jason-3. However, there is a case without overlapping observations between Jason-1 and Jason-2. The problem is successfully solved by using ICESat data as the intermediary.
As a case study, a 25-year-long lake level time series, was generated for the lake Ngangzi Co using the T/P-family altimeter data. The mean lake levels can be retrieved with decimeter accuracy using the presented method. The mean SD is about 10 cm for Jason-1/2/3 and 17 cm for T/P. ICESat and SARAL have much better accuracy than T/P-family satellites, with a mean SD of 4.8 and 6.6 cm, respectively. Envisat also has data over the lake but nearly unusable. In spite of the relatively sparse sampling, ICESat and SARAL data can be used for validation. High correlation more than 0.9 can be observed between the mean lake levels from T/P-family satellites, ICESat and SARAL. Compared to the previous studies and available lake level databases, our result is the most robust time series for Ngangzi Co, with high accuracy and considerably continuous samples from October 1992 to December 2017. Jason-3 is still ongoing and its following mission Jason-CS will be launched in 2020 to extend the current lake level time series, providing un-interrupted lake level records for managing the wetland around Ngangzi Co. Such a long-term record can also be used to study the mechanism that has caused Ngangzi Co’s continuous lake level rise since 1998.