With the drastic change in global climate, the wide distribution of natural lakes over the Qinghai-Tibet Plateau (TP) has attracted extensive attention due to their high climate sensitivity. In this paper, we investigated the dynamics of Paiku Co, the largest inland lake in the Qomolangma Natural Reserve, with the associated response to climate change in the past three decades. The methods used contain the water index method, the spatial and temporal fusion model, the statistical mono-window algorithm, and multi-variable linear regression. Lake area fluctuated greatly in 1990–2000, followed by a continuous shrinkage in 2000–2010, and it stabilized after that (2010–2020). We forecasted that Paiku Co would enter a slow expansion period. Conjoint analysis with climate factors showed that the area variation of Paiku Co was not significantly related to precipitation change, but negatively related to the change of air temperature and lake temperature. We found that the lake change was not dominated by a single factor but showed different climate sensitivity in each period. Especially, there was a common inflection point around 2013 that might herald the occurrence of a new trend of climate change. This article provides new ideas and solutions for the research of lakes in the Qinghai-Tibet Plateau and offers a reference for water resource management.

  • The lake area has experienced a process of sharp shrink – recovery – continuous retreat – stabilization.

  • Paiku Co is mainly affected by temperature and exhibits variable climate sensitivity.

  • The area of Paiku Co stabilized in 2013 and may have a slow upward trend in the future.

Graphical Abstract

Graphical Abstract
Graphical Abstract

The Qinghai-Tibet Plateau is one of the most sensitive areas to global climate change, presenting early warning signs (temperature increasing and glacier melting, etc.) of global warming (Liu & Chen 2000; Kuang & Jiao 2016). The lakes widely distributed on the Qinghai-Tibet Plateau are effective indicators of climate change. For example, between the 1970s and the 1990s, due to the decrease in precipitation, lake area, and water storage also decreased, but after the 1990s, it increased with the increase in precipitation and temperature (Kuang & Jiao 2016; Zhang et al. 2017).

The datasets of lake changes in the Qinghai-Tibet Plateau include in situ measurements and remote sensing monitoring. Compared to remote sensing, the in situ measurements can provide more accurate and reliable data, but the spatial coverage and time continuity are limited. Although some lake studies have used these in situ measurements, they are usually combined with remote sensing data to fill the spatial and temporal gaps (Lei et al. 2014). For extensive studies of the Qinghai-Tibet Plateau, satellite remote sensing is considered as one of the limited practical methods, though the data are limited in satellite sensor temporal and spatial resolutions, and by the weather and terrain. Lake region definition from Landsat images usually includes manual digitization and automated (or semi-automated) water classification. Visual interpretation is difficult to implement due to its high cost of time and labor, especially for large areas. Automated water classification with enough accuracy is necessary for large-scale lake mapping. Many studies have reported various methods of automatic water classification such as image segmentation (Chen et al. 2017; Zhang et al. 2020b) and machine learning (Feng et al. 2019; Wangchuk & Bolch 2020). However, the water index method is still the most commonly used method for extracting water, and it uses the strong reflection and absorptance characteristics of water in the green and near-infrared bands to extract water information. With the proposal of the normalized difference water index (NDWI) (Gao 1996), more and more relevant methods have been proposed (Xu 2005; Pci et al. 2007; Feng 2009; Wang et al. 2019). These new methods can make up for the deficiencies of previous studies, making the water extraction more accurate and automatic.

About 45% of the Qinghai-Tibet Plateau has a high daily cloud cover problem (Yu et al. 2016), especially, Sichuan and eastern Tibet regions are blocked by clouds all year round. In addition, the ice duration in low temperature and high altitude lakes and the drought and flood period of the lakes should also be considered, and these make the available time for remote sensing images severely limited. Google Earth Engine (GEE) is a cloud-based platform which can be used to execute large-scale and long-term geospatial analyses (Gorelick et al. 2017). This public-domain platform utilizes the computational capacities of Google Servers, and it can receive data conveniently and integrate complicated processing. This cloud computing platform has been applied in water extraction and many other fields and has outstanding performance (Dong et al. 2016; Peng et al. 2021). To solve the problem that it is difficult for remote sensing satellites to obtain usable images with high temporal resolution and high spatial resolution at the same time, a method combining multi-source satellite data spatial and temporal adaptive reflectance fusion model (STARFM) is proposed (Gao et al. 2006). Next, an enhanced spatial and temporal adaptive reflectance fusion model (ESTARFM) based on the STARFM algorithm is developed (Zhu et al. 2010), and it improves the accuracy of predicted fine-resolution reflectance, especially for heterogeneous landscapes, and preserves spatial details. Besides, there are some other methods, such as the Flexible Spatiotemporal Data Fusion (FSDAF) method (Zhu et al. 2016), which has the potential to increase the availability of the model.

The current deficiencies and vacancies in the studies of lakes on the Qinghai-Tibet Plateau (Zhang et al. 2020a) are mainly as follows:

  • 1.

    The temporal and spatial monitoring of lake changes mainly focused on the changes in the number of lakes.

  • 2.

    Due to the methods and the study periods covered, there is a lack of a comprehensive and systematic picture of lakes from the 1970s to the present, including interannual and seasonal variations.

  • 3.

    The analysis of lake response to climate change (temperature, precipitation) is common, but the quantitative examinations and other factors are rarely resolved.

  • 4.

    More attention should be paid to future changes in lakes.

Consistent with the above mentioned, current research focused on environmental changes in the entire Qinghai-Tibet Plateau (Zhang et al. 2017; Qiao et al. 2019; Zheng et al. 2021), the research for small areas has some shortcomings such as longer periods (Dai et al. 2013, 2019; Nie et al. 2013;  ,Zan et al. 2021), and we hope to propose a new research method to improve the defects. Especially, Paiku Co is a typical lake in southern Tibet and the largest lake in Xigaze, as the largest inland lake in the Qomolangma Natural Reserve, it also contains abundant natural resources (Nie et al. 2013). Because it is hardly affected by human activities and has a stable ecosystem, research on it can well reflect the impact of climate change on the environment. Analyzing and studying the basin will help to understand the ecological environment changes in southern Tibet and is of great significance to the protection and sustainable development and utilization of nature reserves.

In this study, we take Paiku Co as an example and apply the ESTARFM algorithm to fuse Landsat images (both TM and OLI) from 1990 to 2020 and MODIS images from 2000 to 2020 to obtain complete time-series images of Paiku Co. Then, we integrated modified normalized difference water index (MNDWI) and enhanced water index (EWI) to extract lake water bodies by using temperature and precipitation meteorological station data from 1990 to 2020 and lake surface temperature data obtained by SWM. Finally, linear regression is used to predict the future lake change trend and analyze the response of the lake to climate. Distinct from previous studies on the response of lakes to climate (precipitation contributed 70% of lake change (Zhang et al. 2019)), the variation in Paiku Co was mainly contributed by temperature and was sensitive to changes in different climatic factors. At the same time, there is a common lake/climate change inflection point in this region, which has explanatory effects on the local environment.

Research area

Paiku Co (28 °50′N, 85 °20′E, 4590 m above sea level) is located at the junction of Nyalam County and Gyirong County in the Rikaze Region (Figure 1). It belongs to the southern Tibetan Lake of the Qinghai-Tibet Plateau, which is located at the northern foot of Shishapangma (Dai et al. 2013). Around the lake, there are a variety of rare species and abundant natural resources (Nie et al. 2013). Lake recharge mainly depends on precipitation, runoff, and glacial permafrost melting in the basin, and lake water output is mainly evaporation. As a typical example of the Qinghai-Tibet Plateau Ecosystem, the water resources of the basin are easily damaged and difficult to repair. The study area belongs to the plateau temperate monsoon semi-arid climate, which is affected by the southwest monsoon and the southeast monsoon, with sufficient sunshine, distinct dry and wet seasons, concentrated summer precipitation, and large annual temperature differences. The annual precipitation in the basin is about 680 mm, the annual average temperature is about 4 °C, the annual relative humidity is about 72%, and the annual sunshine hours are 2723.8 h. The total lake area is about 270 km2, and it has a long span of 55 km from north to south and a width of 25 km from east to west. The lake is surrounded by mountains on three sides, with an altitude of 4580 m.

Figure 1

Location of research area. (a) Administrative divisions of the People's Republic of China; (b) and (c) Landsat 8 Image in October 2020.

Figure 1

Location of research area. (a) Administrative divisions of the People's Republic of China; (b) and (c) Landsat 8 Image in October 2020.

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Data

Remote sensing data

Calibrated top-of-atmosphere (TOA) and surface reflectance (SR) images are provided by the United States Geological Survey (USGS) and are fully available and ready to use in GEE for Landsat-5, 8. Calibration coefficients are extracted from the image metadata (Chander et al. 2009). The red, green, near-infrared, and mid-infrared bands in these datasets are used with a resolution of 30 m.

The MOD09A1 V6 image product was used in the ESTARFM method to predict Landsat images. The MOD09A1 V6 product provides an estimate of the surface spectral reflectance of Terra MODIS bands 1–7 at 500 m resolution and corrected for atmospheric conditions such as gasses, aerosols, and Rayleigh scattering. For each pixel, a value is selected from all the acquisitions within the 8-day composite on the basis of high observation coverage, low view angle, the absence of clouds or cloud shadow, and aerosol loading.

The surface emissivity for LST retrievals were from the ASTER GEDv3 dataset developed by JPL (Hulley et al. 2015). This dataset includes the emissivity for the five ASTER bands in the TIR region and is derived with a Temperature–Emissivity Separation (TES) algorithm from all clear-sky ASTER images acquired between 2000 and 2008. The emissivity data have a reported accuracy of ∼0.01 and are provided with a spatial resolution of 100 × 100 m2 (Hulley et al. 2009). The emissivity data are adjusted to match Landsat's thermal bands using the coefficients provided by Malakar et al. (2018).

Meteorological data

Meteorological data sources used in this paper were all acquired from the National Meteorological Information Center. We selected the monthly average temperature and precipitation data from August to September each year from the Nyalam station in 1990–2020.

Information on the atmospheric water vapor content is required to better account for atmospheric contributions in the TIR observations. Total column water vapor (TCWV) values from NCEP/NCAR reanalysis data are available on GEE (Kalnay et al. 1996).

Validation dataset

The lakes larger than 1 km2 in the Tibetan Plateau (V2.0) (1970–2018) derived from the National Tibetan Plateau Data Center were adopted to verify lake extraction accuracy in this study (Zhang et al. 2014, 2019; Zhang 2019).

Method

Water extraction method

The ImageCollection in GEE from September to October with Couldcover <10% is selected and then computed a median value for each pixel as an original image pixel value. Next, the calculation of the water index equation (Equations (1) and (2)) was performed on GEE to generate a water index image.

Since a single water index model always has different advantages and shortcomings, we used both the MNDWI and the EWI to construct a dual-threshold model to complete water body feature extraction. The MNDWI can easily distinguish shadows and water bodies, and EWI can effectively distinguish semi-dry rivers and background noise. When determining the water body index extraction threshold, through the trial-and-error method of human–computer interaction, the MNDWI and EWI thresholds were continuously adjusted at intervals of 0.01, and the extraction results of lakes under different thresholds were compared. Finally, the extraction thresholds of MNDWI and EWI were determined to be 0.15 and 0.1. The image pixels whose MNDWI and EWI values are both larger than the thresholds are determined as water, and the rest background:
(1)
(2)
where Green, NIR, and MIR are the reflection values in the green, near-infrared, and mid-infrared bands, respectively.

Lake surface temperature estimation

The production chain was fully coded in JavaScript using the GEE (Ermida et al. 2020). Figure 2 illustrates the processing chain for generating Landsat LSTs. A cloud mask is applied to both using the quality information bands (module Mask clouds). For each TOA brightness temperature (BT) image, the two closest TCWV NCEP analysis times are selected and interpolated to the Landsat observation time (Kalnay et al. 1996). The SR data are, in turn, used to compute the NDVI, which is then converted to FVC values (Carlson & Ripley 1997) and used together with previously computed ASTER emissivity values for the bare ground to obtain the corresponding Landsat emissivity (Carlson & Ripley 1997; Rubio et al. 1997). Finally, the SMW algorithm is applied to the TOA TB of the Landsat TIR band (Li et al. 2013; Duguay-Tetzlaff et al. 2015); the algorithm coefficients are mapped onto the Landsat image based on TWVC from NCEP and taking the classes defined in SWM algorithm (Equation (3)) (Sun et al. 2004; Freitas et al. 2013):
(3)
where Tb is the TOA BT in the TIR channel and ε is the surface emissivity for the same channel. The algorithm coefficients Ai, Bi, and Ci are determined from linear regressions of radiative transfer simulations performed for 10 classes of TCWV (I = 1,…, 10), ranging from 0 to 6 cm in steps of 0.6 cm, with values of TCWV above 6 cm being assigned to the last class.
Figure 2

The flowchart of the LST generation.

Figure 2

The flowchart of the LST generation.

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ESTARFM algorithm

This algorithm requires at least two pairs of fine- and coarse-resolution images acquired at the same date and a set of coarse-resolution images for desired prediction dates (Zhu et al. 2010). There are four major steps in the ESTARFM algorithm implementation (Gao et al. 2006). First, two fine-resolution images are used to search for pixels similar to the central pixel in a local window. Second, the weights of all similar pixels (Wi) are calculated. Third, the conversion coefficients Vi are determined by linear regression. Finally, Wi and Vi are used to calculate the fine-resolution reflectance from the coarse-resolution image at the desired prediction date (Figure 3).

Figure 3

The flowchart of the ESTARFM algorithm.

Figure 3

The flowchart of the ESTARFM algorithm.

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Linear regression

Ordinary least squares linear regression fits a linear model with coefficients w = (w1, …, wp) to minimize the residual sum of squares between the observed targets in the dataset, and the targets are predicted by the linear approximation.

K-folds cross-validator provides train/test indices to split data in train/test sets. To split datasets into k consecutive folds, each fold is used once as validation while the k − 1 remaining folds form the training set. In this research, k is uniformly set to 10.

The mean score (mean squared error) and the standard deviation are calculated for the model selection and evaluation of estimators.

If is the predicted value of the ith sample, and is the corresponding true value, then the mean squared logarithmic error (MSLE) estimated over is defined as:
(4)

Other method

The Pearson correlation coefficient standard deviation is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations, which is commonly represented by the Greek letter ρ:
(5)
The RMSE (root mean square error) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values are observed. The RMSE represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences:
(6)

ESTARFM complement data

When using the ESTARFM algorithm, the five images (MODIS and Landsat images of corresponding periods in 1999, 2000, 2002, 2003, 2004, and 2012) used are cut to 1000 × 1000 (pixel) size to fit the algorithm and to adjust parameters: set the half window size to 25, set the number of similar pixels to 5 (smaller value has a better performance in this study), set the estimated number of classes to 5, set the range of DN value of the image, −1 and 1, finally set the block to the entire image size for complete image processing. The data used are shown in Figure 4.

Figure 4

(a) 2015 MODIS water index image; (b) 2016 MODIS water index image; (c) 2017 MODIS water index image; (d) 2015 Landsat water index image; (e) 2016 ESTARFM predict water index image; (f) 2017 Landsat water index image.

Figure 4

(a) 2015 MODIS water index image; (b) 2016 MODIS water index image; (c) 2017 MODIS water index image; (d) 2015 Landsat water index image; (e) 2016 ESTARFM predict water index image; (f) 2017 Landsat water index image.

Close modal

The area error between the Landsat original image (Figure 4(c)) and the ESTARFM fusion image (Figure 4(a)) is almost 0.137%, 0.36 km2. Subsequently, the ESTARFM is used to supplement the image data of the years 2002, 2003, 2004, 2007, 2012, 2013, and 2019.

The covariance and correlation coefficients of Figure 5(a) and 5(b) are, respectively, 0.169, 0.989 and 0.192, 0.995. Since the 2016 ESTARFM image is predicted based on the two images in 2015 and 2017, it presented a smaller dispersion in the distribution of pixel points, which also shows that choosing a reference image with better quality (less cloud pollution, clearer water, and land boundaries) will make the image prediction have better adaptability.

Figure 5

Image pixel value scatter. (a) Comparison of Landsat original images and (b) comparison between Landsat image and ESTARFM predict image.

Figure 5

Image pixel value scatter. (a) Comparison of Landsat original images and (b) comparison between Landsat image and ESTARFM predict image.

Close modal

A comparative observation was made on the west bank of the lake with small changes: the shoreline of the selected Landsat image was completely undeterminable due to cloud pollution. By contrast, the ESTARFM fusion image (Figure 6(b)) can clearly observe the shape of the lake bank, and the water body is well distinguished from the land. Compared with the Landsat images available in 2016 (Figure 6(c)), the ESTARFM fusion image has a clearer boundary between the lake and the land. This is due to the addition of similar pixel weights in its prediction; the cloud features above the lake are partially preserved, but they do not have a basic shape. It is feasible that ESTARFM predicts images to complement long-time sequence high-resolution images.

Figure 6

Water index image. (a) Unavailable Landsat 8 Image on September 7, 2016; (b) ESTARFM fusion image; (c) available original Landsat image in September 2016.

Figure 6

Water index image. (a) Unavailable Landsat 8 Image on September 7, 2016; (b) ESTARFM fusion image; (c) available original Landsat image in September 2016.

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Area extraction of the Paiku Co

Integrating the relevant literature (Pci et al. 2007; Xiao et al. 2018; Dai et al. 2019) and the actual situation, we finally chose the extraction scheme that determined the MNDWI threshold as 0.15 and the EWI threshold as 0.1. The binary map of the water body extracted by this scheme has the characteristics of clear boundary delineation and conservative area assessment. Finally, a mask is established on the image boundary, and the pixels affected by the fog obscured part are attributed to the water body.

The water was extracted by binarization using reclassification of an outputted binary graph from a threshold segmentation algorithm. Meanwhile, with the help of visual verification, non-removed lake debris and noise can be removed successfully, thus obtaining the long-term area of Paiku Co as shown in Table 1. There is a data gap in the years 1991,1993, and 1995 due to the lack of remote sensing images.

Table 1

Lake long-term extraction area

YearArea (km2)YearArea (km2)
1990 277.287 2007 270.314 
1992 274.406 2008 270.036 
1994 273.729 2009 268.355 
1996 275.449 2010 268.698 
1997 274.422 2011 268.557 
1998 275.218 2012 268.866 
1999 274.607 2013 269.048 
2000 275.067 2014 269.778 
2001 274.601 2015 269.764 
2002 273.045 2016 269.386 
2003 272.696 2017 269.645 
2004 271.697 2018 269.927 
2005 271.050 2019 269.958 
2006 270.589 2020 269.618 
YearArea (km2)YearArea (km2)
1990 277.287 2007 270.314 
1992 274.406 2008 270.036 
1994 273.729 2009 268.355 
1996 275.449 2010 268.698 
1997 274.422 2011 268.557 
1998 275.218 2012 268.866 
1999 274.607 2013 269.048 
2000 275.067 2014 269.778 
2001 274.601 2015 269.764 
2002 273.045 2016 269.386 
2003 272.696 2017 269.645 
2004 271.697 2018 269.927 
2005 271.050 2019 269.958 
2006 270.589 2020 269.618 

The water body extraction results in 1900, 2000, 2005, 2010, 2014, 2016, and 2018 were selected to compare with the data provided by ‘The lakes larger than 1 km2 in Tibetan Plateau’.

As shown in Table 2, comparing the data provided by the lake dataset, the lake extraction area is all smaller, the deviation rate does not exceed −1.24%, with an average of −0.67%; the extraction accuracy exceeds 98.76%, with an average of 99.33%.

Table 2

Evaluation of lake extraction results’ accuracy

YearExtraction area (km2)Dataset area (km2)Difference (km2)Deviation rate (%)
1990 277.287 280.429 −3.142 −1.13 
2000 275.067 277.032 −1.965 −0.71 
2005 271.050 274.407 −3.357 −1.24 
2010 268.698 270.068 −1.37 −0.51 
2014 269.778 270.696 −0.918 −0.34 
2016 269.386 270.546 −1.160 −0.43 
2018 269.927 270.873 −0.946 −0.35 
YearExtraction area (km2)Dataset area (km2)Difference (km2)Deviation rate (%)
1990 277.287 280.429 −3.142 −1.13 
2000 275.067 277.032 −1.965 −0.71 
2005 271.050 274.407 −3.357 −1.24 
2010 268.698 270.068 −1.37 −0.51 
2014 269.778 270.696 −0.918 −0.34 
2016 269.386 270.546 −1.160 −0.43 
2018 269.927 270.873 −0.946 −0.35 

Lake variation

As shown in Figure 7, from 1990 to 2020, the lake shoreline retreated by 0.289, 0.167, 0.509, 0.550, and 0.249 km at the northeast bank, east bank, southeast bank, southwest bank, and west bank, respectively, and the area decreased by 0.719, 0.349, 3.448, 2.252, and 1.366 km2, respectively.

Figure 7

The shoreline transition of the Paiku Co in 1990–2020. (a) Overall change; (b) west bank shoreline change; (c) southwest bank shoreline change; (d) northeast bank shoreline change; (e) east bank shoreline change; (f) southeast bank shoreline change.

Figure 7

The shoreline transition of the Paiku Co in 1990–2020. (a) Overall change; (b) west bank shoreline change; (c) southwest bank shoreline change; (d) northeast bank shoreline change; (e) east bank shoreline change; (f) southeast bank shoreline change.

Close modal

As shown in Figure 8, in 1990, the area of Paiku Co was the largest in the past 30 years, with a total area of 277.29 km2. From 1990 to 1994, it was a short-term shrinking period, with the area shrinking by 3.56 km2. From 1995 to 2000, the lake area increased, with an increase of approximately 1.34 km2. Afterward, the area of the lake began to shrink significantly. This process ended in 2009, the total area of the reduction was 6.71 km2, the area of the lake was reduced to 268.36 km2, and the smallest area in the past 30 years. After 2010, the lake area has increased little and stabilized at about 269.5 km2.

Figure 8

Variation of lake area.

Figure 8

Variation of lake area.

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As shown in Figure 9, the average change rate of the Paiku Co area is −0.247 km2/a. The maximum expansion in 1998 was 0.797 km2/a; in 2009, the maximum reduction rate was −1.680 km2/a.

Figure 9

Variation rate of lake area.

Figure 9

Variation rate of lake area.

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Lake change trend prediction

The linear regression is applied to fit the lake area change curve. Figure 10 shows a trend of MSE with changing polynomial degrees. When the degree of the polynomial reaches 3, the MSE of the prediction curve is 1.349, and the standard deviation is 1.466, reaching their best, respectively.

Figure 10

Fitting results of different degrees.

Figure 10

Fitting results of different degrees.

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According to the fitting curve prediction (Figure 11), the Paiku Co will show a stable state in the next three years, fluctuating around 269.5 km2, and then there will be an expansion trend of about 1–2 km2, and the lake area is expected to reach 270.95 km2 in 2025.

Figure 11

Lake change trend prediction.

Figure 11

Lake change trend prediction.

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Lake surface temperature estimation

We use the above-mentioned SWM algorithm in the section ‘Lake surface temperature estimation’ to generate long-term time-series land surface temperature images (Figure 12) and take the average of the image pixel values within the lake range as the record value in the year where the image is located.

Figure 12

LST estimation image. (a) 1990 LST image; (b) 2000 LST image; (c) 2010 LST image; (d) 2020 LST image.

Figure 12

LST estimation image. (a) 1990 LST image; (b) 2000 LST image; (c) 2010 LST image; (d) 2020 LST image.

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Variation of climate factors

In the past 30 years, the highest air temperature was 10.6 °C in 2020 and the minimum was 9.3 °C in 2002. Taking 2003 as the boundary: before 2003, except for abrupt and steep rises around 1998, the air temperature fluctuated at a relatively low level; later in 2003, there was an obvious inflection point, and the air temperature fluctuation level thereafter was higher than before. At this stage, the air temperature showed a trend of the first decline and then an increase (after 2014).

The maximum value of precipitation is 332.8 mm in 2011 and the minimum value is 61.6 mm in 1998. The change of precipitation in the past 30 years has always been a wave dynamic with high randomness. The precipitation before 2013 has a pattern of on- and off-year; after 2013, the precipitation has increased year by year, which is somewhat similar to the changing mode of air temperature; in 2011, there was an obvious turning point in precipitation, and the precipitation increased by 180.6 mm. This phenomenon is the epitome of the negative correlation between precipitation and temperature changes, and at this inflection point, the lake surface temperature also shows an obvious positive correlation (Figure 13).

Figure 13

Variation of climate factors.

Figure 13

Variation of climate factors.

Close modal
It can be seen from Figure 14 that the regression equation of LST with respect to air temperature and precipitation presents the best performance with the first-order polynomial. The expression of the equation is:
(7)
Figure 14

Fitting results of LST: (a) precipitation; (b) air temperature.

Figure 14

Fitting results of LST: (a) precipitation; (b) air temperature.

Close modal

In the fitting equation, LST shows a positive correlation with air temperature, which is consistent with the actual situation, while it is less affected by precipitation. It shows that in this study, the monthly LST may be less affected by weather changes and has sufficient stability, while it has sufficient sensing and interpretation capabilities for other related factors.

Relative of Paiku Co with climate factors

The Pearson coefficients of the lake area and air temperature, precipitation, and LST are −0.1318, −0.3402, and −0.5156, respectively.

The changes of precipitation before 2013 show irregular fluctuations, so the regularity of lake changes and precipitation changes is difficult to reflect; after 2013, precipitation showed a regular fluctuation growth trend, and the overall change trend during this period is more consistent with the changing trend of the lake (Figure 15(b)).

Figure 15

Comparison of climate factors and lake area change.

Figure 15

Comparison of climate factors and lake area change.

Close modal

There is a certain negative correlation between lake changes and temperature changes. During the period 2004–2009, the continuous shrinkage of the lake area may be affected by the sudden rise in temperature during this period. There are also three stages of lake change and temperature change, and the boundaries are around 2004 and 2009, but the regularity of lake and temperature changes in the three stages is not uniform (Figure 15(a)).

LST and lake area change show a high negative correlation, which may be evidence that the lake area is dominated by evaporation during the stable period. During 2000–2006, there was a significant negative correlation; after 2010, the LST showed an exponential upward trend, while the lake water volume tended to stabilize (Figure 15(c)).

As shown in Figure 16, using higher-degree equations to fit data will be closer to the true value, but the score in the k-fold cross-test will be very low due to over-fitting. We chose the first-degree equation with the least loss to show the relationship between the lake area and the respective variables, and the equation can be expressed as:
(8)
Figure 16

Fitting results of lake area: (a) air temperature; (b) precipitation; (c) LST.

Figure 16

Fitting results of lake area: (a) air temperature; (b) precipitation; (c) LST.

Close modal

In the multivariate linear regression model, the correlation between the lake and climatic factors is consistent with the above Pearson correlation coefficient. The air temperature also shows a higher influence on the lake, but the influence of precipitation on the lake seems to be less obvious. The result proves that precipitation has a low effect on Paiku Co; although the direct relationship between air temperature and lake change is not strong, in the multivariate regression equation, it shows a high negative correlation, which shows that when precipitation or other climatic factors are in a certain level, the air temperature may dominate the lake area change; lake temperature still plays an indispensable pole in this equation, further supporting its importance in climate response research.

This article uses the GEE platform to shorten the pre-processing time of remote sensing imagery firstly, reduce data redundancy, and enhance the operability of the extraction results; then, the MNDWI and EWI are used together, so that the extraction accuracy reaches more than 98.76%, better than the common NDWI single water index method (Zhou et al. 2021) 93%, and the introduction of image segmentation method (Chen et al. 2017) 88%. And Because Paiku Co's morphology is stable and there are no fine branches, this method is more suitable for this research, and it is better than the newly proposed wide-area automatic extraction machine learning method (97.96%; Wangchuk & Bolch 2020) and deep learning methods (>95%; Li et al. 2021).

For the shortcomings of the long extraction cycle (5–10 years) of the current glacial lake change studies, this paper uses ESTARFM to supplement the long time-series images, shortening the extraction cycle to one year. The ESTARFM algorithm establishes pixel weights based on the theory of similar pixels, uses the sliding window and thin plate spline (TPS) to predict the pixel value of the center pixel, and predicts the image at t1 based on the image change characteristics at t0 and t2. Therefore, it can also achieve the effect of eliminating the image contaminated by clouds and mountain shadows, which solves a major problem in the extraction of lakes in the Qinghai-Tibet Plateau. At the same time, since ESTARFM is only affected by the input image, it can theoretically increase the time resolution of related research to the daily scale or even lower, which can be applied to the monitoring of sudden events such as GLOF and landslides. However, the use of the ESTARFM algorithm is mainly oriented to the complex surface, and other background pixels (bare soil, vegetation, clouds, and fog) are also calculated at the same time, which makes the calculation results less pertinent, and the data redundancy is large, and the running time is long, not suitable for the large-scale automatic extraction of the lake. Optimizing the development of a new spatiotemporal fusion model for remote sensing and radar images of water bodies will be of great significance for the subsequent research on lakes on the Qinghai-Tibet Plateau.

When selecting climate factors, this article is different from the usual lake and climate series of studies. It uses the SWM algorithm to calculate lake surface temperature and adds climate factors to make a new attempt to the relationship between lake and climate and discovered the negative correlation between this new climate indicator and Paiku Co change that can prove the feasibility of this factor. For lake and climate research, the past always focused on a few apparent climatic factors that made the research on the correlation between lake change and climate change, which was not comprehensive and in-depth. In addition, lake temperature has a direct effect on the vegetation and soil adjacent to the lake. For glacier dammed lakes, lake temperature also has a direct impact on the occurrence of GLOF and an indispensable position in the study of disaster prevention and lake ecology. Furthermore, the introduction of more climate factors into research (radiation intensity, length of cloud, and fog period), removal of low-correlation climate factors (wind speed, etc.), and optimization of climate factor datasets (PCA algorithms, etc.) are also urgently needed in future research.

For the prediction of lake change in the future, we chose the linear regression method to fit the lake change curve and the method of prediction in this paper from the perspective of lake morphology changes, and the prediction results are more reliable by increasing the data density (reducing the period). In this study, we can find that lake temperature has a high impact on the area change. Therefore, the air temperature–lake change model can be used to predict lake change studies in the future. At the same time, if a lake shows sensitivity to various factors such as glacier melting and climate factors, a weight relationship can also be established for comprehensive prediction.

Different from previous studies, precipitation has little effect on Paiku Co, while the temperature is the dominant factor in lake changes. The reason may be that the temperature in the summer half-year increases, which causes lake evaporation to be greater than lake recharge (Dai et al. 2013). The lake variation is dominated by different reasons in each period and can be divided into four periods to discuss: (1) About 1990–1995, the temperature and precipitation in this period were at a low level for nearly 30 years, and the lake may be mainly affected by precipitation, and less precipitation recharge causes the lake to shrink rapidly. (2) From 1995 to 2000, the temperature rose and the precipitation decreased, and the lake area increased, which may be due to the rapid melting of glaciers in the area before 2000 (Zhao et al. 2016). (3) From 2000 to 2010, with the increase in temperature and precipitation, the lake variation in this stage is dominated by evaporation. The slower melting rate of glaciers and the reduced supply of water have reduced the area of the lake (Zhang et al. 2020c). (4) From 2010 to 2020, the temperature, precipitation, and lake area all showed an increasing trend, the lake may be mainly recharged by precipitation. After that, the water volume of the lake should reach a balance around 2013, this inflection point is also mentioned in Zhao et al. (2016) and Zhang et al. (2020c), which may indicate a new model of the regional climate. The response of lake changes to climate in the Paiku Co area has different stages, which provides more in-depth research strategies for explaining the laws of climate change in the Qomolangma Natural Reserve, southern Tibet, and even the Qinghai-Tibet Plateau: specific laws based on macro trends should be paid more attention to.

In this article, we used the ESTARFM to supplement the lake image sequence and combined the water index method to complete the extraction of the long-term lake. Then the lake surface temperature was added as a new factor and fitted a multi-variable linear regression with air temperature and precipitation for further analysis. Finally, the linear regression was used to fit the curve to predict the changing trend of Paiku Co in the next five years. During the study period, Paiku Co experienced a process of sharp shrink – recovery – continuous retreat – stabilization. Paiku Co showed higher sensitivity to temperature, and the factors leading to its change in different periods were variable.

This article provides multiple new ideas for the study of lake changes on the Qinghai-Tibet Plateau:

  • 1.

    The multi-source remote sensing image fusion method can well perfect the long-time sequence research and can be developed for the research that needs more accuracy to improve the time resolution.

  • 2.

    To prove the correlation between lake temperature and lake area change, follow-up research can be introduced.

  • 3.

    The interannual variability of some lakes may be less affected by common climate factors, such as air temperature and precipitation, and more factors should be considered when probing the causes of lake change.

  • 4.

    The inflection point of climate and lake change in the Paiku Co area in 2013 was found, which may have an explanatory effect on the Qinghai-Tibet Plateau or local environmental change.

However, there are still many shortcomings that need to be improved: the lake extraction method can be optimized; the spatial–temporal fusion algorithm can be adjusted to fit the study of lakes in the Qinghai-Tibet Plateau; the correlation of climate factors still needs to be further supplemented and studied. Furthermore, more decision-making indicators can be added for forecasting on the basis of exploring the correlation of climate factors.

Paiku Co is an inland lake in the Himalayas, which is less affected by human activities, showing an evolutionary law that can be interpreted. The climate change in the basin can be explained through lake change, which has the value of applying to the local/entire Qinghai-Tibet Plateau. The fragile ecosystem of the Qinghai-Tibet Plateau, especially the Himalayas, has attracted more and more attention, and the research on its climate response needs to be deepened. We believe that such research can provide continuous and effective help in solving water resource and environmental problems.

This work was supported by the Open Foundation of the Research Center for Human Geography of Tibetan Plateau and its Eastern Slope (Chengdu University of Technology), grant no. RWDL2021-ZD003; Open Foundation of Sichuan Center for Disaster Economic Research, grant no. ZHJJ2021-ZD001; Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Natural Resources; the National Key Research and Development Program of China, 2021YFC3000401.

X.D. and Z.Y. drafted the manuscript and were responsible for the research design, experiment, and analysis. Z.W., X.G., and W.L. reviewed and edited the manuscript. Z.Y., G.Q., J.L., and H.L. supported the data preparation and the interpretation of the results. All of the authors contributed to editing and reviewing the manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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