Frozen Soil Advances the Effect of Spring Snow Cover Anomalies on Subsequent Precipitation over the Tibetan Plateau

Kai Yang aKey Laboratory of Arid Climate Resource and Environment of Gansu Province (ACRE), Research and Development Center of Earth System Model (RDCM), College of Atmospheric Sciences, Lanzhou University, Lanzhou, China

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Chenghai Wang aKey Laboratory of Arid Climate Resource and Environment of Gansu Province (ACRE), Research and Development Center of Earth System Model (RDCM), College of Atmospheric Sciences, Lanzhou University, Lanzhou, China

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https://orcid.org/0000-0002-7122-7160
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Abstract

Frozen soil distributed over alpine cold regions causes obvious changes in the soil hydrothermal regime and influences the water–heat exchanges between land and atmosphere. In this study, by comparing the effects of snow cover anomalies and frozen soil thawing anomalies on the soil hydrothermal regime, the impact of the frozen soil thawing anomalies in spring on precipitation in early summer over the Tibetan Plateau (TP) was investigated via diagnostic analysis and model simulations. The results show that a delay (advance) in the anomalies of frozen soil thawing in spring can induce distinct cold (warm) anomalies in the soil temperature in the eastern TP. These soil temperature cold (warm) anomalies further weaken (enhance) the surface diabatic heating over the mideastern TP; meanwhile, the anomalies in the western TP are inconspicuous. Compared to the albedo effect of snow cover anomalies, impacts of frozen soil thawing anomalies on soil hydrothermal regime and surface diabatic heating can persist longer from April to June. Corresponding to the anomalous delay (advance) of frozen soil thawing, the monsoon cell is weakened (enhanced) over the southern and northern TP, resulting in less (more) water vapor advection over the eastern TP and more (less) water vapor advection over the southwestern TP. This difference in water vapor advection induces a west–east reversed pattern of precipitation anomalies in June over the TP. The results have potential for improving our understanding of the interactions between the cryosphere and climate in cold regions.

Significance Statement

Frozen soil and snow are widely distributed over alpine and high-latitude cold regions, and their feedbacks to climate have attracted much attention. The purpose of this study is to investigate the role of frozen soil in effects of snow cover anomalies on surface diabatic heating and its feedback to subsequent precipitation over the Tibetan Plateau. The results highlight that frozen soil modulates the effect of snow cover anomalies on the soil hydrothermal regime from April to June and interseasonal variations of frozen soil thawing anomaly zones result in a thermal contrast between the western and eastern Tibetan Plateau, which further lead to a reversed pattern of early summer precipitation anomalies over the Tibetan Plateau. These findings emphasize the role of frozen soil in land–atmosphere interactions.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Kai Yang, yangkai@lzu.edu.cn; Chenghai Wang, wch@lzu.edu.cn

Abstract

Frozen soil distributed over alpine cold regions causes obvious changes in the soil hydrothermal regime and influences the water–heat exchanges between land and atmosphere. In this study, by comparing the effects of snow cover anomalies and frozen soil thawing anomalies on the soil hydrothermal regime, the impact of the frozen soil thawing anomalies in spring on precipitation in early summer over the Tibetan Plateau (TP) was investigated via diagnostic analysis and model simulations. The results show that a delay (advance) in the anomalies of frozen soil thawing in spring can induce distinct cold (warm) anomalies in the soil temperature in the eastern TP. These soil temperature cold (warm) anomalies further weaken (enhance) the surface diabatic heating over the mideastern TP; meanwhile, the anomalies in the western TP are inconspicuous. Compared to the albedo effect of snow cover anomalies, impacts of frozen soil thawing anomalies on soil hydrothermal regime and surface diabatic heating can persist longer from April to June. Corresponding to the anomalous delay (advance) of frozen soil thawing, the monsoon cell is weakened (enhanced) over the southern and northern TP, resulting in less (more) water vapor advection over the eastern TP and more (less) water vapor advection over the southwestern TP. This difference in water vapor advection induces a west–east reversed pattern of precipitation anomalies in June over the TP. The results have potential for improving our understanding of the interactions between the cryosphere and climate in cold regions.

Significance Statement

Frozen soil and snow are widely distributed over alpine and high-latitude cold regions, and their feedbacks to climate have attracted much attention. The purpose of this study is to investigate the role of frozen soil in effects of snow cover anomalies on surface diabatic heating and its feedback to subsequent precipitation over the Tibetan Plateau. The results highlight that frozen soil modulates the effect of snow cover anomalies on the soil hydrothermal regime from April to June and interseasonal variations of frozen soil thawing anomaly zones result in a thermal contrast between the western and eastern Tibetan Plateau, which further lead to a reversed pattern of early summer precipitation anomalies over the Tibetan Plateau. These findings emphasize the role of frozen soil in land–atmosphere interactions.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Kai Yang, yangkai@lzu.edu.cn; Chenghai Wang, wch@lzu.edu.cn

1. Introduction

The Tibetan Plateau (TP), with an average altitude of more than 4000 m with a complex underlying surface (e.g., glacier, snow cover, and frozen soil), is a region highly vulnerable to climate changes (Liu and Chen 2000; Chen et al. 2015). Both observations and model simulations have suggested that the climate over the TP has undergone significant changes and show large spatial variability (e.g., Lu and Liu 2010; Wang et al. 2014), thereby further influencing the ecological and hydrological processes and land–atmosphere interaction over the TP. A recent study (Yang and Wang 2022) shows the east–west reverse coupling between spring soil moisture and summer precipitation. Many studies have revealed that the thermal and dynamic effects of the TP have great influences on the atmospheric circulation and climate of East Asia and the globe (e.g., Ye et al. 1957; Flohn 1957, 1960; Ye and Gao 1979; Yanai et al. 1992; Wu and Zhang 1998; Duan et al. 2013; Wu et al. 2012, 2014). The thermal effect of TP mainly arises from surface diabatic heating, and the variation in the surface diabatic heating is closely linked to the land surface processes over the TP (Luo and Yanai 1983; Duan and Wu 2005).

Snow and frozen soil are widely distributed over the TP. Impacts of spatiotemporal anomalies of the snow cover over the TP on the subsequent atmospheric circulation and climate have been recognized from albedo effects and hydrological effects of the snow cover on surface energy budget and moisture storage (e.g., Barnett et al. 1989; Douville and Royer 1996; Peings and Douville 2010; Wang et al. 2017). The freezing/thawing of frozen soil greatly affects the surface energy balance and water cycle (Zhao et al. 2004; Yang et al. 2007; Yang and Wang 2019a). Studies have indicated that soil freeze–thaw anomalies over TP have considerable impacts on the summer precipitation in East Asia (Wang et al. 2003, 2008, 2020a). Wang and Shang (2007) suggested that an increase in soil moisture induced by the thawing of frozen soil in spring has considerable effects on the subsequent precipitation and promotes the onset of the rainy season over the TP. Xue et al. (2018, 2019) suggested that the spring land surface and subsurface temperature anomalies over the TP have significant effects on the subsequent precipitation in East Asia. However, the impacts of land surface process anomalies on the exchanges of water and heat between land and atmosphere still remain unclear, for example, melting of snow and thawing of frozen soil are not uniform over the whole TP (e.g., time for thawing of frozen soil in the southeastern TP is earlier than that in the northwest TP; Yang and Wang 2019a), as well as due to the differences in topography and altitude, which should lead to the spatial heterogeneity of surface diabatic heating. The impacts of the heterogeneity of surface diabatic heating on the thermal forcing of the TP to the surrounding atmospheric circulation should be investigated.

Along with the variation of the land surface condition from the winter to the summer (i.e., snow accumulation and melt, freeze–thaw cycle of frozen soil), the properties and strength of surface diabatic heating undergo largely spatiotemporal changes over the TP (Chapin et al. 2005; Guo et al. 2011; Yang and Wang 2019a). As snow covers the frozen soil, the seasonal freeze–thaw cycle of frozen soil is closely related to snow (Zhou et al. 2013; Zhao et al. 2018). High albedo of snow decreases the absorbed solar radiation at the surface, further leading to less energy into soil. Otherwise, the snow acts as a barrier to the heat loss of the frozen soil, especially thick snow (Zhang et al. 2021). Owing to the low thermal conductivity and large heat capacity of the snow, the heat exchange between soil and atmosphere is weakened, and the influence of external climatic conditions on the thermal status of frozen soil is delayed (Goodrich 1982; Ma and Hu 1995; Yao et al. 2019). In past several decades, the TP has been warming significantly, exacerbating the snow-melting and permafrost degradation, thereby affecting the soil hydrothermal regime (Kang et al. 2010; Wang et al. 2020b). These effects of frozen soil and snow further influence the exchanges of water and heat between the land and atmosphere (Yang et al. 2014). Frozen soil is the most distinct feature of the underlying surface over the TP, and its changes and responses to the climate change have been studied extensively (e.g., Cheng and Wu 2007; Oelke and Zhang 2007; Wu and Zhang 2008; C. Wang et al. 2019). The feedback of frozen soil to the climate change lays emphasis on its carbon release process (e.g., Zhang 2007; Ding et al. 2017), while how the frozen soil that is under the snow makes its feedback to climate through its hydrothermal regime anomalies is still an open question. In other words, how coupling between snow and frozen soil affects the soil hydrothermal regime (i.e., soil temperature and moisture) and leads to the persistent surface diabatic heating anomalies needs to be further explored.

This study aims to explore how frozen soil hydrothermal regime anomalies affect the precipitation during rainy season and the associated possible physical mechanism. The rest of this paper is organized as follows. Section 2 introduces the data, methodology, and model setup. Section 3 presents a diagnostic analysis of the relation between the hydrothermal condition of frozen soil in spring and subsequent precipitation in early summer. Four experiments designed to validate the impacts of frozen soil thawing anomalies on the subsequent precipitation are described in section 4. The possible mechanism is explored in section 5. The discussion and main conclusions are given in section 6.

2. Data and methodology

a. Datasets

In this study, the monthly soil temperature data at 1° × 1° spatial resolution during 1979–2010 was obtained from the Global Land Data Assimilation System (GLDAS; https://disc.gsfc.nasa.gov/datasets?keywords=GLDAS&page=1) version 2 based on the Noah land surface model. The GLDAS generates satellite- and ground-based observational data using advanced land surface modeling and a data assimilation technique (Rodell et al. 2004).

Monthly precipitation data were obtained from NOAA’s Precipitation Reconstruction over Land (PREC/L; https://psl.noaa.gov/data/gridded/data.precl.html; Chen et al. 2002) dataset with 0.5° × 0.5° spatial resolution for the period 1979–2010. To further confirm the results, the monthly precipitation derived from 3-h data of the China Meteorological Forced Dataset (CMFD) with 0.1° × 0.1° spatial resolution for the period 1979–2010 was used; this dataset is a fusion product based on satellite precipitation data and in situ data from 740 China Meteorological Administration stations (He et al. 2020), and it is widely used in studies over the TP (e.g., Sun et al. 2020). Daily Global Precipitation Measurement (GPM; https://disc.gsfc.nasa.gov/datasets?keywords=GPM&page=1; Huffman et al. 2015) precipitation data with 0.1° × 0.1° spatial resolution are used to evaluate the model capability in simulating early summer precipitation over the TP.

Further, the weekly Northern Hemisphere snow cover extent (SCE) data of version 4 (Brodzik and Armstrong 2013) from the National Snow and Ice Data Center (NSIDC) (https://nsidc.org/data/nsidc-0046) for period 1979–2010 with Equal-Area Scalable Earth (EASE) Grid 2.0 projection at a 25-km spatial resolution was used, in the EASE-Grid datasets, for each 25 km × 25 km cell, SCE is a simple binary variable of the presence or absence of snow cover, weekly EASE-Grid SCE data was converted to monthly mean on regular 1° × 1° grids. The daily snow-depth dataset for 1979–2010 derived from SMMR, SSM/I, and AMSR-E passive microwave remote sensing data with a horizontal resolution of 0.25° × 0.25° was used (Che et al. 2008; Che and Dai 2015). The monthly snow-depth data were averaged from the daily dataset.

b. Methods

To analyze the relation between the hydrothermal regimes anomalies of frozen soil in spring and subsequent precipitation over the TP, we employed the empirical orthogonal function (EOF) to investigate the spatiotemporal characteristics of interseasonal variations of soil temperature at depths of 0–1 m from April to June.

To diagnose the water vapor transport, the convergence of vertically integrated water vapor flux for an air column was calculated as follows:
Q=1g0PsqVdp,
where g is the gravitational acceleration; Ps is the surface pressure; q is the specific humidity; V is the wind vector; p is the pressure. In this study, we used the output from the model to calculate −∇ ⋅ Q.
To investigate the roles of local evapotranspiration (ET) and remote moisture flux convergence [MFC, i.e., Eq. (1)] on precipitation, the framework adopted in the studies of Schär et al. (1999), Asharaf et al. (2012), and Wei et al. (2015) was used. It is assumed that the water vapor transported through a region and from local ET are well mixed. Then, precipitation (P) is related to ET, moisture inflow (IN), and precipitation efficiency (χ) as follows:
P=χ(ET+IN),
where the precipitation efficiency χ is defined as the percentage of moisture entering a region and falls as precipitation and is calculated as the ratio of P and ET + IN. IN is moisture entering a region; it is different from MFC, which is the moisture entering minus the moisture leaving a region, but is closely related to MFC. From Eq. (2), the precipitation anomalies induced by anomalous wet or dry soil can be written as follows:
ΔP=Δχ(ET+IN)+χΔET+χΔIN+Δχ(ΔET+ΔIN),
where the four terms on the right side represent the efficiency effect, surface effect, remote effect, and residual, respectively.

c. Model

The Advanced version of the Weather Research and Forecasting Model (WRF-ARW, version 4.2) was used in this study. WRF-ARW is a limited-area, nonhydrostatic mesoscale modeling system with a terrain-following hydrostatic-pressure vertical coordinate. It has options for physical parameterizations. WRF has been widely used in TP climate simulations, previous studies (e.g., Gao et al. 2015; Liu et al. 2022) evaluated the capability of WRF simulations over TP. Based on these evaluations, here we used the single-moment three-class scheme (WSM3) microphysics parameterization (Leung et al. 2003); we used the Yonsei University (YSU) scheme (Hong and Pan 1996) for planetary boundary layer parameterization, Dudhia scheme for shortwave radiation parameterization (Dudhia 1989), Rapid Radiative Transfer Model (RRTM) scheme for longwave radiation parameterization (Mlawer et al. 1997), and the Grell–Devenyi ensemble scheme (Grell 1993) for convective parameterization. The land surface scheme was selected as the Noah-MP land surface model (Niu et al. 2011). The soil freeze–thaw parameterizations in Noah-MP are augmented compared to the Noah LSM and include a frozen soil scheme that produces greater soil permeability and no iteration parameterization for supercooled water (Niu and Yang 2006). In Noah-MP, the soil ice content in the soil-thawing process is calculated as follows:
wicen+1=wicenHΔtLf,
where wicen and wicen+1 are the soil ice content (kg m−2) at the current and next time step; Lf (J kg−1) is the latent heat of fusion; H=(cΔz/Δt)(TfT) is the excess or deficit of energy (W m−2) consumed in thawing or released in freezing; c is the soil volumetric heat capacity (J m−3 K−1); Δz is the thickness of the layer (m); Δt is the time integral step (s); T is the soil temperature (K); Tf is the freezing temperature (273.15 K). The energy consumed in the soil thawing process was used to readjust the soil temperature.

3. Relation between the hydrothermal regime anomalies of frozen soil in spring and subsequent precipitation

The changes in the frozen soil hydrothermal regime are reflected by the anomalous variations in soil moisture and temperature, causing anomalies in surface diabatic heating (Yang et al. 2007; Yang and Wang 2019b). Studies have shown that the anomalies of frozen soil thawing over the TP significantly influence the summer precipitation in China through its impacts on TP surface diabatic heating (Wang et al. 2003, 2008, 2020a).

The anomalies of the frozen soil hydrothermal regime are partly reflected in the anomalous variations of soil temperature. To analyze the characteristics of frozen soil hydrothermal regime anomalies from spring to early summer, the EOFs of soil temperature at depths of 0–1 m in April, May, and June over the TP during 1979–2010 were obtained. The first mode (EOF1) of April soil temperature represented the long-term trend of warming over the whole TP (Fig. S1 in the online supplemental material). To focus on the interannual variation in soil temperature, we analyzed EOF2 of April soil temperature, with a variance contribution of 15.9%; it reflected the homogeneous anomalies of April soil temperature in most regions of the TP, especially the maximum load vectors (LVs) located over the southern and eastern TP, except for the opposite variations over the edge of the northwestern TP (Fig. 1a). The patterns of LVs of EOF2 for May and June soil temperatures are similar to that of April soil temperature. Nevertheless, the zone with the maximum LVs of May soil temperature is located in the midsouthern region of the TP, which is adjacent to the 0°C isotherm of April soil temperature; the zone with maximum LVs of June soil temperature shifts to the mideastern regions of the TP as the frozen soil in these regions thaws in May and June. These patterns imply that the interseasonal variations of zones position with large interannual variability of soil temperature from April to June are linked to the frozen soil thawing anomalies. The associated principal component (PC2) shows distinct interannual variations (Fig. 1b), and the evolutions of PC2 of EOF2 for May and June soil temperature are generally consistent with the evolution of PC2 of April soil temperature. The correlations between PC2 of April soil temperature and that of May and June soil temperature are 0.50 (p < 0.05) and 0.47 (p < 0.05), respectively. Thus, the soil temperature anomalies linked to frozen soil thawing anomalies can persist from spring to early summer.

Fig. 1.
Fig. 1.

Relation between soil temperature anomalies in early spring and subsequent precipitation over the Tibetan Plateau (TP). (a) Second leading spatial pattern (EOF2) of load vectors (LVs) for April soil temperature at depths of 0–1 m during 1979–2010, with a variance contribution of 15.9%. Blue and purple contours represent the LVs of EOF2 for May and June soil temperature (contours values are −0.06, −0.08, and −0.10; thicker contours mean larger values), respectively; red, orange, and yellow contours represent the 0°C isotherms of climatological April, May, and June soil temperature, respectively, for 1981–2010. (b) The associated principal components (PCs) of EOF2 for April, May, and June soil temperature, respectively, and the correlation (r) between them are 0.50 and 0.47 (p < 0.05). (c) Correlation between PC2 of EOF2 for April soil temperature and June precipitation from PREC/L, slash and lattice shading represent values significant at p < 0.1 and p < 0.05 by the Student’s t test. (d) As in (c), but for the China Meteorological Forced Dataset (CMFD) precipitation.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

Frozen soil thawing anomalies are associated with the soil hydrothermal regime anomalies, and they cause surface diabatic heating anomalies, which influence the subsequent atmospheric circulation and local precipitation. To diagnose the relation between the hydrothermal regime anomalies of frozen soil in spring and the subsequent precipitation over the TP, the correlations between PC2 of EOF2 for April soil temperature and June precipitation over the TP were calculated using PREC/L and CMFD datasets (Figs. 1c,d). The results indicate that anomalous delay of frozen soil thawing accompanied by the cold anomalies of soil temperature in April result in less June precipitation over the central-eastern TP and more subsequent precipitation over the southwestern TP.

The variability of the near-surface soil temperature is suggested to be closely related to the snowfall and snowmelt processes though snow albedo feedback (Ye Liu et al. 2020). To investigate the linkage between soil temperature anomalies and snow cover anomalies during spring, the mean and standard deviation of monthly snow cover from March to June for 1979–2010 are shown in Fig. 2. Areas with the maximum snow cover standard deviation in March appear in the southeastern TP (Fig. 2a) and Himalayas and western TP; these results are consistent with the zone with the maximum interannual variability of April soil temperature in the southern and eastern TP (Fig. 1a). In April, the snow cover standard deviation in the southeastern TP decreases, while the snow cover standard deviation in the Himalayas and western TP generally remains steady (Fig. 2b). Until May and June, the snow cover standard deviations in the southeastern TP continue decreasing remarkably and become small (Figs. 2c,d). These results show that the interannual variability of snow cover in the southeastern TP varies clearly from March to June; however, the interannual variability of soil temperature always appears over the southeastern TP and has good persistence from March to May (Fig. 1a,b). Thus, these results imply that soil temperature anomalies may be linked not only to snow cover anomalies but also to other land surface processes such as frozen soil thawing during the spring.

Fig. 2.
Fig. 2.

Spatial pattern of mean (shading) and standard deviation (contours) of snow cover (%) in (a) March, (b) April, (c) May, and (d) June during 1979–2010. The dotted box (28.5°–36.5°N, 88.5°–102°E) represents the area with the maximum standard deviation of snow cover.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

To explore the linkage between soil temperature anomalies and snow cover anomalies, Fig. 3 shows the correlation between PC2 of April soil temperature and snow cover in March and April. The relation between April soil temperature anomalies and snow cover in the preceding month (March) shows a loosely positive correlation over most regions of the TP, especially over the southeastern TP (Fig. 3a), which means the cold (warm) anomalies of soil temperature has linkage with the snow cover, but it is not significant. The pattern of the relation between April soil temperature anomalies and simultaneous (April) snow cover anomalies is similar with that for March but the significantly positive correlation in the southeastern TP is more obvious than that in March (Fig. 3b). The results indicate that the impacts of snow cover anomalies on subsequent soil temperature will be greatly attenuated and that soil temperature anomalies are mainly linked to the simultaneous snow cover anomalies. Nevertheless, correlations between PC2 of April soil temperature and series of snow cover averaged over the southeastern TP in March and April are positive (Fig. 3c), but not significant, it implies the anomalies of soil temperature in April is partly related to the snow cover anomalies.

Fig. 3.
Fig. 3.

Relation between soil temperature anomalies and snow cover (SC) over the TP. (a) Correlation (r) between PC2 of April soil temperature and March snow cover during 1979–2010. The slash and lattice shading represent values significant at p < 0.1 and p < 0.05 by the Student’s t test. (b) As in (a), but for correlation between PC2 of April soil temperature and April snow cover. (c) Series of snow cover averaged over region [the dotted box in (a), 28.5°–36.5°N, 88.5°–102°E]; r = 0.20 (p > 0.1) and r = 0.22 (p > 0.1) are the correlations between PC2 of April soil temperature and averaged snow cover in March and April, respectively. Snow cover data are detrended.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

To analyze the insulating effect of snow cover, correlations between soil temperature and snow depth in March and April were made (Figs. 4a,b), which shows cold (warm) anomalies of soil temperature in the southeastern TP is positively related to the larger (smaller) snow depth, especially in April, it also implies the insulating effect of relatively thin snow cover over the TP on soil temperature in spring seems minor, compared to the cooling effect through high albedo of snow cover, which is consistent with the results in previous studies that insulating effect on frozen soil below mainly appears in soil being frozen with thick snow cover (e.g., T. Wang et al. 2019; Zhang et al. 2021). The comparisons of PC2 of April soil temperature and the series of snow depth averaged over the southeastern TP in March and April (Fig. 4c) also show April soil temperature is significantly correlated with the snow depth in April (r = 0.34; p < 0.05) rather than the snow depth in March (r = 0.20; p > 0.1). These results further imply that the persistence of soil temperature anomalies from April to June are linked to other surface processes (such as frozen soil thawing in spring) except for the snow cover anomalies.

Fig. 4.
Fig. 4.

As in Fig. 3, but for relation between soil temperature anomalies and snow depth (SD) over the TP, r = 0.20 (p > 0.1) and r = 0.34 (p < 0.05) are the correlations between PC2 of April soil temperature and averaged snow depth in March and April, respectively.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

Along with snow cover changes caused by melting in spring, frozen soil undergoes thawing. Generally, with regard to the anomalous delay of frozen soil thawing, two situations can be considered from the observations (Fig. S2):

  1. The depth of the frozen soil layer is greater in colder autumn and winter and because more energy is needed for thawing frozen soil, the thawing process is slower. This induces cold anomalies of soil temperature in the spring of the next year.

  2. The soil is frozen normally in the autumn and winter, but a colder near-surface temperature in the spring (such as the cold induced by a heavier snow cover) of the next year slows down the thawing of the frozen soil compared to the normal condition.

The above two situations can be described in a schematic diagram shown in Fig. 5. The next section describes a series of experiments designed to analyze the impacts of snow cover anomalies and frozen soil thawing anomalies on the soil hydrothermal regime and surface diabatic heating.

Fig. 5.
Fig. 5.

Schematic diagram of the soil freeze–thaw anomalies. Black and blue lines represent the 0°C soil temperature (Tsoil) isotherm under normal and anomalous conditions. (a) Colder autumn and winter cause an increase in the depth of the frozen soil layer, thereby slowing down the soil thawing process and resulting in cold anomalies in the soil temperature because more energy is required for thawing the soil. (b) Soil is normally frozen in the preceding autumn and winter, but because of the colder spring, soil thawing is slower, and there are cold anomalies of soil temperature as less energy is used for soil thawing.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

4. Simulated advance of frozen soil in effect of snow cover on early summer precipitation

a. Experiment design

Snow cover above the frozen soil affects the hydrothermal regime of frozen soil (T. Wang et al. 2019). To compare the impacts of snow cover anomalies and frozen soil thawing anomalies on surface diabatic heating and subsequent precipitation, four experiments based on WRF were conducted (Table 1).

Table 1

Design of experiments.

Table 1

One is the control experiment (CTL), in which the snow cover and frozen soil thawing are normal, and the soil ice content is calculated by Eq. (4).

The impacts of snow cover anomalies on land surface process generally include the albedo effect and hydrological effect due to the snow melting (e.g., Barnett et al. 1989). The snow albedo ranges from 0.5 to 0.9, the snow cover anomalies can induce changes in ground albedo by about 0.3–0.4 over the TP (Li et al. 2018), which can account for about 50% of ground albedo when land surface is fully covered by the snow; the liquid water from snow melting can increase the soil moisture. Besides, the variations in snow depth have impacts on the thermal conductivity and insulating effects of snow on the soil temperature (e.g., Trujillo and Molotch 2014; Li et al. 2021). On an interannual scale, the variability of snow cover can account for about 50% of the mean (Fig. 2). Therefore, to fully account the effects of snow cover and snow depth anomalies, 50% increase in snow cover fraction and corresponding increase of snow depth over the whole TP were imposed in the sensitive experiment (hereinafter, referred to as SNOW).

A distinct feature of soil freeze–thaw process that distinguishes it from unfrozen soil is the phase changes of the soil water. Difference of soil liquid water content between frozen and unfrozen soil can be larger than 0.1 mm3 mm−3 (Yang and Wang 2019a), while the averaged soil water content in spring is about 0.2–0.3 mm3 mm−3, change in soil ice is generally equal to that of liquid water (Δwice ≈ Δwliq). Thus, to impose a delay of frozen soil thawing in the presummer period when frozen soil begins to thaw, a sensitivity experiment (hereinafter FT+) was performed with that the content of soil ice thawed at every integral step was reduced by 50% over the TP in Noah-MP. Another sensitivity experiment (hereinafter FT−) was also performed with an imposed advance of frozen soil thawing in the presummer period, the soil ice at every integral step is increased by 50% over the TP in Noah-MP. The detailed modification in WRF is as follows:
wicen+1=wicenHΔtLf×α,
where wicen+1 is the prognostic soil ice content, α represents the imposed proportion of soil ice melting at every integral step in sensitivity experiment FT+ (α = 0.5) and FT− (α = 1.5), and other variables have been defined in Eq. (4).

The initial lateral boundary conditions and sea surface temperature (SST) were interpolated from ERA-Interim (Dee et al. 2011). All experiments had the same domain, covering nearly the whole Asian continent (Fig. 6a), and the horizontal grid was 30 km with 137 × 195 grid cells. There were 33 vertical levels. To eliminate the impacts of atmospheric variability embedded in the initial and boundary conditions, all numerical experiments contain 10 members, which were conducted with two cases in 2004 and 2014 combining five different initial times. The criterion for case selection is the preceding SST in Niño-3.4 region have no significant anomalies, which aims to exclude the influence of ENSO on precipitation. Specifically, we used 0000, 0600, 1200, and 1800 UTC 1 March and 0000 UTC 2 March 2004 as the initial date, and simulations were ended at 1800 UTC 30 June 2004, so as done in 2014. The ensemble means of each member for different experiments are used for analysis.

Fig. 6.
Fig. 6.

(a) The simulation domain by the WRF Model; the filled color represents the elevation (m), and the black solid line represents the boundary of the TP. Distribution of June precipitation: (b),(c) GPM observed June precipitation; (d),(e) CTL simulated June precipitation; and (f),(g) scatter of June precipitation (mm day−1) between CTL simulation and GPM observation. Panels (b), (d), and (f) and (c), (e), and (g) represent cases in 2004 and 2014, respectively.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

WRF has been widely used to simulate the weather and climate over the TP and its surrounding regions, and it can capture the characteristics of atmospheric circulation and reproduce the spatiotemporal distribution of precipitation over the TP (e.g., Gao et al. 2015). To evaluate the capability of WRF in simulating the precipitation in the rainy season, the June precipitation simulated by the control experiment was compared with the GPM precipitation data (Huffman et al. 2015). The WRF simulations (Figs. 6d,e) can reproduce observed precipitation spatial characterizations in June that precipitation is mainly distributed over the eastern and southern TP (Figs. 6c,d). Although WRF overestimates June precipitation and has wet biases over the TP, the simulation and observation are generally consistent in spatial distribution (r = 0.33, p < 0.01; r = 0.76, p < 0.01) (Figs. 6f,g), the systematic wet biases can be reduced in simulated precipitation anomalies by subtractions between CTL and sensitive experiments. Evaluations also shows WRF has capability in reproducing spatial–temporal distributions of soil temperature and snow cover from March to June (Figs. S3, S4). This means that WRF is suitable for simulating the climate over the TP.

b. Results

The distribution of precipitation differences between CTL and the sensitivity experiments are shown in Fig. 7. With a heavier snow cover over the southeastern TP during spring, anomalies in June precipitation simulated in SNOW are significantly negative over most regions of the eastern TP, whereas the June precipitation over the western TP is positive (Fig. 7a). This pattern of precipitation anomalies is generally similar to that of the correlation between April soil temperature anomalies and June precipitation, although the positive anomalies of precipitation over the southwestern TP are underestimated. When the thawing of frozen soil is delayed anomalously, the June precipitation simulated in FT+ decreases over the central-eastern and western TP and increases over the southwestern TP (Fig. 7b), this pattern of precipitation anomalies is similar to the simulation results of SNOW, but the anomalies of June precipitation are larger than that of SNOW experiment. The pattern of precipitation anomalies simulated in FT+ is generally consistent with the diagnostic results (Figs. 1c,d), thereby verifying the impacts of the hydrothermal regime anomalies of frozen soil in the early spring on subsequent precipitation over the TP. When the thawing of frozen soil is anomalously advanced, the pattern of June precipitation anomalies simulated in FT− (Fig. 7c) is generally inversed compared to the pattern simulated in FT+, with significantly positive precipitation anomalies in most regions of the mideastern TP and western TP, negative precipitation anomalies appear over edges of the southwestern TP. These results further support the relation between frozen soil thawing anomalies during spring and June precipitation over the TP.

Fig. 7.
Fig. 7.

Anomalies of June precipitation (mm day−1) over the TP simulated from experiment (a) SNOW, (b) FT+, and (c) FT−. Slash and lattice shading represent values significant at the p < 0.1 and p < 0.05 level by the Student’s t test, respectively.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

During spring, the snow cover changes as snow melts, affecting the hydrothermal regime of the frozen soil (Zhang 2005). Heat transport in frozen soil can also feedback to the variations of snow temperature; thus, these should be connected to each other. The role of thawing of frozen soil in determining the climatic effects of snow cover anomalies should be examined. A comparison of the precipitation anomalies simulated in SNOW and FT+ shows that the peak of precipitation anomalies and areas with significant precipitation anomalies in FT+ are larger than those in the case of SNOW; this means the effects of frozen soil thawing anomalies on subsequent precipitation may be more dominant than the effects of snow cover anomalies alone during spring. In other words, the effects of snow cover anomalies are regulated or advanced through its impacts on the thawing of frozen soil. Note that although snowmelt provides a large supply of water to the land surface during spring, the infiltration rates into icy soils are low, and much of the water may be converted to runoff (Metcalfe and Buttle 2001). Frozen soil thawing can greatly affect the soil temperature and moisture in the spring (Wang et al. 2008). Thus, the hydrological effects of snow on soil moisture, which is thought to persist longer on the impacts of subsequent climate (Barnett et al. 1989; Douville and Royer 1996), include the effects of frozen soil thawing on the liquid water content of the soil.

5. Possible mechanism linked to advance of soil-thawing anomalies in effects of spring snow cover anomalies on the subsequent precipitation

To analyze the changes in the soil hydrothermal regime related to the snow cover anomalies and frozen soil thawing anomalies, Figs. 8 and 9 shows the soil temperature and moisture and their anomalies from April to June. When the snow cover over the eastern TP is heavier, the soil temperature and soil moisture (i.e., liquid water) simulated in SNOW are significantly lower than those in the case of CTL from April to May (Figs. 8a, 9a), whereas the anomalies of soil temperature and moisture clearly weaken until June (Figs. 8b, 9b). When the thawing of frozen soil is delayed, the negative anomalies of soil temperature simulated in FT+ in April are mainly located over the southeastern TP, except for the northwestern TP; in May, the negative anomalies of soil temperature appear over the midsouthern TP, after the frozen soil over the southern TP starts thawing; in June, the negative anomalies of soil temperature appear over the mideastern region of the TP (Fig. 8c). Frozen soil thawing anomalies will lead to anomalous variations in soil moisture, along with the thawing of the soil from the southeastern TP toward to northeastern TP during April–June. The zones with significant anomalies of soil moisture are located at or around the 0°C isotherms of soil temperature (Fig. 9c) and shift with the movement of these isotherms. The spatial variations in soil temperature and moisture from April and June are consistent with the EOF results, thereby further confirming the interseasonal variations of zones of frozen soil thawing anomalies over the TP. When the frozen soil thawing advances, the patterns of soil temperature and moisture simulated in FT− (Figs. 8d, 9d) show inverse with that of FT+, and significant anomalies of soil temperature and moisture appear in May and June over the mideastern TP. These zones shift with the movement of the 0°C isotherms of soil temperature. These results illustrate that the soil hydrothermal regime anomalies in the presummer period are closely related to the frozen thawing anomalies.

Fig. 8.
Fig. 8.

(a) Evolutions of soil temperature (°C) average over the region indicated by the dotted box shown in Fig. 2a (28.5°–36.5°N, 88.5°–102°E), and distribution of soil temperature anomalies (sensitivity experiment minus CTL) from spring to early summer (April–June) simulated by (b) SNOW, (c) FT+, and (d) FT−. Slash shading represents values significant at the p < 0.1 level by Student’s t test. The layer depth of soil temperature is 0–1 m. The contour represents the 0°C isotherm.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

Fig. 9.
Fig. 9.

(a) Evolutions of soil moisture (mm mm−3; liquid water) average over the region indicated by the dotted box shown in Fig. 2a (28.5°–36.5°N, 88.5°–102°E), and distribution of soil moisture anomalies (sensitivity experiment minus CTL) from spring to early summer (April–June) simulated by (b) SNOW, (c) FT+, and (d) FT−. Slash shading represents values significant at the p < 0.1 level by Student’s t test. The layer depth of soil moisture is 0–1 m. The contour represents the 0°C isotherm.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

Soil temperature anomalies simulated in SNOW are distinct in April, but their persistence seems short, and they weaken rapidly and become indistinctive in May and June (Fig. 8a). In contrast, soil temperature anomalies simulated in FT+ and FT− can persist steadily until June (Figs. 8c,d). Through inducing cold anomalies of soil temperature in April and May, frozen soil thawing delays with drier soil moisture (liquid water) anomalies, which persists to June (Fig. 9c,d), and this feature is consistent with the evolutions of soil moisture simulated in FT+ and FT− (Fig. 9a). This further supports the viewpoint that the effects of snow cover anomalies should be regulated or advanced through its impacts on thawing of frozen soil.

The surface diabatic heating changes with the soil hydrothermal regime anomalies. When the early spring snow cover is heavier, the surface sensible heat (SH) in May simulated in SNOW show significantly negative anomalies in the midwestern TP, while the negative anomalies of latent heat (LH) in May mainly appear over the eastern and northwestern TP; until to June, negative anomalies of SH still exist over the eastern TP, while the SH anomalies in June are small. When the thawing of the frozen soil is delayed, the SH simulated in FT+ has negative anomalies in most regions of the TP, especially in the southeastern TP (Fig. 10c); the pattern of LH anomalies is similar to that of soil moisture, and distinctly negative anomalies are observed over the southeastern TP. Anomalies of SH and LH in April can persist until June (Fig. 10d). When the thawing of frozen soil is advanced, the SH anomalies in April simulated in FT− are significantly positive in most regions of the TP, while the SH anomalies are weakly negative in interiors of TP; until May and June, the positive anomalies of SH mainly appear over the mideastern TP (Fig. 10e). The LH anomalies simulated in experiment FT− in April are relatively small because the soil only begins thawing at the edge of the southeastern TP. The thawing of frozen soil proceeds toward the northwest in May and June, and the LH in the mideastern TP shows significantly positive anomalies (Fig. 10f), whereas the anomalies of SH and latent heat (LH) in the western TP are weak. This analysis shows that there is a clear difference in the surface diabatic heating anomalies of the mideastern TP and western TP. For a quantitative comparison of the anomalies of SH and LH between the mideastern TP (ETP) and western TP (WTP), the regional average of SH anomalies and LH anomalies were calculated (Table 2). The anomalies of SH and LH, especially the LH anomalies, in the ETP are generally more obvious than that in the WTP. This implies the anomalies of frozen soil thawing in the presummer period can create a thermal contrast between the western and eastern TP.

Fig. 10.
Fig. 10.

Simulated surface diabatic heating anomalies (W m−2) over the TP. Anomalies (sensitivity experiment minus CTL) of (a) surface sensible heat (SH) and (b) surface latent heat (LH) during May–June from SNOW, the gray contour in each panel represents the 0°C isotherm of soil temperature simulated in CTL. (c),(d) As in (a) and (b), but for FT+. (e),(f) As in (a) and (b), but for FT−. Slash shading represents values significant at the p < 0.1 level by Student’s t test. The contour represents the 0°C isotherm.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

Table 2

Comparison of averaged SH and LH anomalies (W m−2) between the eastern Tibetan Plateau (ETP, 25°–40°N, 90°–100°E) and western Tibetan Plateau (WTP, 25°–40°N, 80°–90°E). The bold font means the larger absolute value between WTP and ETP.

Table 2

The TP surface diabatic heating anomalies can lead to changes in the thermal forcing of the TP to the surrounding atmosphere, and thus lead to changes in the anomalies of atmospheric circulation above and around the TP. Figure 11 shows the simulated atmospheric circulation anomalies in early summer (June) around the TP, anomalies of vertical circulation and water vapor transport simulated from SNOW experiment are changed slightly (Figs. 11a,d,g), which is due to the short persistence of soil moisture anomalies and slight surface diabatic heating anomalies. When thawing of frozen soil anomalously delays, because of the cold anomalies of soil temperature and dry anomalies of soil moisture, the surface sensible and latent heat fluxes show significantly negative anomalies in June over the mideastern TP, the weakened surface diabatic heating to the above atmosphere result in cold anomalies of atmospheric temperature in the middle–upper troposphere. The meridional vertical circulation shows an anomalous downward motion over the southern TP (about 30°–32.5°N), whereas an upward motion developed over the south side of the TP; this circulation corresponds to the weakened monsoon cell near the TP in June (Fig. 11b). The longitude–pressure cross sections of air temperature show significantly cold anomalies above the TP, whereas the near-surface temperature anomalies over the eastern region (about 90°–95°E) are colder than those over the western region. This anomalous thermal contrast between the western and eastern TP results in larger anomalous downward motions over the eastern TP (Fig. 11e). Along with the atmospheric thermal anomalies, an anomalous anticyclone develops over the mideastern TP corresponding to the anomalies of vertical circulation over and around the TP; this anticyclone is accompanied by anomalous cyclones over southwestern and northeastern sides of the TP (Fig. 11h). Atmospheric circulation anomalies cause changes in water vapor transport. The convergence of vertically integrated water vapor flux −∇ ⋅ Q for an air column [Eq. (1)] is shown in Figs. 11h. When the anomalies of −∇ ⋅ Q over the eastern TP are negative, whereas those of −∇ ⋅ Q in the western TP are positive. This pattern is generally the same as the pattern of June precipitation anomalies.

Fig. 11.
Fig. 11.

Simulated atmospheric circulation anomalies (sensitivity experiments minus CTL) in early summer (June) around the TP. (a)–(c) Latitude–pressure cross sections of temperature anomalies (shading; K), zonal wind anomalies (contours; m s−1), and meridional circulation anomalies (vectors; m s−1; vertical velocity has been amplified by a factor of 500) averaged over 80°–100°E. (d)–(f) As in (a), but for longitude–pressure cross sections averaged over 30°–35°N. (g)–(i) Moisture flux convergence (MFC) anomalies (shading; mm day−1) and 500-hPa horizontal wind anomalies (vectors; m s−1). Latticed shading and green vectors represent values of temperature anomalies, zonal wind anomalies, and meridional circulation anomalies, respectively, significant at the p < 0.05 level by Student’s t test. Black shading represents topography.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

When thawing of frozen soil anomalously advances, the anomalies of atmospheric circulation were generally inverse with that of FT+ experiment. Atmospheric temperature around the TP in the middle–upper troposphere shows positive anomalies, which lead to anomalous upward motions, the monsoon cell enhances (Fig. 11c). For zonal circulation, due to the warmer anomalies of atmospheric temperature in eastern TP, significant anomalous upper motions appear over there (Fig. 11f). Correspondingly, there are anomalous cyclone at over the southeastern TP and anomalous anticyclone over the southwest side of TP, this benefits the water vapor convergence (positive anomalies of MFC) over the eastern TP (Fig. 11i), which leads to more June precipitation over there.

To validate the WRF-simulated anomalies of atmospheric circulation, we compared the simulated anomalies of horizontal wind and relative vorticity with the regressions of horizontal wind and relative vorticity from ERA5 dataset by using PC2 of EOF2 for April soil temperature. The patterns are generally consistent (Fig. S5), except for some differences in details that may be attributed to disturbances by other external forcing, e.g., sea surface temperature anomalies over the Indian Ocean and North Atlantic Ocean (Sun et al. 2019; Y. Liu et al. 2020).

The presence of water vapor is a necessary condition for precipitation. The frozen soil thawing anomalies can affect the water vapor in the atmosphere by changing the local ET that is related to changes in soil moisture and by affecting the water vapor transport that is related to changes in atmospheric circulation. The onset of the Indian monsoon generally occurs in early June after a surface low pressure system moves over southwest India (Wu et al. 2013). The southwesterly winds on the southern side of the TP transport abundant water vapor from the Bay of Bengal and the Indian Ocean to the eastern TP; in contrast, the central and western inner regions of the TP are at altitudes higher than 4000 m, and water vapor is hardly transported here. Figure 12 shows the influences of different processes on the precipitation anomalies over TP. The amount of water vapor that enters a region and precipitates is quantified by precipitation efficiency χ [Eq. (2)]. Changes in χ are fragmented, anomalies of χ are dominantly positive from SNOW and FT+ experiments, while they are negative from the FT− experiment, which means negative feedback of χ to the precipitation in the eastern TP (Figs. 12a,e,i). The local effects of ET decrease in most regions of the TP, from SNOW and FT+ experiments, while increase from the FT− experiment, which implies changes in local effects of ET play positive and negative roles in precipitation anomalies over the eastern and western TP, respectively. (Figs. 12b,f,j) The pattern of the anomalies of remote effect of χΔIN is similar to that of precipitation (Figs. 12c,g,k). Comparisons of the efficiency effect, local effect, and remote effect of soil-thawing anomalies indicate that precipitation in June is dominated by remote moisture advection, especially over the eastern TP. The local effects caused by decreasing ET make a secondary contribution to the low precipitation over the eastern TP. These indicate the dominant effect of remote moisture advection on early summer precipitation.

Fig. 12.
Fig. 12.

Roles of different processes efficiency effect, local effect, remote effect, and residual on the precipitation (mm day−1) from experiments SNOW, FT+, and FT−.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

6. Discussion and conclusions

In this study, by comparing the effects of snow cover, the impacts of frozen soil thawing anomalies in spring on soil hydrothermal regime and subsequent precipitation over the TP was investigated. Both the diagnostic analysis and model simulations demonstrated that delays in the thawing of frozen soil in spring can lead to less precipitation in the central-eastern TP and more precipitation in the southwestern TP in June, and vice versa. Influence of heavier snow cover anomalies in spring on subsequent precipitation is similar to that of frozen soil thawing delay. Impacts of spring snow cover anomalies over the TP on locally subsequent precipitation is advanced through its impacts on thawing of frozen soil.

The possible mechanism linked to the modulation of soil-thawing anomalies in effects of snow cover anomalies in spring on the subsequent precipitation over the TP was investigated. The results of numerical experiments show that delays in thawing of frozen soil over the south and eastern TP in April induce cold anomalies in soil temperature and dry anomalies in soil moisture, which can persist well into June and result in significant weakening of the surface diabatic heating over the mideastern TP. Frozen soil thawing promotes the effect of snow cover anomalies on the soil hydrothermal regime in spring; through frozen soil thawing, effect of snow cover anomalies on soil temperature and moisture in spring can persist to June.

When soil thawing anomalously delays, with the surface diabatic heating anomalies induced by soil thawing anomalies over the mideastern TP, an anomalous downward motion develops over there, and anomalous upward motions develop over the southern and northern sides of TP with a weakened monsoon cell around the TP. Owing to the significant cold anomalies over the eastern TP, an anomalous thermal contrast exists between the western and eastern TP. Correspondingly, an anomalous anticyclone appears in the middle troposphere over the mideastern TP, whereas anomalous cyclones appear over the southwestern and northeastern sides of the TP. The June precipitation over the TP is mainly affected by the remote moisture advection (i.e., MFC), whereas the local effects of ET anomalies play a secondary role over the central and eastern inner regions of the TP. The atmospheric circulation anomalies cause a decrease in the convergence of water vapor over the eastern TP and an increase in the convergence of water vapor over the southwestern TP. A combination of anomalies of the water vapor and dynamic conditions (i.e., ascending motion) result in reversed patterns of precipitation anomalies in early summer over the eastern and western TP. These results are summarized in Fig. 13.

Fig. 13.
Fig. 13.

Schematic diagram of physical processes for impacts of frozen soil thawing (FT) anomalies on subsequent precipitation over TP from a perspective of moisture flux convergence (MFC). The red ringed arrows labeled A denote the anomalous anticyclone in the upper troposphere induced by the delayed frozen soil thawing. The blue ringed arrows labeled C denote the anomalous cyclone in the upper troposphere.

Citation: Journal of Hydrometeorology 24, 2; 10.1175/JHM-D-22-0083.1

Along with the global warming, the land surface process of the TP has undergone distinct changes such as seasonal snow melting, glacial ablation, and permafrost degradation. Elements of land surface over the TP (e.g., snow, frozen ground) interact with each other through their impacts on water–heat transport (e.g., Trujillo and Molotch 2014), studies have suggested the impacts of snow cover on the hydrothermal regime of frozen soil (Li et al. 2021; Zhang et al. 2021). These changes of cryospheric components provide significant feedback to the climate over the TP (Xue et al. 2018; Yang et al. 2019). The results of this study reveal the frozen soil play a key role in effects of snow cover anomalies on soil hydrothermal regime and surface diabatic heating. This study has potential for improving our understanding of the feedback of cryosphere to the atmosphere.

Acknowledgments.

This study was supported by the National Natural Science Foundation of China (91837205), National Key R&D Program of China (2020YFA0608404), Major Science and Technology Project of Gansu Province (20ZD7FA005).

Data availability statement.

All data that support the findings of this study are included within the article (and supplemental material). GLDAS version 2.0 dataset can be obtained from https://disc.gsfc.nasa.gov/datasets?keywords=GLDAS&page=1, PREC/L dataset can be obtained from https://psl.noaa.gov/data/gridded/data.precl.html, GPM dataset can be obtained from https://disc.gsfc.nasa.gov/datasets?keywords=GPM&page=1, SCE dataset of NSIDC can be obtained from https://nsidc.org/data/nsidc-0046, CMFD dataset and daily snow-depth dataset can be obtained from http://data.tpdc.ac.cn/en/.

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