Introduction

The permafrost is frozen soil, sediment or rock that remains under 0 °C for at least two consecutive years (Brown et al. 1998). There are different layers, of which frozen ground represents just one portion. The active layer is the surface layer of soil that is seasonally frozen in winter and thaw each summer, causing relatively large surface movements at the order of centimetres, or even decimetres over periods of months (seasonal variations) and years (cf. Biskaborn et al. 2015). The talik is an unfrozen ground layer that lies below the active layer and above the permafrost. As seen in Fig. 1, the permafrost is found in large parts of the Northern Hemisphere, mostly in Siberia, Canada, Alaska, Greenland, and the northern parts of Sweden and Norway (Schaefer et al. 2012). Climate warming is more rapid in the northern high-latitude regions and causes thawing of the permafrost over a great expanse of area in the Arctic region (Liu et al. 2010). This has major impact on the arctic water cycle, as ground ice melts and flow pathways between layers and groundwater increase. The permafrost thaw is a very complex phenomena that can in some cases lead to the water storage change that could be detected in gravity variations. Soils in the Arctic permafrost region are estimated to hold about twice as much carbon as the atmosphere (Hugelius et al. 2011). As previously frozen permafrost organic carbon thaws and decomposes, there is a potential positive feedback between the permafrost thaw and the global warming if the Arctic turns from a net sink to a net source of carbon. Hence, studying thawing permafrost is very important, not only from a perspective of localized geo-hazard such as erosion, damage to buildings and infrastructure, but also with respect to its possible global impact due to greenhouse gas emissions.

Fig. 1
figure 1

Permafrost distribution in the northern high latitudes. Image credit: Philippe Rekacewicz, 2005, UNEP/GRID-Arendal maps and graphics library based on International Permafrost Association (1998) circumpolar active-layer permafrost system (CAPS), version 1.0. https://www.wunderground.com/resources/climate/melting_permafrost.asp

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The permafrost regions are one of the most heavily impacted regions by the climate change. Studying the permafrost might allow us to investigate a long-term development of the earth’s shape interior, gravity field, climate change and assessment of its impact. The permafrost thawing has been investigated using satellite gravimetry techniques (GRACE; Tapley et al. 2004) in many publications in addition to streamflow analyses (e.g. Sjöberg et al. 2013) that use thermal sensors in boreholes that measure the thickness of the active permafrost layer. For example, Velicogna et al. (2012) studied the permafrost thawing using GRACE data in the Lena river basin (cf. Muskett and Romanovsky 2009, 2011; Vey et al. 2013) and Shabanloui and Müller (2015) conducted a similar study for the whole Siberia (cf. Chao et al. 2011). They determined the water storage changes attributed to the permafrost thawing using GRACE data and compared their results with various hydrological effects such as the soil moisture and the river run-off. The importance of the permafrost for the earth’s ecosystem (in terms of the released carbon dioxide and nitrogen into the atmosphere due to thawing of permafrost active layer) was also recognized by Treat et al. (2014), Yang et al. (2013), Schaefer et al. (2011) and others.

In this study, we propose a unique approach to study the permafrost thawing using satellite data, e.g. GRACE and other satellite- and ground-based observations in order to determine surface changes/deformations in the northern high-latitude region. For this purpose, the mass variations due to the permafrost thawing are estimated in terms of the groundwater level change in the study region. By using the outcomes of this study, we try to find geophysical mechanisms being the most plausible, e.g. the thawing of permafrost and the glacial isostatic adjustment (GIA). The satellite-based data, e.g. GRACE, is collected from low-orbited dedicated missions, which provide homogeneous and global coverage. However, these data suffer from inherent data processing problems and need to be addressed properly in order to achieve reliable and accurate results. Another task to be tackled is finding an optimal method for data noise filtering (especially for GRACE data (Sjöberg and Bagherbandi 2017, Sect. 8.7) and meteorological signals (rain, snow water, surface water, etc.). How to extract the permafrost signal from satellite data is an important challenge here. For example, studying temporal gravity changes and their relation with the permafrost using GRACE data requires the knowledge about the land uplift (GIA) (Peltier 2004; Ågren and Svensson 2007) and the continental hydrological signal (GLDAS, Global Land Data Assimilation System; Rodell et al. 2004). The potential of the GRACE for detecting mass changes related to different phenomena has been studied before and during the first years of its operation, for instance, by Wahr et al. (1998, 2004) and Swenson et al. (2003). It is important to mention here that the gravity data collected by GRACE require applying a smoothing procedure in order to reduce the effects of errors present in the short-wavelength component. Various methods have been proposed to filter the GRACE data (cf. Swenson and Wahr 2006; Wouters and Schrama 2007; Klees et al. 2008; and Kusche et al. 2009). Among them, we could mention the most commonly applied isotropic Gaussian (Wahr et al. 1998) or the non-isotropic (Han et al. 2005) filters. However, none of these methods accounts for a correlated noise in data.

In this study, we estimate water storage changes due to permafrost thawing (not dry permafrost, bare rocks, thawing) using satellite gravimetry methods in the study region. Therefore, studying the contribution of some disturbing signals such as land uplift (GIA), surface water and surface snowfall on the signal detected by GRACE is necessary. Moreover, we also address the determination of the permafrost-related near-surface mass changes (due to permafrost thawing) and their correlation with released greenhouse gases.

Monitoring near-surface mass change by GRACE

Today, the most successful data for studying temporal changes in the gravity field stem from the very long record of satellite laser ranging for very long wavelengths (Moore et al. 2005), and more recently also from the accurate gravity-dedicated satellite mission GRACE for shorter/more regional phenomena (cf. Lemoine et al. 2007). GRACE is appropriate for studying some geodynamic phenomena such as GIA, climate change and permafrost thawing, because these phenomena are related to a mass change and consequently propagated into gravity field change. Moreover, these changes occur over relatively large areas, thus having prevailing long-wavelength spatial pattern that could be detected by GRACE that could measure secular gravity changes related to near-surface mass changes.

A satellite disturbing potential model (T) typically consists of numerical values for the potential coefficients (\(C_{nm}\)). A time-dependent change in the earth’s gravity field due to mass transport causes changes in the harmonic coefficients. These changes can be described by the residual spherical harmonic coefficients \(\Delta C_{nm}\) that are obtained after subtracting the mean value from monthly solutions. The absolute disturbing potential and its changes are then described by

$$\left( {\begin{array}{*{20}c} T \\ {\Delta T} \\ \end{array} } \right) = \frac{GM}{R}\sum\limits_{n = 0}^{{n_{\text{max} } }} {\left( {\frac{R}{r}} \right)}^{n + 1} \sum\limits_{m = - n}^{n} {\left( {\begin{array}{*{20}c} {C_{nm} } \\ {\Delta C_{nm} } \\ \end{array} } \right)} Y_{nm} \left( {\theta ,\lambda } \right),$$
(1a)
$$\Delta C_{nm} = C_{nm} - \bar{C}_{nm} ,$$
(1b)

where \(\bar{C}_{nm}\) is the mean value of spherical harmonics over time, \(\Delta T\) is either the change in T from one time to another or the difference between T at one time and the time average of T, GM is the geocentric gravitational constant (i.e. the product of Newton’s gravitational constant and the total mass of the earth including the atmosphere), R the Earth’s mean radius, \(n_{\text{max} }\) is maximum degree of harmonic expansion, \(\left( {r,\theta ,\lambda } \right)\) are, respectively, the geocentric radius, co-latitude and longitude of the computational point, \(Y_{nm}\) is the surface spherical harmonic of degree n and order m, and

$$\Delta C_{nm} = \left\{ {\Delta C_{nm} } \right\}_{\text{surface mass}} + \left\{ {\Delta C_{nm} } \right\}_{\text{solid mass}} .$$
(2)

As seen in Eq. (2), the residual spherical harmonic coefficients \(\Delta C_{nm}\) consist of the direct gravitational contribution of the surface mass \(\left\{ {\Delta C_{nm} } \right\}_{\text{surface mass}}\) and the additional contribution of the surface mass load \(\left\{ {\Delta C_{nm} } \right\}_{\text{solid mass}}\) that deforms the underlying solid earth. Hence, we have (cf. Wahr et al. 1998)

$$\left[ {\begin{array}{*{20}c} {\left\{ {\Delta C_{nm} } \right\}_{\text{surface mass}} } \\ {\left\{ {\Delta C_{nm} } \right\}_{\text{solid mass}} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {{3 \mathord{\left/ {\vphantom {3 {\left[ {4\pi R\bar{\rho }(2n + 1)} \right]}}} \right. \kern-0pt} {\left[ {4\pi R\bar{\rho }(2n + 1)} \right]}}} \\ {{{3k_{n} } \mathord{\left/ {\vphantom {{3k_{n} } {\left[ {4\pi R\bar{\rho }(2n + 1)} \right]}}} \right. \kern-0pt} {\left[ {4\pi R\bar{\rho }(2n + 1)} \right]}}} \\ \end{array} } \right]\iint\limits_{\sigma } {\Delta \sigma \left( {\theta ,\lambda } \right)Y_{nm} }\left( {\theta ,\lambda } \right)d\sigma ,$$
(3)

where \(\Delta \sigma \left( {\theta ,\lambda } \right)\) is the surface density change (mass/area), and \(\bar{\rho }\) is the earth’s mean density. The load Love numbers \(k_{n}\) are modelled based on some available earth model (e.g. Farrell 1972; Sun and Sjöberg 1999; Bevis et al. 2016).

By repeating GRACE satellite tracks for measuring the gravity field, the linear least-squares regression analysis can be applied to determine temporal changes (i.e. secular trend) of the disturbing potential (cf. Sjöberg and Bagherbandi 2017, Chapt. 2). The regression equations are given by:

$$a + bt_{i} + \sum\limits_{j = 1}^{J} {\left( {c_{j} \cos \omega_{j} t_{i} + d_{j} \sin \omega_{j} t_{i} } \right)} = \Delta T_{i} - \varepsilon_{i}; \quad i = 1, \ldots ,n,$$
(4)

where \(\omega_{j} = 2\pi /T_{j}\), periods are denoted by \(T_{j}\) and J is the number of periodic signals included in the adjustment. Considering a linear regression (i.e. \(a + bt_{i} = \Delta T_{i} - \varepsilon_{i}\)) in time \(\left( {t_{i} } \right)\) with observation equations (Eq. 4), the secular change of the spherical harmonic coefficients (\(\mathop C\nolimits^{ \cdot }_{nm}\)) is given by:

$$\mathop C \nolimits^{ \cdot }_{nm} = \frac{1}{4\pi }\iint\limits_{\sigma } {{\mathbf{b}}Y_{nm} \left( {\theta ,\lambda } \right)d\sigma }.$$
(5)

where \({\mathbf{b}}\) is a matrix which includes the computed secular trends using Eq. (4).

Sjöberg and Bagherbandi (2017, Sect. 8.7) showed that estimated rates of a secular trend in the gravity field do not differ significantly when either including or not periodic terms in the analyses. Using \(\mathop C \nolimits^{ \cdot }_{nm}\), the secular changes of the disturbing potential and gravity disturbance can be described up to some limited degree \(n_{\text{max} }\) as follows (Sjöberg and Bagherbandi 2017, Chapters 3 and 8)

$$\mathop T\limits^{ \cdot } = \frac{GM}{R}\sum\limits_{n = 0}^{{n_{\text{max} } }} {\left( {\frac{R}{r}} \right)}^{n + 1} \sum\limits_{m = - n}^{n} {\mathop C\nolimits^{ \cdot }_{nm} } Y_{nm} \left( {\theta ,\lambda } \right),$$
(6)
$$\delta \mathop g\limits^{ \cdot } = \frac{GM}{{R^{2} }}\sum\limits_{n = 0}^{{n_{\text{max} } }} {\left( {\frac{R}{{r_{P} }}} \right)}^{n + 2} \left( {n + 1} \right)\sum\limits_{m = - n}^{n} {\mathop C\nolimits^{ \cdot }_{nm} } Y_{nm} \left( {\theta ,\lambda } \right),$$
(7)

According to Sjöberg and Bagherbandi (2017), Chapter 8, the near-earth’s surface mass change rate can be determined from

$$\dot{\kappa } \approx \frac{{\bar{\rho }R}}{3}\sum\limits_{n = 0}^{{n_{\text{max} } }} {\frac{2n + 1}{{1 + k_{n} }}} \sum\limits_{m = - n}^{n} {\mathop C\nolimits^{ \cdot }_{nm} Y_{nm} \left( {\theta ,\lambda } \right)} .$$
(8)

The monthly mass changes propagate into changes in the earth’s gravity field. For computational purposes, these mass changes are often considered as being concentrated in a very thin layer of water thickness changes. Their vertical extent is measured in centimetres of the equivalent water thickness. To get a general picture of the lateral distribution of mass anomalies, one may also represent the secular trend of the disturbing potential in terms of the total water storage (TWS) changes. Using GRACE data, we estimate the secular trend of TWS change according to Wahr et al. (1998) by

$$\mathop {\text{TWS}}\limits^{ \cdot } = \frac{{R\bar{\rho }}}{{3\rho_{w} }}\sum\limits_{n = 0}^{{n_{\text{max} } }} {\frac{2n + 1}{{1 + k_{n} }}} \sum\limits_{m = - n}^{n} {\mathop C\nolimits^{ \cdot }_{nm} Y_{nm} \left( {\theta ,\lambda } \right)} ,$$
(9)

where \(\rho_{w}\) is the water density.

GRACE data and processing procedure for permafrost studies

There are different products for GRACE, monthly, weekly and 10-day solutions provided by several analysis centres. The three main analysis centres are: Center for Space Research (CSR) at the University of Texas at Austin, Jet Propulsion Laboratory (JPL) in Pasadena and GeoForschungsZentrum (GFZ) in Potsdam. In addition, there are solutions from the University of Bonn (ITG), the Centre National d’Etudes Spatiales (CNES) in Toulouse and the Technical University Delft (DEOS Mass Transport model). For this study, we used the Release-05 GRACE level-2 monthly time-variable gravity field products from CSR over the period from August 2002 to May 2016 provided in terms of the fully normalized geopotential spherical harmonic coefficients to determine the TWS changes. These GRACE data were filtered and corrected for GIA, hydrological signal and glaciers melting in order to estimate the equivalent water height secular trend due to the permafrost thawing layer (EWHP). The filtering and correction procedures are briefly summarized in the next sections.

Noise filtering

The epoch-wise GRACE gravity field models require smoothing in order to reduce the effects of errors at short wavelengths. The GRACE data contain coloured noise that shows up in the provided spherical harmonic coefficients (Kusche et al. 2009). Basically, truncating the spherical harmonic series at long wavelengths, where the noise is not yet significant, yields the loss of an unacceptably high portion of the signal. The noise can usually be described by systematic/correlated stripping patterns. The reason for this is the mission geometry, as GRACE twin-satellites fly in the same near-polar orbital plane, and the inter-satellite ranging observable used in gravity modelling transforms into a distinct along-track sensitivity (Sjöberg and Bagherbandi 2017, Chap. 8). Deficiencies in de-aliasing models cause an anisotropic error that cannot be removed, for instance, by applying the Gaussian isotropic filter. Instead, the de-correlation method should be used in the post-processing of GRACE data, such as those discussed by Kusche (2007), Klees et al. (2008) and Kusche et al. (2009). Kusche’s technique uses a priori synthetic model of the observation geometry for the de-correlation. In this study, we used Kusche’s technique (DDK2 filer) to remove stripping patterns in the CSR GRACE data (see Joud et al. 2017).

GIA correction

In the study region, the earth’s crust is rising continuously since the last glacial maximum due to de-loading of the former ice sheet. The process of ongoing relaxation due to the viscoelastic structure of the earth mantle is known as glacial isostatic adjustment (GIA). The land uplift is well documented from various studies (see e.g. Ekman 1991 and Peltier and Argus 2015 for historical reviews). Although GIA is a well-known process for more than a century, it still attracts the attention of geoscientific community due to its extended number of applications in the understanding, modelling, measuring and correcting for different phenomena related to the present issues of interest to the global society.

GIA causes changes in the earth’s gravity field. The estimation of mass changes, obtained from GRACE data, in terms of the equivalent water thickness will not be correct without removing the GIA contribution. For this purpose, the land uplift rate should be converted to equivalent land uplift water height (ELUWH) by

$$\mathop {\text{ELUWH}}\limits^{ \cdot } = \frac{{\bar{\rho }}}{{3\rho_{w} }}\sum\limits_{n = 0}^{{n_{\text{max} } }} {\frac{2n + 1}{{1 + k_{n} }}} \sum\limits_{m = - n}^{n} {\mathop h\nolimits^{ \cdot }_{nm} Y_{nm} \left( {\theta ,\lambda } \right)},$$
(10)

where \(\mathop h\limits^{ \cdot }\) is the land uplift rate.

Hydrological corrections

The hydrological monthly data from the global land data assimilation system (GLDAS) hydrological model over the period from January 2002 to May 2016 with 0.25 × 0.25 or 1.0 × 1.0 arc-degree spatial resolution can be extracted (Chen et al. 1996; Koren et al. 1999) via the Hydrology Data and Information Service Center (HDISC). GLDAS provides global information on land surface status (e.g. surface temperature, soil moisture, precipitation, river run-off, etc.) with three-hour or monthly temporal resolutions based on integrating satellite and ground-based observation data. Four land surface models are currently used by GLDAS, specifically Mosaic, NOAH, CLM and VIC (see Rodell et al. 2004). In this study, we used the NOAH model according to Chao et al. (2011), which has a total of four soil layers thickness (i.e. 0–10, 10–40, 40–100 and 100–200 cm). The precipitation and other hydrological parameters are very important because their effect on the water storage change is significant in the study area (see Fig. 5). The regression analysis has been used to calculate the secular trend of the hydrological data (similar to Eq. 4).

Ice-melting correction

For extracting the water storage change due to permafrost thawing, the effect of ice-mass loss of Greenland ice sheet triggered by regional warming should be removed from GRACE data. The rate of ice elevation change from 2003 to 2012 was computed by using altimeter surveys from NASA’s ATM flights during 2003–2012 supplemented with high-resolution ice, cloud and land elevation satellite (ICESat) data from 2003 to 2009 (cf. Khan et al. 2014). The result shows that large areas in the centre of the Greenland ice sheet (GrIS) have few or no measurements during the period between 2010 and 2012. Thus, the variability in the elevation change rate during this period is not fully covered in the elevation change estimates. To overcome this problem, the ENVISAT radar altimeter measurements have been used from April 2009 to March 2012. This dataset is obtained from the RA-2 SGDR product (see Khan et al. 2014), while the standard (SGDR) corrections for atmospheric propagation and tides were applied. Observables provided by a radar altimetry suffer from problems with the slope effect; therefore, in this study, we did not use data around the edge of the GrIS (from the ice margin and about 50–70 km inland). While other studies have made attempts to merge laser altimetry data with radar altimetry data, here we used the elevation change rates estimated from ENVISAT and laser altimetry separately and combined these rates. Ice-melting results using the above-mentioned data are presented in Fig. 2. Similar to Eq. (10), the correction due to equivalent ice-melting water height was computed.

Fig. 2
figure 2

Observed elevation change rates (m/year) in Greenland obtained from ICESat mission during periods: a from April 2003 to April 2006, b from April 2006 to April 2009 and c from April 2009 to April 2012

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The near-earth surface mass variations obtained from GRACE data are related to hydrological (water) variations. These variations are, however, attributed not only to the permafrost thawing, but also to the precipitation and run-off variations. Therefore, the secular trend of equivalent water height due to permafrost thawing (EWHP) was estimated by removing the signals triggered by the GIA and hydrological contributions from the obtained \(\mathop {\text{TWS}}\limits^{ \cdot }\)(Eq. 9). This procedure is described by the following scheme:

$$\mathop {\text{EWHP}}\limits^{ \cdot } = \mathop {\text{TWS}}\limits^{ \cdot }_{\text{GRACE}} - \mathop {\text{EWHP}}\limits^{ \cdot } - \mathop {\text{WS}}\limits^{ \cdot }_{\text{snow}} - \mathop {\text{WS}}\limits^{ \cdot }_{\text{canopy}} - \mathop {\text{WS}}\limits^{ \cdot }_{\text{run - off}} - \mathop {\text{WS}}\limits^{ \cdot }_{\text{SoilMoisture}} - \mathop {\text{WS}}\limits^{ \cdot }_{\text{ice - melting}} ,$$
(11)

where \(\mathop {\text{ELUWH}}\limits^{ \cdot }\) is the land uplift water equivalent height (Eq. 10), \(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{snow}}\) is the water storage due to the water equivalent of snow, \(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{canopy}}\) is the canopy water storage, \(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{run - off}}\) is the water storage variation due to run-off river, \(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{SoilMoisture}}\) denotes the water storage due to soil moisture variation (accumulated soil moisture internally from different layers) and \(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{ice - melting}}\) is water storage from the ice melting in Greenland (for this study).

Results

Using the static 30-day GRACE gravity field solutions over the period from 2002 to 2016, the residual spherical harmonic coefficients were determined according to Eq. (1b), and consequently the disturbing potential changes were computed according to Eq. (1a). The spectral rates of the gravity field change (in terms of \(\mathop C\nolimits^{ \cdot }_{nm}\)) were then determined using a time-series analysis according to Eq. (5). After obtaining the values of \(\dot{C}_{nm}\), the total water storage (\(\mathop {\text{TWS}}\nolimits^{ \cdot }\)) was computed from Eq. (9). The resulting secular rates were then filtered and corrected for the contributions of GIA, hydrology (such as precipitation, soil moisture, river run-off and canopy using GLDAS data), and ice melting (in Greenland) in order to be used for calculating the equivalent water height trend due to permafrost thawing (\(\mathop {\text{EWHP}}\limits^{ \cdot }\)).

The obtained \(\mathop {\text{EWHP}}\limits^{ \cdot }\) from the GRACE data is verified using in situ data, e.g. land surface temperature from GLDAS (Rodell et al. 2004 and Swenson et al. 2003), borehole data and carbon dioxide changes (e.g. using NASA’s EOS Aqua mission, see https://mirador.gsfc.nasa.gov/collections/AIRX3C2M__005.shtml). We expected to obtain a correlation between the rate of groundwater change (obtained from GRACE data) and in situ data. The distribution of permafrost monitoring stations (boreholes) in the study region is shown in Fig. 6b. More information about these stations can be found through the global terrestrial network for permafrost through http://gtnpdatabase.org/, where the following important data are available: surface temperature, ground temperature, active layer thickness, surface soil moisture and air temperature.

To remove the effect of GIA from the secular rate of total water storage (\(\mathop {\text{TWS}}\limits^{ \cdot }\)) obtained from GRACE, we used the ICE-6G (VM5a) model (Peltier and Argus 2015). This model shows the rate of radial displacements (Fig. 3a). Red and yellow areas in the figure indicate rising due to removal of the ice sheets. In ICE-6G (VM5a), the most recently available GPS observations have been employed. For this purpose, the land uplift rate was converted to equivalent land uplift water height (ELUWH) using Eq. (10). The result of the ELUWH is presented in Fig. 3b.

Fig. 3
figure 3

Regional maps of: a the land uplift rate obtained from the ice model ICE-6G (VM5a) and b the equivalent land uplift water height change (\(\mathop {\text{ELUWH}}\limits^{ \cdot }\))

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The resulting secular rates of TWS from the CSR GRACE data centre are shown in Fig. 4a. We further removed \(\mathop {\text{ELUWH}}\limits^{ \cdot }\) (Fig. 4b) from \(\mathop {\text{TWS}}\limits^{ \cdot }\). Figure 4b shows the resulting values of \(\mathop {\text{TWS}}\limits^{ \cdot }\) without the presence of GIA, and especially it can be seen that the land uplift signal is removed in Laurentia and Fennoscandia.

Fig. 4
figure 4

Regional maps of the equivalent water height secular trends (\(\mathop {\text{TWS}}\limits^{ \cdot }\)) obtained from the CSR GRACE data over the period from August 2002 to May 2016: a before and b after removing the equivalent land uplift water height change

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Since GRACE detects all hydrological changes as well as the water level change due to the permafrost, we further modelled and removed the hydrological signals (in terms of the equivalent water height) from the secular rates of the TWS. In order to filter out the non-permafrost signals, we used GLDAS hydrological model. In Fig. 5, we illustrate the hydrological parameters adopted in our computation, particularly soil moisture, precipitation (snow), canopy and river run-off that were obtained from the GLDAS model using Eq. (4). It is worth mentioning that most of the hydrological signals, such as precipitation, are hidden implicitly in the soil moisture variations, i.e. one part of the precipitation is converted to the river run-off water masses, while the other part is evaporated. Therefore, we were able to filter out the effect of precipitation by subtracting the soil moisture rate from the TWS rate. The result after subtracting the hydrological signals is shown in Fig. 6a.

Fig. 5
figure 5

Regional maps of the equivalent water height secular trends according to the GLDAS/NOAH land hydrological model due to hydrological contributions in terms of the water equivalent of a soil moisture (\(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{SoilMoisture}}\)), b snow (\(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{snow}}\)) and ice melting (\(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{ice - melting}}\)), c canopy (\(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{canopy}}\)), d river run-off (\(\mathop {\text{WS}}\nolimits^{ \cdot }_{\text{run - off}}\)) and e soil surface temperature

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Fig. 6
figure 6

a Regional map of the equivalent water height secular trend due to permafrost thawing after removing hydrological contribution obtained using GRACE and ICESat data and GLDAS/NOAH land hydrological model during 2002/08–2016/05 in the northern high-latitude region. Blue small circles show locations of selected stations, b shows the distribution (boreholes stations) and secular trend of equivalent water height due to permafrost in the study region

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Table 1 shows the summary of different corrections to the total water storage computed from GRACE data, i.e. GIA, hydrological signal and glaciers melting. The results show that the gravitational effect of some corrections (such as river run-off and canopy) is in general at least one order of the magnitude smaller than the EWHP.

Table 1 Statistics of total water storage (\(\mathop {\text{TWS}}\limits^{ \cdot }\)), GIA, hydrological signal and glaciers melting. Unit: cm/year
Full size table

As emphasized by Lawrence et al. (2015), the large-scale permafrost thaw predicted by GRACE results in significant soil drying due to an increased drainage following permafrost thaw, even though permafrost domain water inputs are projected to rise. This phenomenon could clearly be recognized in our result shown in Fig. 6a. The results show positive trend for the water level after the permafrost layer thawing in selected stations (about 3–4 cm/year; see Table 2 for more details). This was confirmed in previous studies by Brown et al. (2000), Frauenfeld et al. (2004), Zhang et al. (2005) and Lemke et al. (2007). They reported a notable increase in Siberian permafrost active layer since 1950s. Muskett and Romanovsky (2009) demonstrated an increase in the groundwater storage in Lena, Ob’ and Yenisei basins in Siberia. Wu and Zhang (2010) reported a similar trend at the Tibetan Plateau. An increasing water level can also be caused by the topography/slope of surrounding areas of the stations, as more water masses are transported from higher to lower elevations after the permafrost layer thawing. For this reason, a much more relevant is the study of the lowland permafrost in unconsolidated sediments that are not ice-rich and aquifer can infiltrate additional water after permafrost thaw. It usually stores considerable amounts of water in form of ground ice. However, the permafrost thaw processes are quite complex even in lowland regions. Depressions form after the melt of ground ice/water and thermokarst lakes form (Phillips et al. 2003). These lakes usually undergo a cyclic growth and drainage. Ice wedges and related ice wedge polygons are also very important source of ground ice/water in these environments. However, in some locations the type of the permafrost contains significant amounts of ground ice of very different origins (French and Hugh 2013, Chapter 7). It can happen that the thawed soil/sediment is already saturated with water, and then an increase in water storage might not be possible in some areas, leading to a mass decrease, as is the case in the southern parts of Alaska and Greenland (e.g. in the areas with negative equivalent water height trend in Fig. 6a).

Table 2 Secular trends of EWHP, average surface temperature and CO2 at selected stations
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Comparison with greenhouse gases and temperature changes

The permafrost regions cover almost 80% of the study area, while locally reaching a maximum thickness up to about 1 km (Yakutia in central Siberia). Therefore, it is expected that the permafrost thawing plays a significant role in the climate change and mass transportation (cf. Steffen et al. 2012; Shabanloui and Müller 2015). Greenhouse gases emissions due to the permafrost thawing further change the ecosystem (Treat et al. 2014; and Yang et al. 2013). A large amount of carbon was stored in the permafrost by a process that took thousands of years. Mixing of soil layers due to repeated freeze–thaw processes (Cryoturbation) in the active layer accelerates the burial process by mixing the carbon-rich organic soil from the surface down to the permafrost horizon (Zech et al. 2008). Warming in high latitudes leads to a soil warming and permafrost thaw, which results in carbon decomposition by soil microbes (Schuur et al. 2009) and releasing the greenhouse gases as carbon dioxide and methane (Koven et al. 2011). Studies and observations indicate a notable widespread permafrost thawing in the Northern Hemisphere (Lemke et al. 2007). For example, Osterkamp (2007) reported an increasing trend in the permafrost temperature by 2–3 °C over the last two decades at depth of 20 m and also at depths up to 20 m increased 0–2 °C in Canada (cf. Smith et al. 2004 and Lemke et al. 2007). Similar results presented in Siberia by Lemke et al. (2007) show the temperature increases between 0.3 and 2.8 °C at depths up to 10 m.

For this study, we used the monthly gridded 2.5 × 2.0 arc-degree data about greenhouse gases emissions provided by NASA (https://mirador.gsfc.nasa.gov/collections/AIRX3C2M__005.shtml). In particular, we used data of the AIRS mid-tropospheric carbon dioxide collected by the atmospheric infrared sounder (AIRS) and the advanced microwave sounding unit (AMSU) instruments on board of the Aqua satellite in mole fraction units (PPM in volume). These data cover the period of 110 months from 1 January 2003 to 1 February 2012. AIRS is a facility instrument lunched into 705 km altitude and covered a period from 1 September 2002 to 29 February 2012.

The CO2 time series is illustrated in Fig. 7 at four selected stations in Siberia (Turukhansky), North Alaska (Sagwon) and two more stations in Canada (Yukon and East of Hudson Bay), where reliable in situ data are available for the same time span as GRACE data. CO2 variations at these four stations are obviously not fully attributed to only the permafrost thawing, but are also affected by different phenomena. The analysis of the CO2 data shows generally positive trend in the study region. The permafrost contains a staggering 850 gigatonnes of frozen carbon (i.e. dry ice) that is much more than the total of the carbon currently contained in the earth’s atmosphere, much of which could be released in the form of methane (https://nsidc.org/cryosphere/frozenground/methane.html). Temperature, CO2 and methane changes are capable of retaining heat in the atmosphere that may accelerate the possibility of catastrophic global warming (cf. Schaefer et al. 2011). It was confirmed by several studies that thawing soils due to permafrost active layer are now the causes pouring carbon dioxide into the air.

Fig. 7
figure 7

Carbon dioxide (CO2) trend at selected stations in the study region. Note that “n” denotes on the number of months from initial epoch

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The secular trends in CO2 and soil temperature (provided via NOAH-GLDAS) were extracted for the study region and compared with the EWHP obtained from GRACE (see Fig. 8). The slope of linear trend of the EWHP, soil surface temperature and CO2 at selected stations is summarized in Table 2. The result shows that the secular trends at all stations are rising, with a relatively small increase in the soil surface temperature corresponding to relatively large secular trends in the EWHP and CO2.

Fig. 8
figure 8

Equivalent water height due to permafrost (EWHP) time series at selected stations in the study area. Note that “n” denotes the number of months since the initial epoch

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Discussion

The permafrost plays important role also in present-day processes related to the earth’s system, because there is a good data record suitable for studying the long-term characteristics of this phenomenon. In this study, we focused on a large-scale permafrost monitoring as well as an identification of permafrost hotspots using GRACE monthly solutions. However, these data required the application of additional corrections in order to achieve reliable and accurate products. We studied the permafrost thawing according to Eq. (11) by applying two numerical steps. Firstly, we removed the GIA effect from TWS obtained from GRACE data. This correction was computed according to the ICE-6G (VM5a) model (Peltier and Argus 2015). In this step, the role of GIA in the permafrost thawing determination is a vital issue to derive the EWHP secular trend. It is thus important to choose the most accurate GIA model; see an overview of different GIA models in Huang (2013). Our test results, not shown herein, revealed that the ICE-6G (VM5a) model has the best RMS fit with the GPS velocity rates in Fennoscandia and Laurentia. We further used the GLDAS data to investigate and remove the effect of various hydrological contributions in the EWHP modelling. By analogy with the role of GIA model in the EWHP determination, it is also important to study and choose the best and most precise hydrological model that we did not focus on this matter in this paper. Other large-scale lithospheric motions, such as tide effects, will not affect our results due to their periodic character. Moreover, most of these periodic motions have already been removed from the GRACE data.

The EWHP map in Fig. 6a revealed the gravity signature of which pattern corresponds with a total ground water change due to the permafrost layer thawing. Negative values prevail over regions with glacial cover where the ice masses are decreasing (Greenland and Alaska), while other areas are dominated by positive values (i.e. increasing equivalent water storage). A possible method to overcome this issue (i.e. problem of removing the effect of ice melting from EWHP in Fig. 4b) is to use external ice data information such as ICESat data. However, even after removing the surface mass change obtained from ICESat data, a strong negative ice-melting effect in Greenland and Alaska still remains. This ice-melting signal is stronger than the permafrost active layer signal particularly in Greenland and Alaska. Possible reasons for ice melting involve global warming, seasonal and inter-annual periodic signals and warm winds from oceans towards continents. The ice-melting effect is remained even after correcting TWS using ICESat data in the EWHP (Fig. 6a), because the ICESat measures only a surface mass change instead of a mass change in deeper layers.

According to the calculated EWHP values in the northern high-latitude region, our results and those from the other studies are similar. For example see Velicogna et al. (2012) and Shabanloui and Müller (2015). We find that the EWHP varies from 2 to 4 cm/year. Shabanloui and Müller (2015) studied the permafrost thawing in Siberia based on GRACE solutions and GLDAS model. They reported that the time series as well as secular trends of GLDAS hydrological mass variations are similar to GRACE results, but in some periods of time differences are obvious. The permafrost thawing dynamics and geophysical processes are very complex. However, we should emphasize that the permafrost is a phenomenon that cannot be associated only with the presence of underground ice. Its degradation is not only the melting of the ice. We also observed differences between the GRACE and GLDAS time series that might be explained by permafrost thawing effects not modelled in GLDAS. Therefore, GLDAS does not include permafrost contributions and it shows the precipitation and surface water masses. Hence, the estimated positive secular trends for the GRACE minus GLDAS results during the period of 2002–2016 may show that the permafrost thawing is progressing in the target region. This is the reason why we removed soil moisture, canopy and river run-off (obtained using GLDAS model) from GRACE observations in order to model the permafrost thawing more realistically. In addition, it should be emphasized that our obtained results using GRACE data are preliminary and can be improved if one combines it with in situ data (e.g. using the published data in the Global Terrestrial Network for Permafrost (GTN- P)). It is also worth mentioning that it would be possible to determine the uncertainty of EWHP, if we had access to all errors in Eq. (11). Only the accuracies of the harmonic coefficients are available for the GRACE data.

The surface temperature is a main component in the climate change and permafrost carbon feedback processes. The obtained soil surface temperature (from GLDAS) varies from − 3 to 3 °C/year in the study region and it shows generally positive trend with a maximum impact in the northern part of Canada (see Fig. 5e). Few scattered areas include small parts in Greenland, and Canada has a negative temperature trend. Three locations out of the four selected stations show positive trend ranged from + 0.013 to + 0.081 °C/year, and one shows average negative trend of − 0.114 °C/year (see Table 2). Therefore, as the air and soil temperature rose over time, the active layer part of the permafrost and the permafrost temperature will increase forming a talik layer, where the permafrost top part remains at 0° C and the bottom of the active layer froze/melt seasonally.

The CO2 analysis shows a positive trend all over the study region, ranging from 1.9 to 2.5 PPM/year. The trend for the selective stations ranges from 2.16 to 2.31 PPM/year. Our results show that CO2 increases in average of 2.2 PPM/year in the selected regions, and there is correlation between the secular trend of greenhouse gases and the equivalent water height (i.e. EWHP shown in Fig. 8) that is due to the thawing process and temperature increase. Consequently, our results can be used to determine future emissions and the impact of CO2/methane releases. The comparison of the permafrost equivalent water thickness with CO2 secular trends in Fig. 7 shows that frozen soils (permafrost) are unleashing an increasing amount of CO2 into the air as they thaw in summer or subsequently fail to refreeze as they once did, particularly in late fall and early winter. However, we should emphasize that the release of CO2 in the seasonally frozen layer, i.e. the active layer is sporadically occurring but the biologic processes of release and consumption, is highly variable and not well understood nor measured at sufficient detail and scale for a meaningful conclusion at this time. Our results also indicate an increasing amount of CO2 loss (Fig. 7) as well as an increasing surface temperature at selected stations (Fig. 9) in late spring and summer as the climate warmest steadily. Obviously, the large areas of permafrost in Canada and Siberia are partially responsible for some of the carbon dioxide emissions into the atmosphere. Since the Carbon dioxide can originate from anywhere on the Earth, proving that the carbon is coming from the thawed permafrost need special measuring tool and looking at the isotopic signatures to see that the carbon is old or coming from recent carbon cycling. Schaefer et al. (2012) stated that permafrost carbon starts thawing when the active layer exceeds certain thickness in the warm year. Therefore, in our case we conclude that the obtained CO2 could be partially or completely from the thawed permafrost.

Fig. 9
figure 9

Soil surface temperature time series at selected stations in the study region. Note that “n” denotes the number of months from initial epoch

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Conclusions

We have used monthly GRACE data, GIA and GLDAS models to study the groundwater storage change and permafrost thawing in the northern high-latitude region. The used time series covered the period from August 2002 to May 2016. Subtracting the GIA effect and hydrological water cycle contribution from the total water storage obtained using GRACE data reveals changes in the groundwater storage. Our result shows that the GIA effect is significant for determining the water storage change. We postulate that these water storage changes can be related to the permafrost thawing. We obtained negative values of the equivalent water height in Greenland and Alaska regions and we removed these effects from the groundwater storage using ICESat data. Permafrost thawing might be detected with positive values of the equivalent water height, and it quantifies the increase in the ground water storage. We showed that the ground water storage is changing by up to 3.4, 3.8, 4.4 and 4.0 cm/year in Siberia, North of Alaska and Canada (Yukon and Hudson Bay), respectively, most probably due to permafrost thawing using GRACE, GLDAS and ice-melting data. We also illustrated those greenhouse gases, i.e. carbon dioxide (CO2) and methane, increased up to 2.2 PPM/year in the study areas over the same period. Temperature also shows positive trend generally and in the study area as well as CO2 and equivalent water height trend (due to permafrost thawing) which might confirm the permafrost carbon feedback process.