IGFS 2014 pp 189-197 | Cite as

Mass Variations in the Siberian Permafrost Region Based on New GRACE Results and Auxiliary Modeling

  • Akbar ShabanlouiEmail author
  • Jürgen Müller
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 144)


GRACE (Gravity Recovery And Climate Experiment) determines the integral mass variations in the Earth system with a high spatial-temporal resolution. These mass variations should be adequately separated for better understanding of the individual signal contributions. In Siberia, the temporal mass variations are related to hydrological processes including thawing of permafrost layers. Permafrost layers with different thickness cover about 80% of Siberia. These frozen sheets play an important role for sea level rise and the global hydrological water cycle. In this study, the integral mass variations in Siberia are precisely estimated based on the new release of GRACE (RL05a) from GeoForschungsZentrum (GFZ) in Potsdam. In addition, various hydrological contributions (lake level variation, river run-off, etc.) can be estimated from different models and specific data. Here, mass variations in the Siberian permafrost region based on GRACE results and different hydrological models/data [i.e., GLDAS (Global Land Data Assimilation System) and GPCP (Global Precipitation Climatology Project)] are jointly investigated.


GRACE Mass variation Hydrological model GLDAS GPCP Permafrost thawing 

1 Introduction

Since 2002, the GRACE satellite mission is in a near polar orbit for recovering the static and time-variable parts of the Earth’s gravity field (Tapley et al. 2004). The time-variable part of the Earth’s gravity field is related to mass re-distribution in the Earth system. GRACE monitors the sum of all mass variations occurring in the Earth’s system. It cannot directly separate the different sources and effects. Therefore, an efficient separation technique and very precise background models have to be used for understanding mass variations in different regions over the globe. The provided time series of monthly gravity field solutions in the analysis centres (ACs) are already corrected for variations caused by atmosphere and ocean (Flechtner and Dobslaw 2014). Based on time-variable gravity field coefficients from GRACE, a number of studies to estimate secular trends and periodical changes for different regions have been successfully performed, such as mass balance in Greenland (Velicogna and Wahr 2013), hydrological mass variations in the Amazon basin (Werth et al. 2009), mass losses in Antarctica (Sasgen et al. 2013), mass variations in Siberia, Russia (Steffen et al. 2012; Vey et al. 2013; Chao et al. 2011), hydrological storage changes over Siberia (Frappart et al. 20062011; Muskett and Romanovsky 2009), water depletion in India and China (Tiwari et al. 2014; Rodell et al. 2009; Zhong et al. 2009), terrestrial water budget in the Eurasian pan-Arctic (Landerer et al. 2010), hydrological mass variation in Australia (Seoane et al. 2013), global large-scale groundwater variations from satellite gravimetry and hydrological models (Jin and Feng 2013) and contribution of terrestrial water derived by GRACE in polar motion (Jin et al. 2012). A secular trend in terms of Equivalent Water Thickness (EWT) has been estimated for all those regions. Estimated periodical terms include semi-annual, annual and some further periods.

By increasing the time-span of GRACE observations, mass variation signals including secular and (long-) periodical contributions in different regions can be precisely estimated. One of the challenging regions, which is not sufficiently investigated so far, is the permafrost region in Siberia, Russia. During the past decades, the permafrost regime in the Siberian region has experienced significant changes in terms of permafrost thawing due to climate warming. As an example, Yang et al. (2013) found that the average fresh water discharge from the six largest Eurasian rivers to the Arctic ocean has increased by 7%. Lena, Yenisei and Ob are the three largest rivers in the Siberian permafrost region that flow into the Arctic ocean from south to north. Parts of the signal due to permafrost thawing can be detected based on the level (discharge) changes of those rivers. As the permafrost region covers almost 80% of Siberia with a maximum thickness of 1 km in Yakutia (central Siberia), it is expected that permafrost thawing due to climate change plays a key role in mass (water) balance in this region (Steffen et al. 2012). In addition, the permafrost has caught an extreme capacity of carbon-dioxide (CO2) and nitrogen (N) that, if released, will play an important role for the Earth’s ecosystem in the near future (Treat et al. 2014). Therefore, surface and sub-surface mass variations in Siberia based on the gravitational approach from GRACE monthly solutions are determined, using GRACE data covering almost 12 years. In addition, the GLDAS hydrological model (Rodell et al. 2004) has been used to obtain the soil-moisture contribution, and GPCP precipitation data for estimating precipitation trends in the target region.

2 GRACE Data and Analysis

2.1 Processing Procedure

The GRACE L1b data are officially processed by different analysis centres (ACs), e.g. GFZ, JPL and CSR, as well as by other institutes such as ITG (University of Bonn, Germany), AIUB (University of Bern, Switzerland) and TU Delft (Delft University of Technology, The Netherlands) to produce GRACE L2 data in terms of static and time-variable spherical harmonic coefficients. These processing centres apply different strategies and background models.

Therefore, also different mass variation signals are obtained from GRACE L2 products when used for further analysis in selected regions, e.g. basins with large signals such as in the Amazon. Processing of GRACE data from different ACs in the Siberian region with small mass variation signals delivers about the same results and no significant differences are detected (see Fig. 1). Thus, in this study, only the recently released GRACE (RL05a) products of GFZ are used to determine Total Water Storage Changes (TWSC) in the Siberian permafrost region. The following steps have been applied:
  • GSM data: GRACE Level 2 monthly time-variable gravity field products are provided in terms of fully normalized geo-potential spherical harmonic coefficients. We used GFZ solutions from January 2003 to December 2013 (122 months).

  • Zonal term replacement: The zonal term c2, 0 of the monthly gravity field coefficients is replaced by the solution from Satellite Laser Range observations (Cheng et al. 2013).

  • Filtering: The monthly gravity field products are affected by correlated noise at higher frequencies. The correlated noise shows up in terms of striping effects in the mass variation results (e.g. gravity anomalies), when represented in a geographical plot. The striping errors are caused by the orbit design of GRACE-type configurations, incomplete reduction of non-tidal high frequencies of mass variations and limitation in the processing of the Earth gravity field. Therefore, an effective filter has to be applied to separate signal from noise. The normalized spherical harmonic coefficients can be smoothed in many different ways (Jekeli 1981; Swenson and Wahr 2006; Kusche 2007; Klees et al. 2008; Davis et al. 2008) of which we have tested several for Siberia.

  • Mass variation products: For our purpose, the mass variations in the permafrost region are estimated in terms of EWT. Therefore, the filtered spherical harmonic coefficients from the previous step are used to determine the global TWSC based on an approach presented by Wahr et al. (1998).

  • Glacial Isostatic Adjustment (GIA) corrections: Vey et al. (2013) showed that the ice history over Siberia does not reveal large-scale ice sheets during the last glacial maximum (LGM). In addition, by applying the two ice models RSES and ICE-5G with different lithospheric thicknesses, no significant GIA effects were found in central Siberia (Velichko et al. 2011; Vey et al. 2013).

Fig. 1

Secular trend estimation based on monthly gravity field solutions of GFZ-RL05a in the period of 2003–2013, zonal term c2, 0 replaced and a 1D Gaussian filter with radius 350 km applied. The study area and three river basins i.e. Lena, Yenisei and Ob in Siberia are indicated by red color

GRACE monthly gravity field solutions contain the integral gravity variations that could be caused by changes in Atmosphere, Ocean, Hydrology, Ice and Solid Earth (AOHIS). High-frequency atmospheric and oceanic mass variations are removed during processing of GRACE L1 data (AOD1B products) (Flechtner and Dobslaw 2014). Thus, the mass variations that are contained in GRACE L2 data have ice, hydrology and solid Earth changes as potential sources. Depending on the location of the Region Of Interest (ROI), one or more Signals Of Interest (SOI) can be related to the mass changes. For example, mass variations in the Siberian permafrost region are related to hydrological (water) variations that are only partly caused by permafrost thawing but also by precipitation and run-off variations. To estimate secular and periodical contributions, the following equation is used (Ogawa 2010):
$$\displaystyle{ \mathit{EWT}(\lambda,\phi,t) = a + bt +\sum \limits _{ f=1}^{4}(c_{ f}\cos (\omega _{f}t) + s_{f}\sin (\omega _{f}t)) +\varepsilon. }$$
\(\mathit{EWT}(\lambda,\phi,t)\) represents the equivalent water thickness at the node position \(\left (\lambda,\phi \right )\) at time t. The parameters a and b are bias and secular trend. The periodical parts are expressed in terms of cosine and sine coefficients c f and s f . The amplitudes c f and s f correspond to the angular frequency ω f . In this study, the expansion term for the periodical term is chosen as 4. The periods of 161 days, 1, 2. 5 and 3. 7 years are taken into account. The 161-day period is included to consider effects from the insufficient ocean tide background model (Ray et al. 2003). Ray et al. (2003) showed that aliasing terms exist for the S2,  K2,  K1 tide components that result in 161-day, 3. 7-year and 7. 4-year periods, respectively. Contribution of K1 is not well retrievable due to its long aliasing period and the shorter time span of available GRACE monthly solutions. It is not considered further on. Schmidt et al. (2008) found a long-periodic wave of about 2. 5 years on the global scale in GRACE data and the hydrological models for the GRACE period. They also showed that the 2. 5-year period is also retrievable in hydrological models for a longer period of data. Seasonal and annual (and inter-annual) mass variations are usually related to the (sub-)surface water storage changes that can be considered as the largest contribution to the temporal gravity changes (Ray et al. 2003). Noise and other un-modeled terms are characterized by \(\varepsilon\). Equation (1) can be solved by some standard least-squares adjustment. The quality of estimated secular trends and periodical terms strongly depend on the GRACE time span (interval) and the number of selected periodical terms. In other words, the modeled periodical terms should absorb all existing significant periodical signals in the (pseudo)-observations.

It should be mentioned that depending on ROI and SOI, appropriate post-processing techniques including filtering have to be used to separate the signals. From the several filter techniques published and used in the last years, the performance of the 1D isotropic Gaussian (Jekeli 1981), the 2D Fan (Zhang et al. 2009) and DDK filters (Kusche 2007) are tested for use in the permafrost region. In addition to these common filters, a de-striping filter has been applied to the spherical harmonics to minimize the effect of errors due to the north-south stripes in GRACE monthly solutions (Swenson and Wahr 2006).

3 GRACE Derived Mass Variations

After successful application of corrections due to the zonal coefficient, appropriate filtering and de-correlation, the EWT are computed at the nodes of an equiangular grid with 1× 1 taking into account the maximum degree of 90. Figure 2a–c show the performance of different filter techniques with different settings. Figure 2a shows the secular mass variations in the Siberian permafrost region by applying an isotropic 1D Gaussian filter with radius 350 km for GFZ monthly solutions. The double peak features in terms of minimum and maximum surface mass variation (i.e. EWT change) of 1. 5 cm/a and 1. 9 cm/a are visible in the basin of the Yenisei river. The minimum occurs around the Aral Sea and north-west of China. The basins of the Lena and Yenisei rivers (especially southern part) clearly show mass increase in the permafrost region. Figure 2b shows the secular mass variations for the same target region by applying the 2D-Fan filter with radius 350 km. The mass variation pattern is almost the same as for the Gaussian filter with radius 350 km. The double peaks (positive and negative secular trends) are almost the same as in the Gaussian case. But it seems that the signals, after applying the 2D-Fan filter, are smoothed more than by the Gaussian filter. Figure 2c shows the secular surface mass variations by applying the DDK3 filter (Kusche 2007) corresponding to a smoothing radius of approximately 350 km. Weaker smoothing (DDK3) obviously leaves an unrealistically strong variability in GRACE. The surface mass variations are amplified by a factor of 2 for the mass increasing rate and a factor 1. 3 for the mass decreasing rate in this region. Table 1 shows the corresponding statistics for different filter settings. To study the estimated surface mass variations in the Siberian permafrost region in more detail, the station Vilyuysk located near the Vilyuy river on the left tributary of the Lena river is selected as an example. Velicogna et al. (2012) showed a mass increase for the whole Lena basin using the CSR solution in the period of 2002–2010. We also estimated a mass increase based on the GFZ-RL05a solution for the Vilyuysk region in the period of 2003–2008 (see Fig. 3a) and a slight mass decrease in the period of 2008–2013 (see Fig. 3b). Figure 4 shows a positive secular trend (mass increase) of 25 mm/a for the station Vilyuysk in the period of 2003–2008, and a negative secular trend (mass decrease) of − 1 mm/a in the period of 2003–2013. To test the effect of selecting different time spans on estimated secular trends, we changed the periods, e.g., by taking the maximum peak in May 2008 for the first part trend estimation. The positive secular trend did not change significantly (from 2. 5 to 2. 2 cm/a). The secular trend of the second period changed from − 0. 1 to − 0. 4 cm/a. Such a shift would only slightly affect the major findings of the paper. If more data are available, we will test the negative secular trend estimation for the mass decrease in this region for the period beyond 2013.
Fig. 2

Secular trend estimation based on monthly gravity field solutions of GFZ-RL05a in the period of 2003–2013, zonal term c2, 0 replaced and various filters applied. (a): 1D Gaussian filter with radius 350 km (b): 2D Fan filter with radius 350 km (c): DDK3 filter

Fig. 3

Secular trends of mass variations in Siberia based on GRACE for the period of (a): 2003–2008 and (b): 2008–2013 (Station Vilyuysk is marked with a red star)

Table 1

Statistical values of secular trend estimation for different filters using GFZ-RL05a data in Siberia covering the period of 2003–2013


Gaussian filter (350 km), de-striping + c2, 0 replaced

Fan filter (350 km), de-striping + c2, 0 replaced

DDK3 + c2, 0 replaced


Min. (cm/a)





Max. (cm/a)





RMS (cm/a)





Mean (cm/a)





4 Hydrological Mass Variations

Auxiliary hydrological models, e.g. GLDAS (Rodell et al. 2009) and precipitation data from GPCP centres (Adler et al. 2003) are used to compare those estimated GRACE secular trends. GLDAS provides hydrological parameters with a temporal resolution of 1 month and a spatial resolution of 1× 1 for all land regions north of 60 South. GLDAS is generated by an optimal combination of all land (surface) data; e.g. soil-moisture in different depths or snow cover, and constrained by different satellite data. But permafrost contributions such as continuously frozen ground or thawing and freezing processes at the surface are not considered in GLDAS (Rodell et al. 2004). Hydro-climatic changes of permafrost layers in Siberia are complex and also include not stationary pattern changes (Milly et al. 2008). In this study, to be consistent with the procedure of GRACE data analysis, the same processing strategy and filter-techniques were applied to the GLDAS model. We then suppose that the remaining mass variation signals can be considered as permafrost layer changes.

Considering the hydrological model of GLDAS in the Siberian permafrost region for the period of 2003–2008, the maximum and minimum of soil moisture is found in the southern and western part of the Lena river. However, for the period of 2008–2013, soil moisture decreases in the same region which corresponds to the water mass decrease determined by GRACE. Therefore, the Lena basin may be affected by permafrost thawing. Figure 5a, b show several similarities to the GRACE results for the maximum and minimum in the Lena region, especially for the mass increase in the period of 2003–2008 and mass decrease in the period of 2008–2013. Figure 4 shows the time series of mass variations in terms of EWT at the selected station Vilyuysk based on GRACE solutions, the GLDAS model and differences between GRACE and GLDAS results. The times series as well as secular trend of GLDAS hydrological mass variations are similar to the GRACE results, but in some periods of time major differences are obvious. In addition, some studies show that the eastern part of Lena, especially the Kolyma river, experiences a strong mass increase during the period of 2003–2008 (Majhi and Yang 2008).
Fig. 4

Time series of mass variations at the station Vilyuysk based on GFZ-RL05a solutions (blue), GLDAS model (red) and difference between GRACE and GLDAS results (gray) in the period of 2003–2013, and the corresponding estimated secular trends for the periods of 2003–2008 and 2008–2013

Fig. 5

Secular trends of soil-moisture variations in Siberia from the GLDAS model for the periods of (a): 2003–2008 and (b): 2008–2013

The differences between GRACE and GLDAS time series might be explained by permafrost thawing effects that were not modeled in GLDAS. The secular trends of 1. 4 cm/a and 0. 7 cm/a during the periods of 2003–2008 and 2008–2013 are estimated for the selected station. As GLDAS does not include permafrost contributions, these results may point to permafrost changes in the Lena basin. Therefore, the estimated positive secular trends for the GRACE minus GLDAS results during the period of 2003–2013 may show that permafrost thawing is proceeding in the target region. But permafrost thawing dynamics and geophysical processes behind it are very complex. By increasing the time span and accuracy of GRACE observations (e.g. with the launch of GRACE follow on in 2017) as well as the availability of more precise hydrological models, permafrost thawing processes in Siberia might be better determined and physically interpreted in near future.

There is some evidence that mass increase and decrease in the permafrost region, especially in the Lena basin, are related to increase and decrease of precipitation. To test this assumption, we used GPCP data with a monthly temporal resolution for the period of 2003–2013. Figure 6a shows an increase of precipitation for the period of 2003–2008 that corresponds to soil moisture increase determined by GLDAS and surface mass increase estimated by GRACE. For the period of 2008–2013, a decrease of precipitation is visible in this region, that can be compared to the decrease of surface mass variations determined by GRACE. This means, in addition to permafrost thawing caused by climate warming, the precipitation rate has to be considered as an important second cause for mass variations in the Siberian permafrost region. Thus, with increasing permafrost thawing and consequently increasing permafrost active layers, which may absorb much water such as soil moisture, as well as an increasing precipitation rate (e.g. as can be seen in Fig. 5a), mass increase results in the period of 2003–2008. In the period of 2008–2013, based on the negative trend determined by GRACE and the negative precipitation trend, we expect that the permafrost thawing activities have slowed down in Siberia.
Fig. 6

Precipitation trend estimation in Siberia based on the GPCP model for the period of (a): 2003–2008 and (b): 2008–2013

5 Conclusions and Outlook

Our investigations of mass variations in Siberia from GRACE and hydrological models mainly focused on the permafrost regime. It should be mentioned that the lower degree of the spherical harmonics (i.e. zonal term c2, 0) has a significant impact on the mass variation estimations. Using different filter techniques (isotropic and non-isotropic) gives slightly different mass variation trends in Siberia. In addition, the 2D Fan-filter with radius 350 km and after replacing of c2, 0 from SLR solutions seems to be an optimal filter for Siberia. Vey et al. (2013) found that 30–60% of total mass variations in the permafrost region of Siberia can be related to surface water storage changes. Thus combined with our recent results, permafrost thawing can reach up to 1. 3 cm/a EWT for the period of 2003–2008. Vey et al. (2013) also studied the potential benefit of combining GRACE gravimetry, satellite altimetry and satellite imagery data. Thus, future studies of temporal mass variations should include data from further space-borne missions, e.g. satellite altimetry and satellite imagery, to constrain hydrological mass variations in the Siberian permafrost region. The separation of GRACE mass variations can be improved by assimilation of lake surface extent measurements and height variations from satellite altimetry (e.g. Jason-2) and hyper-spectral satellite (e.g. Landsat) data with different temporal-spatial resolutions. Based on these three techniques, the real (sub)-surface mass variation pattern in the Siberia might be better understood.



We would like to thank the GeoForschungsZentrum (GFZ) in Potsdam and the German Space Operations Center (GSOC) of the German Aerospace Center (DLR) for providing continuously and nearly 100% of the raw telemetry and L2 data of the twin GRACE satellites.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of GeodesyUniversity of HannoverHannoverGermany

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