The area of Kazakhstan (40° ≤ latitudes ≤ 56° and 46° ≤ longitudes ≤ 88°) is located in the core of Eurasia with a territorial area of 2.72 km² × 106 km² (Figure 2). This region consists mainly of plains, lowlands, and hills, with fewer mountains, rivers, and lakes. The plains are mostly located in the west, north, and southwest, while the central area is dominated by the Kazakh Hills. To the east and southeast lie the Altai and Tianshan Mountains. Between the Caspian Sea and the Tianshan Mountains, farmland, grasslands, and deserts extend from north to south. Farmlands are concentrated in the northern plains, eastern areas, and eastern foothills, while grasslands are found primarily in the central, northeastern, and northwestern plains. Deserts are mainly located in the central and southern regions. Forests are relatively scarce, mainly situated in the Altai Mountains in the east, the Tianshan Mountains in the south, and the hilly and mountainous areas in the north (Kraemer et al., 2015; Urazaliyev et al., 2024). The spatiotemporal variations in the gravitational field within this area can result primarily from the dynamic redistribution of mass within the Earth’s system. Key contributors to these mass redistribution include declining Caspian Sea levels, ongoing degradation of the Aral Sea, accelerated melting of glaciers in the Tien Shan mountains, and persistent tectonic activity. Nonetheless, spatiotemporal variations of geoid heights in this area remain uninvestigated. In 2024, Kazakhstan experienced extreme hydrological events, such as large-scale flooding, anomalously high precipitation levels, and heightened tectonic activity in adjacent regions (e.g., Van Dijk et al., 2025). Such extreme events can induce significant temporal variations of the Earth’s gravitational field and geoid heights within the area of Kazakhstan.

Within the course of this study, spatiotemporal variations of geoid heights across Kazakhstan for the period 2019–2024 were investigated using GRACE–FO satellite mission data, accessed via the International Centre for Global Earth Models (ICGEM; Ince, 2019). Specifically, Release–06.3 (RL06.3) GRACE–FO based monthly Global Geopotential Models (GGMs), provided by the Helmholtz Centre for Geosciences (GFZ; Dahle et al., 2019), were utilized. The first–degree (degree −1) and the second–degree (degree −2) spherical harmonic coefficients of these GGMs were replaced by their corresponding ones obtained by the solution presented in (Sun et al., 2016) and satellite laser ranging (SLR) data (Loomis et al., 2019), respectively. To reduce the noise included in those GGMs, the decorrelation filter DDK3 was applied (Kusche et al., 2009). This filter provides a balance between noise reduction and preservation of the signal (Godah et al., 2017a). In addition, these GGMs were truncated at degree and order (d/o) 60 (approx. 330 km) which corresponds to the spatial resolution of the DDK3 filter. It is important to note that while the DDK3 filter significantly reduces noise in GRACE–FO–based GGMs, signal leakage or attenuation from nearby areas—particularly those with strong local gradients, such as mountainous regions and coastlines—could impact the determination of gravity functionals from GRACE–FO–based GGMs. In this study, these signal leakage or attenuation were assumed insignificant and would not alter the conclusions of this research. However, we suggest that future research should focus on studying these leakage effects on obtaining gravity functionals (e.g., temporal variations of geoid height) more rigorously over the area of Kazakhstan using GRACE–FO–based GGMs.

In addition to GRACE–FO data, monthly Caspian Sea level records for the period 2019–2024 obtained from the National Hydrometeorological Service of the Republic of Kazakhstan (Kazhydromet; https://www.kazhydromet.kz/) were used to evaluate the hydrological contributions to temporal variations of geoid heights, especially in western Kazakhstan. These records could be beneficial for quantifying the impact of large–scale surface water mass fluctuations on regional gravitational field dynamics. Furthermore, climatic information was also used to assess the impact of precipitation variability and its influence on regional hydrology and thereby temporal variations of geoid heights in Kazakhstan. In particular, data on the dynamics of precipitation in the western area of Kazakhstan, Kostanay, and Kyzylorda regions were obtained from the Famine Early Warning Systems Network (FEWS NET; https://earlywarning.usgs.gov/fews/), operated by the United States Geological Survey (USGS). The precipitation trends in these regions were utilized to support the interpretation of mass redistribution signals detected by GRACE/GRACE-FO, particularly within areas prone to drought or seasonal water stress.

Furthermore, earthquake statistics from the USGS Earthquake Catalog (https://earthquake.usgs.gov/) for the area of Kazakhstan were analyzed for the 2019–2024 period. Information on the timing, magnitude, and depth of seismic events in Kazakhstan and surrounding regions were used to investigate potential relations between abrupt geoid anomalies and tectonic activity. The inclusion of seismic data will help to identify geophysically active zones and improve the interpretation of short-term fluctuations in the residual component of the geoid height time series.

Moreover, within the course of this study, time series of vertical ellipsoidal height in a daily interval from five continuously operating GPS (Global Positioning System) reference stations (CORS)—KRTV, TASK, SUMK, CHUM, and BIKO (see Figure 2)—were utilized. These time series were obtained from the Nevada Geodetic Laboratory (NGL; https://geodesy.unr.edu/NGLStationPages/gpsnetmap/GPSNetMap.html; Blewitt et al., 2018). The NGL processes three-dimensional daily position estimates in a consistent global terrestrial reference frame, such as IGS20 (International GNSS Service reference frame 2020). Data processing is carried out by the NGL using the GipsyX software developed by the Jet Propulsion Laboratory (JPL), incorporating precise satellite orbit and clock products, tropospheric delay modeling, corrections for ocean and solid Earth tides, antenna phase center calibrations, and other GNSS processing standards (cf. https://geodesy.unr.edu/gps/ngl.acn.IGS20.txt).

Maps of ΔN for January 2019–December 2024 over Kazakhstan are shown in Figure 3. It should be mentioned that these ΔN were determined using the average SHCs for the first year of this investigation (i.e., year 2019). The time series of the mean values of ΔN over the whole area of Kazakhstan is illustrated in Figure 4.

The results presented in Figures 3, 4 reveal a distinct pattern of seasonal variation of geoid heights, with the highest values observed at the beginning of spring–due to the accumulation hydrological mass, and the lowest at the end of summer caused by terrestrial water mass loss through evaporation. The results illustrated in Figure 3 demonstrate that ΔN can be seen not only across different epochs but also vary among different subareas of Kazakhstan during the same period. These findings indicate that the differences in ΔN from one epoch to another (e.g., April 2019 and October 2023) within the same subarea can reach up to 18 mm, and there may be a difference of approx. 10 mm between two distinct subareas at the same time (e.g., December 2023). Figure 3 also indicates differences in the amplitudes of ΔN over Kazakhstan within the years investigated. This can be ascribed to inconsistent changes in hydrological and climatic conditions, including extreme weather events, within those years. Furthermore, Figure 4 reveals a general downward trend in the geoid height until 2022, indicating long-term changes in mass distribution in the region. However, since 2023, the trend has shown signs of stabilization, which may indicate a slowdown in mass loss processes over Kazakhstan.

Figure 5 shows seasonal variations of geoid heights over Kazakhstan for the period 2019–2024, based on data from the GRACE–FO data. The average of these seasonal variations is illustrated in Figure 6. Figures 5, 6 reveal that the amplitude of ΔN over Kazakhstan over the period investigated is approximately 3.5 mm. It confirms the results provided in Figures 3, 4 as the maximum values of ΔN are recorded in the spring (March–May), and the minimum ones in the fall (September–November), which reflects the influence of seasonal processes associated with the redistribution of hydrological mass in the region. The estimated ΔN amplitude in Kazakhstan is consistent with values reported over the Ob River basin, which encompasses parts of Kazakhstan (Godah et al., 2020). It also falls within the range of ΔN amplitudes observed in different regions around the world. For instance, Godah et al. (2017b) reported ΔN dispersions (maximum–minimum) ranging from 4 mm to 9.6 mm across Central Europe. On a broader scale, Godah et al. (2020) showed that dispersion of ΔN can vary significantly among major river basins, with extremes such as 30 mm over the Amazon River basin in South America and 7 mm over the Orange River basin in South Africa. In contrast, Zhang et al. (2024) estimated an annual ΔN amplitude of 1.9 ± 0.02 mm over the Mississippi River basin in North America. Figure 5 shows the average seasonal variations of the geoid in Kazakhstan for the period from 2019 to 2024. It illustrated that in fall, geoid heights are decreasing in the northern and central regions, which is associated with the accumulation of snow cover and soil freezing. At the same time, geoid heights over the Caspian Sea remain relatively stable. The most significant change occurs in spring–geoid heights rise in the areas of large rivers (Irtysh, Syr Darya, Ural) due to frequent floods caused by melting snow and glaciers in the Altai and Tien Shan mountains. This leads to an increase in the hydrological mass and a redistribution of the load on the lithosphere. In summer, the geoid height stabilizes. In the southern regions, a slight decrease is observed, associated with a decrease in river runoff and evaporation. At the same time, the level of the Caspian Sea also decreases, which is reflected in negative changes in the geoid height. In autumn, the geoid height begins to gradually decrease, caused by the reduction of water reserves in rivers and underground waters. During this period, precipitation partially compensates for the losses.

Figure 7 shows long-term (trend) variations of geoid heights over Kazakhstan for the period from 2019 to 2024. It indicates a continuous decrease in geoid heights over the whole area of Kazakhstan from the winter of 2020 to the winter of 2023. From the winter of 2023, long-term (trend) variations of geoid heights over Kazakhstan are negligible (i.e., approx. Zero per year). It also demonstrates that long-term (trend) variations of geoid heights over Kazakhstan are dependent on the region. The maximum decrease in geoid heights during this period is observed in the Caspian Sea region, where the change was −7.83 mm over 5 years (approx. −1.57 mm yr⁻¹). In the southeastern regions, including Almaty and Tien Shan, the geoid decrease was 3 mm over 5 years (approx. −0.6 mm yr⁻¹). In the central regions of Kazakhstan, the change is less pronounced as it is about −1.5 mm over 5 years (approx. −0.3 mm yr⁻¹), while in the northern regions, the changes are minimal approximately–0.5 mm over 5 years (approx. −0.1 mm yr⁻¹). Overall, those long–term (trend) variations can be observed in the western part of Kazakhstan, which is associated with changes in the water level of the Caspian Sea that related to the redistribution of water mass and isostatic processes in the lithosphere (Rakhimbayeva et al., 2023; Drygval et al., 2024; Kholoptsev and Naurozbayeva, 2024).

Figure 8 shows the relation between the change in the water level of the Caspian Sea according to Kazhydromet data and ΔN in the northern and middle areas of the Caspian Sea. It indicates that the Pearson correlation coefficient between ΔN and the changes in the water level is 0.91. To ensure the statistical robustness of this relationship, this correlation was computed from deseasonalized monthly time series covering 2019–2024, thereby minimizing the influence of annual periodic components. Cross-correlation analysis revealed that the strongest correlation occurs with a lag of 1.5-month, indicating that the geoid variations slightly lag behind the sea-level changes, likely due to the delayed lithospheric response to water mass redistribution. A simple linear regression model between ΔN and the Caspian Sea level change yielded a slope coefficient of a = 4.8 × 10⁻³ mm yr⁻¹, R-squared = 0.83, and p-value < 0.01, confirming a significant and physically consistent dependence.

The water level in the Caspian Sea dropped by 1.2 m between 2019 and 2024, accompanied by a decrease in the geoid to 5.9 mm in coastal regions. The main mechanisms of this relation include several factors. First, a decrease in the mass of water because of evaporation or reductions in Volga, Ural and Kura rivers flow reduces the total volume of water mass, which weakens the local gravitational field (Völgyesi and Tóth, 2005; Safarov et al., 2024). Second, a decrease in the water load on the lithosphere causes an isostatic reaction - the crust begins to slowly rise, which also affects the geoid surface (Hofstetter and Lister, 1989). Third, opening coastal areas are subject to erosion and changes in groundwater, as well as new sedimentation, which changes the distribution of mass and additionally affects the gravitational parameters (Kooi and Groen, 2003). Climate models predict further reductions of Sea level due to increased evaporation and reduced river inflow, which may strengthen the negative trend of geoid heights (Koriche et al., 2021). These changes require constant monitoring, as they affect the geodynamics of the region, the ecosystem, infrastructure, and water resources (Putans et al., 2022).

In general, ΔN in southeastern Kazakhstan, reaching approximately −0.6 mm yr⁻¹, are caused by combined effects of tectonic, glaciodynamic, and isostatic processes in the Tien Shan as this region is a subject to horizontal compression caused by the extrusion of stable blocks (Burchfiel et al., 1999), which leads to the activation of tectonic movements. Continental collision in the Cenozoic caused the rise of the Tien Shan and the corresponding subsidence of adjacent basins, forming the modern morphostructural configuration (Pan et al., 2019). The results obtained Pan et al. (2019) revealed that GPS (Global Positioning System) and GRACE data allow the separation of contributions from glacier melting and tectonic processes to vertical crustal movements in the Tianshan region. According to their results analysis, the average vertical velocity from GPS observations is 0.72 ± 0.12 mm yr⁻¹. The elastic deformation caused by variations in the mass of surface fluids is estimated at 0.39 mm yr⁻¹, while the contribution from local glacier melting does not exceed 0.19 mm yr⁻¹. The authors concluded that the present-day uplift of the Tianshan (approx. 0.33 mm yr⁻¹) is primarily associated with crustal shortening and thickening due to horizontal compression. Due to climate warming in recent decades, there has been a reduction in Tien Shan glaciers, reaching 8.5% since the 1970s (e.g., Brun et al., 2017). Deglaciation leads to crustal unloading and its compensatory uplift, partially leveling the tectonic signal. The elastic response of the crust to the loss of glacial mass affects the gravitational field and, accordingly, causes changes in geoid heights.

Overall, the results presented in Figures 3, 8 are consistent with the information in Figure 1. An increase in geophysical mass signals—such as those masses induced from hydrology or seismic activity—leads to an increase in gravitational potential, resulting in a rise in geoid height, and vice versa.

In 2024, significant ΔN that exceeds the average seasonal and long-term trend of ΔN over Kazakhstan were determined (Figures 3, 4). These changes can be associated with a number of natural processes, including increased seismic activity, extreme floods, and changes in the water level of the Caspian Sea. Data from the GRACE–FO satellite mission allows for estimating significant mass redistribution caused by such natural phenomena that may impact the gravitational field in Kazakhstan. In Sections 4.3.1, 4.3.2, the relationship between ΔN and (1) floods and (2) tectonic activity, are respectively addressed.

A preliminary comparison was conducted between vertical ellipsoidal height changes (Δh) derived from GPS data and ΔN obtained from GRACE-FO-based GGMs. Time series of daily Δh from five GPS CORS—KRTV, TASK, SUMK, CHUM, and BIKO—located within or near the study area (see Figure 2) were analyzed. Corresponding time series of monthly ΔN at the locations of these stations were also examined. To explore the temporal patterns in both Δh and ΔN associated with mass transport processes within the Earth’s system, sinusoidal functions were fitted to each time series. Figure 14 presents these Δh and ΔN time series along with their respective sinusoidal fits.

Figure 14 demonstrates that for all GPS CORS used, seasonal variations in Δh derived from GPS data are inversely correlated with corresponding changes in ΔN obtained from GRACE‒FO data, especially during periods of peak hydrological mass accumulation in spring (March‒May) and depletion in summer (June‒September). This finding supports the interpretation that an increase in mass above the geoid causes the geoid height to rise while simultaneously exerting mass loads that result in the downward displacement of the Earth’s surface; conversely, a decrease in mass produces the opposite effect (see Godah et al., 2017b; 2025). Additionally, Figure 14 illustrates that for all GPS CORS utilized the amplitude of Δh from GPS data is notably larger than that of ΔN from GRACE‒FO data. This can be justified to the fact that the Earth’s surface deforms elastically under loading, which GPS captures as point-based vertical displacements. In contrast, the geoid surface responds to changes in gravitational potential and is represented as a smooth surface at coarse spatial resolution (3° × 3°), averaging out localized mass changes. Figure 14 also depicts that for all GPS CORS used the phase shifts between Δh derived from GPS data and ΔN from GRACE‒FO data are approximately 7 or 8 months. These amplitudes and phase shifts are consistent with those reported by Godah et al. (2020) for the Ob River basin, which includes Kazakhstan. Overall, the preliminary results from the comparison between Δh from GPS data and ΔN from GRACE‒FO–based GGMs indicate that GRACE–FO data effectively captures ΔN in the region. However, a more comprehensive analysis involving additional GPS CORS across Kazakhstan and longer time series is recommended to better understand the relationship between GPS–derived Δh and GRACE‒FO–derived ΔN in the context of hydrological mass variations and seismic activity.