Decadal-Scale Warming Signals in Antarctic Ice Sheet Interior Revealed by L-Band Passive Microwave Observations from 2015 to 2025

Highlights

What are the main findings?

• SMAP L-band brightness temperature (T_B) data (2015–2025) reveal a significant warming trend (>1.5 K over a decade) over West Antarctica, while East Antarctica shows seasonally dependent but no long-term T_B trend.
• The τ-z model suggests that SMAP T_B signals are most sensitive to internal ice temperatures at depths of 500–2000 m, thereby linking T_B variability to subsurface thermal dynamics.

What is the implication of the main finding?

• The observed L-band T_B warming over West Antarctica is not caused by internal ice shelf temperature increases, differing from changes at the Antarctic margins.
• These results offer new insights into the thermal processes of the Antarctic ice sheet, enhancing our understanding of its role in global climate research and sea-level projections.

Abstract

The Antarctic ice sheet, Earth’s largest ice mass, is vital to the global climate system. Analyzing its thermal behavior is crucial for sea-level projections and ice shelf assessments; however, internal temperature studies remain challenging due to the harsh environment and limited access to the site. Using ten years of Soil Moisture Active Passive (SMAP) satellite passive microwave brightness temperature (T_B) data (2015–2025), we examined changes in T_B across Antarctica. Results show a stronger warming trend in West Antarctica, with T_B increasing by over 1.5 K over a decade, while East Antarctica remains relatively stable, showing only seasonal summer warming and winter cooling. Furthermore, T_B in the Antarctic region correlates best with internal temperatures at depths of 500–2000 m, as indicated by the effective soil temperature, as demonstrated by the modeling data and the τ-z model’s inference. However, the total enthalpy is inconsistent with the T_B trend and exhibits the opposite effect when combined with the sensing depth. By comparing the weak trend in surface ice temperature changes, we conclude that the T_B warming trend observed on the western side of the Antarctic over the past decade does not originate from the increasing temperatures within the internal ice shelves, which differs from the increase in temperatures at the Antarctic margins.

1. Introduction

As the largest freshwater reservoir on Earth, the Antarctic ice sheet plays a pivotal role in global climate systems and sea-level dynamics [1,2]. Its thermal structure, particularly the vertical temperature profile across various ice depths, is critical in assessing ice sheet stability, forecasting melting trends, and deepening our understanding of climate change processes [3,4,5,6]. The internal temperature distribution governs key ice sheet behaviors, including ice flow, basal sliding, and deformation, and is a vital indicator of dynamic processes within the ice mass. Fluctuations in internal temperature arise from a complex interplay of geothermal heat flux, atmospheric conditions, and insolation, all of which influence ice viscosity and movement patterns [7]. Consequently, precise and detailed information on the ice sheet’s thermal regime is essential for predicting its evolution and potential contributions to global sea-level rise.

The Antarctic ice sheet also serves as a sensitive barometer for climate change [8,9]. Monitoring its internal temperature variations provides invaluable insights into broader climate trends and the impacts of global warming on polar regions. Such knowledge is crucial for developing effective policies and mitigation strategies to address the adverse effects of climate change [10,11]. Thus, understanding the thermal dynamics of the Antarctic ice sheet is not merely an academic exercise but a practical necessity for addressing one of the most urgent challenges of our time.

Recent studies have highlighted the spatial heterogeneity of internal temperature trends across the Antarctic ice sheet [12]. Ice core records and thermodynamic modeling have revealed pronounced warming signals in the West Antarctic sector, associated with enhanced basal melting and ice shelf instability at millennial timescales [13]. These findings highlight the crucial role of subsurface thermal processes in shaping ice sheet dynamics. However, despite progress in linking surface climate variability to subsurface thermal regimes, the drivers of decadal-scale temperature fluctuations in Antarctica’s interior—and their potential feedback on ice sheet mass balance—remain poorly constrained.

Satellite remote sensing has emerged as a powerful tool for investigating ice sheet properties, but technical challenges persist. The Soil Moisture Active Passive (SMAP) satellite [14], originally designed to monitor soil moisture over terrestrial surfaces, provides brightness temperature (T_B) data that, in principle, could offer insights into ice sheet temperatures [15]. However, SMAP was not explicitly intended for deep temperature profiling of ice sheets, and interpreting its data in this context requires innovative methodologies and rigorous processing techniques [16,17,18,19].

Several key challenges hinder the effective use of SMAP data for Antarctic ice sheet studies. First, the microwave emissions measured by SMAP are influenced by various factors, including ice texture, density, and temperature gradients, making it challenging to isolate thermal signals from other effects [20]. Second, existing models for interpreting T_B data in polar regions often lack the spatial and temporal resolution to capture fine-scale thermal variations within the ice sheet [21]. Third, while some studies have attempted to link SMAP T_B data to subsurface temperatures, these efforts have been limited by uncertainties in model parameters and a lack of ground-truth validation [22,23,24].

Moreover, the decadal-scale variability of Antarctic ice sheet temperatures remains poorly understood [25]. While millennial-scale trends have been documented in ice core records, fewer studies have focused on shorter timescales, leaving gaps in our knowledge of how recent climate changes affect the ice sheet’s thermal state. Addressing these gaps is essential for improving projections of ice sheet behavior under future warming scenarios.

This study aims to investigate the internal temperature profile of the Antarctic ice sheet using SMAP T_B data spanning the past decade. We will integrate SMAP’s signals with the τ-z model [15], a framework for interpreting microwave T_B regarding subsurface thermal properties. Our research objectives are as follows: first, to decipher the complex temperature variations within the ice sheet; second, to assess its stability and melting trends in response to changing climate conditions; and third, to contribute to the advancement of glaciology and climate science by offering new insights and evidence.

2. Materials and Methods

2.1. SMAP SPL3FTP

SMAP, a NASA-led initiative, provides crucial insights into Earth’s surface conditions, especially in polar regions. Among its data products, the SMAP L3 Radiometer Global and Northern Hemisphere Daily 36 km EASE-Grid Freeze/Thaw State, Version 4 (SPL3FTP, https://nsidc.org/data/spl3ftp/versions/4#anchor-documentation, accessed on 4 May 2025) is pivotal for studying freeze–thaw dynamics. Specifically tailored for Antarctica, this dataset focuses on brightness temperature retrieved from SMAP’s passive microwave radiometer in the L-band, which penetrates snow and ice to indicate surface freeze–thaw states [26].

With a spatial resolution of 36 km and a temporal coverage from 31 March 2015 to 31 March 2025, SPL3FTP provides a comprehensive view of Antarctica (Figure 1). Processing involves calibrating raw measurements, correcting for instrumental and environmental factors, and deriving T_B, which are then gridded, averaged, and accompanied by standard deviations. The ice sheet coverage exhibits high T_B values above 180 K, with a very low standard deviation of less than 10 K. In contrast, the open water area shows a T_B average of about 80 to 220 K, varying with the seasons and high standard deviations, which is also determined by the ice being frozen/thawed. This ensures data accuracy and readiness for analysis to isolate the coverage of continental ice sheets. For Antarctic research, SPL3FTP presents an opportunity to investigate freeze/thaw cycles, ice stability, and climate trends. The L-band’s sensitivity to surface conditions, combined with the dataset’s resolution and coverage, makes it invaluable for advancing our understanding of Earth’s frozen environments.

Figure 2 illustrates a latitude-time cross-section of T_B observations depicted in Figure 1. Notable contrasts in T_B signatures are observed, distinguishing between the ice sheet and the seasonal transition zones, with a pronounced difference of approximately 140 K between ice and open-water surfaces. Latitudes within the seasonal transition zone (63.07°S–77.81°S in the west and 60.69°S–70.65°S in the east) exhibit elevated T_B exceeding 220 K during winter months, attributed to snow cover, enhancing surface emissivity and modifying the underlying medium’s radiometric response.

2.2. Antarctica Ice Temperature (T) Profile

The dataset comprises temperature (T) profiles (referred to as Macelloni’s/T profiles hereafter) that extend vertically through the ice sheet, providing valuable insights into its thermal state [23,27]. Macelloni’s study retrieves internal temperature profiles of the Antarctic Ice Sheet using SMOS (Soil Moisture and Ocean Salinity) L-band passive microwave observations (2010–2020) and the Tau-Omega radiative transfer model. By leveraging L-band’s penetration into dry snow and ice, the method simulates T_B based on ice dielectric properties, snowpack characteristics, and geothermal gradients, optimizing parameters (e.g., basal temperature, heat flux) to match SMOS data. Validation against ice core measurements and climate models reveals vertical temperature gradients from the surface (−20 °C to −30 °C) to bedrock (−10 °C to 0 °C), with regional variations driven by geothermal heat flux (40–80 mW/m²) and ice dynamics. While SMOS’s coarse resolution (~50 km) limits small-scale analysis, this work demonstrates the potential of passive microwave remote sensing for large-scale ice sheet thermal monitoring, complementing sparse ice core data and informing sea-level rise projections. Future directions include integrating altimetry/gravity data to refine bedrock topography constraints. It is noted that Macelloni’s profile is independent of the SMAP.

2.3. Tau-z (τ-z) Model

Without considering the impact of soil roughness and vegetation, the primary control function for the ice sheet at the L-band is described by the microwave transfer function as,

$$T_B={e_{L}T}_{eff}$$

(1)

where $e_L$ is the emissivity of ice bulk determined by the density and temperature at the L band. Soil effective temperature (T_eff) synthetically reflects the effect of T profiles due to deeper penetration depth at the L-band. The soil moisture with a fixed wavelength determines T_eff. In 1978, Wilheit expressed T_eff [28] as

$$T_{\mathit{eff}}={\int }_0^{\infty }T(z)\alpha (z)\mathit{exp}[-{\int }_0^z\alpha (z^{\prime })d{z}^{\prime }]\mathit{dz}$$

(2)

where z is the depth from the surface to the ice layer concerned. T(z) is the physical temperature at depth z, and α(z) is an attenuation coefficient determined by dielectric constant ε and wavelength λ. ε′ and ε″ are the real/imaginary parts of the dielectric constant profiles determined primarily by T. The detailed form of α(z) is

$$\alpha (z)={\displaystyle \frac{4\pi }{\lambda }}{\epsilon }^{"}(z)/2{[{\epsilon }^{\prime }(z)]}^{1/2}$$

(3)

With Lv’s scheme [15,29], soil optical depth (τ) is derived in Equation (2) as

$${\tau }_z={\int }_0^z\alpha (z^{\prime })d{z}^{\prime }$$

(4)

So, T_eff is rewritten as

$$T_{eff}={\int }_0^{+\infty }T\left(\tau \right)e^{-\tau }d\tau$$

(5)

Compared to Equation (4), Equation (5) takes the integral of τ instead of soil depth z. Subsequently, τ is further replaced with t = 1 − e^−τ, and Equation (5) evolves to

$$T_{eff}={\int }_0^{1}T\left(t\right)dt$$

(6)

It is hard to retrieve T_eff from Equation (1) because the equation is not closed, i.e., there are at least two inputs, soil moisture and soil temperature, on the right side and only one output (T_B) on the left. However, T_eff can be obtained for the ice sheet over the Antarctic continent since ε is not affected by soil moisture and is relatively stable.

The τ-z model, a physically based exponential decay framework, quantifies the microwave sensing depth in snowpack, ice, and soil media by integrating dielectric permittivity, electromagnetic frequency, and incidence angle [15,18]. While its simplicity and adaptability across heterogeneous media are advantageous, the model’s accuracy depends on assumptions of medium homogeneity and precise characterization of dielectric properties.

Within the τ-z paradigm, microwave sensing depth for soil moisture retrieval is parameterized by the dimensionless optical depth (τ) rather than geometric depth (z). The governing factors of microwave-derived soil temperature-depth profiles encompass both physicochemical attributes of the substrate and electromagnetic wave characteristics. Physically, soil bulk density, volumetric water content, particle size distribution, and structural heterogeneity exert primary controls on penetration depth, with increases in moisture content and clay fraction typically reducing effective sensing depth through enhanced microwave attenuation. The τ-z model was proposed in 2019 [15] to quantify the relationship between the depth of T (z_Teff) and τ, where τ increases with the soil depth. In Equation (6) [30,31], as a τ value corresponds to only one depth for a specific T profile, we can use τ to replace physical soil depth. Furthermore, since the soil depth is between [0, +∞) and τ, we can define t = 1 − e^−τ, i.e., t ∈ [0, 1).

$$\left\{\begin{array}{c}T\left(\tau \right)={\int }_0^{\tau }(T_s+a{e}^{-\tau }\tau )d\tau (\tau <{\tau }_{\mathit{deep}})\\ T\left(\tau \right)={\int }_0^{{\tau }_d}(T_s+a{e}^{-\tau }\tau )d\tau (\tau \ge {\tau }_{deep})\end{array}\right.$$

(7)

where T_s is the surface temperature, a is the soil temperature gradient in K/τ, T_d is the soil temperature, which can be considered constant at an annual scale, and τ_d is the τ that corresponds to T_d [15]. Then, the τ-z model defines the depth of soil temperature z_Teff (i.e., τ_Teff in terms of τ), which equals T_eff. T_eff is the soil temperature at the soil temperature sensing depth. Building on Equation (7), we next derive τ_Teff according to its definition as,

$${\tau }_{\mathit{Teff}}=-\mathit{In}\left(1-{t|}_{{\displaystyle \frac{T_{\mathit{eff}}}{T_d-T_s}}=1-{(1-t)}^b·(-log(1-t)+1)}\right)$$

(8)

where ${\displaystyle \frac{T-T_d}{T_s-T_d}}$ can be rewritten as T_{eff_nor} [15]. With the uniform ε′and ε″ hypothesis as in Equation (3), this result enables us to generalize z_Teff as

$$z_{\mathit{Teff}}=\lambda {\tau }_{\mathit{Teff}}{[{\epsilon }^{\prime }(z)]}^{1/2}/2\pi {\epsilon }^{"}(z)$$

(9)

z_Teff depends on the shape of the ice sheet temperature profile.

While the τ-z model has been widely applied to retrieve soil moisture over terrestrial surfaces, its adaptation to Antarctic ice sheets introduces unique challenges and opportunities due to key environmental differences. Unlike non-frozen soils, where liquid water content strongly influences T_B, Antarctic ice sheets lack subsurface liquid water, rendering the effects of soil moisture negligible. Furthermore, ice sheet profiles remain relatively stable over decadal timescales within the L-band penetration depth (~1 × τ depth), in contrast to dry soils, which are highly sensitive to short-term variations in surface temperature. These distinctions necessitate tailored modifications to the τ-z model, including the parameterization of vertical thermal gradients governed by geothermal heat flux and basal melting (rather than surface moisture), depth-resolved inversion for multi-decadal thermal signals, and stability constraints that enable long-term trend analysis without interference from seasonal moisture fluctuations. Since the ice sheet over the Antarctic continent has existed for millions of years and the T profile evolves slowly, it provides an ideal environment for testing the τ-z model. For the dielectric model of the ice sheet, we choose the empirical model [32] as,

$$\left\{\begin{array}{c}{\epsilon }^{\prime }=3.2\\ {\epsilon }^{"}=a\lambda +b/\lambda \end{array}\right.$$

(10)

where

$$\left\{\begin{array}{c}a=0.00504+0.0062\times \left({\displaystyle \frac{300}{T}}-1\right)e^{-22.1\times \left({\displaystyle \frac{300}{T}}-1\right)}\\ b={\displaystyle \frac{0.0207}{T}}{e}^{{\displaystyle \frac{335}{T}}}/{\left(e^{{\displaystyle \frac{335}{T}}}-1\right)}^2+1.16\times {10}^{-11}/{\lambda }^2+e^{-10.02+0.0364\times (T-273)}\end{array}\right.$$

(11)

T is the ice temperature in Kelvin. A flowchart summarizing the methodological process is presented in Figure 3, where Plan A is used to retrieve z_Teff and Plan B is used for validation. It should be noted that T_s and T_d can also be obtained from other sources; however, to maintain consistency, we also preserve Macelloni’s profile.

3. Results and Discussion

Utilizing Lv’s methodology, Figure 4 compares the microwave sensing depth (z_Teff, Plan A) estimated from the theoretical τ–z model, and that derived from the Antarctic ice temperature profile (T), which coincides with z_Teff defined by T_eff (Plan B). The flowchart illustrates that the estimation of sensing depth is deduced without requiring detailed knowledge of the temperature (T) profile. The inputs used in this flowchart include T_s (the temperature of the top layer of ice), T_d (the temperature of the bottom layer), and T_B, as measured by SMAP. It is crucial to highlight that T_eff depicted in the flowchart is derived from T_B (Plan A), with the simplification of disregarding the emissivity (ε) variations across the ice sheet, as indicated by Equation (1). Furthermore, the validation sensing depth is determined by identifying the depth at which the temperature T aligns with T_eff, a value also obtained from the T profile through Equation (2). The results demonstrate the robust performance of the τ-z model in capturing the vertical thermal structure of the Antarctic ice sheet. There is an agreement between the modeled evidence and the observed T_eff-z_Teff relationship, with a root mean square error (RMSE) of approximately 79.57 m. Compared to the ice sheet’s average z_Teff over the Antarctic continent (500–1500 m, as shown in Figure 5), the relative error is 8%. The error is smaller within 1500 m by about 3% (the dark-blue dashed box in Figure 4), but increases rapidly when z_Teff > 1500 m (the blue area in Figure 4).

In microwave remote sensing, particularly concerning the L-band, the penetration depth of electromagnetic waves into the subsurface is a topic of interest. When examining the contributions of different soil (or, in this context, ice) layers to the observed signal, it becomes evident that the upper layer, despite having the same mass as the bottom layer, plays a more dominant role in the signal received at the L-band. This phenomenon can be attributed to the inherent properties of the L-band, which enable greater penetration into the subsurface while still being significantly influenced by near-surface conditions.

Figure 5 presents a comprehensive depiction of the z_Teff map, which represents z_Teff as defined within the framework of the τ-z model across the vast expanse of the Antarctic continent. This map offers critical insights into the vertical reach of T measurements inferred from microwave remote sensing data. A notable observation from Figure 5 is that the z_Teff values predominantly fall within the 500–1500 m range for most pixels. This finding is consistent with and corroborated by the results presented in Figure 3. This alignment highlights the robustness and internal consistency of the τ-z model in predicting z_Teff across diverse geographical regions of Antarctica.

However, it is imperative to acknowledge a significant limitation in the analysis due to the absence of a comprehensive T profile dataset. This data gap particularly affects the margins of the Antarctic continent, where the lack of empirical data precludes the accurate determination of z_Teff from modeling results. Consequently, large swaths of these peripheral regions remain without validated z_Teff values, highlighting a critical area for future data collection and model refinement.

Despite this limitation, one of the strengths of the z_Teff map lies in its continuous spatial distribution. This continuity stems from z_Teff derived from the T profile, a parameter inherently independent of terrain variations, land/sea transitions, and other surface features. Consequently, the z_Teff map provides a seamless representation of z_Teff across the Antarctic, facilitating a more holistic understanding of the thermal dynamics at play.

This spatial continuity aligns perfectly with the fundamental assumptions of the τ-z model, which posits that z_Teff is a clearly defined depth parameter that exhibits minimal variation when the dielectric constant profile remains constant. In other words, the model assumes that the z_Teff is primarily influenced by the thermal properties of the subsurface rather than by external factors such as terrain or surface features. The consistency observed in the z_Teff map across the Antarctic continent strongly supports this assumption, reinforcing the validity and utility of the τ-z model in microwave remote sensing applications.

Figure 6 presents a compelling analysis of the correlation coefficients (R) between various temperature-related parameters and ice temperature (T) from different layers over a 10-year period. Specifically, it compares the T_B mean values, T_eff, and T_surf (the top layer in Macelloni’s data, which corresponds to the penetration depth in this case) with T at each layer, depicted by blue, red, and yellow curves. The dotted line indicates the R-value of 0.89 between the 10-year T_B mean values and T_eff. A detailed examination of the T_B mean values reveals a notable decline in R from approximately 0.88 at the top layer (50 m) to −0.3 at the bottom layer (4500 m). This reduction in R serves as empirical evidence supporting the penetration depth theory, which posits that the top layers contribute more significantly to the observed signal due to their closer proximity to the surface and, consequently, their stronger influence on the L-band emission.

Turning to T_eff, the correlation coefficient exhibits a distinct pattern. It increases from 0.97 at the surface to nearly 1.0 at 500 m and then gradually decreases to 0.5 around 3000 m. The consistently higher R values for T_eff than those for T_B indicate that T_eff is more strongly influenced by the temperature profile throughout the ice column. Notably, the variation in T_eff closely aligns with T at depths of 500–600 m, suggesting that this depth range is particularly critical for understanding the ice’s thermal dynamics, likely due to thermal diffusion characteristics or dielectric properties.

It is important to recognize that R depicted in Figure 4 is more closely related to the spatial variations in T_eff and T_surf rather than to the absolute values of T. While the equivalent values of T profile are essential for interpreting the thermal state of the subsurface, they do not directly correspond to the definition of R used in this analysis.

For T_surf, the correlation coefficient rapidly declines from 1 (indicating perfect self-correlation at 50 m) to less than 0.5 at around 2000 m. This decline is more pronounced than that observed for T_B and T_eff, suggesting that T_surf is more sensitive to surface conditions and less influenced by deeper layers. However, it is crucial to exercise caution when interpreting R values beneath 3000 m, as the T profile dataset lacks sufficient calculation points to ensure the reliability of these correlations.

Figure 7 illustrates the temperature trend from 31 March 2015 to 31 March 2025, as a rate of temperature increase or decrease in K/year. In the west of the Antarctic continent, T_B increases at a rate of 0.15 K/year at Ellsworth Land, but at a rate of −0.15 K/year at Marie Byrd Land. The terrain and surrounding area may cause a substantial trend shift in the western part. Although both regions are home to many glaciers and ice shelves, the glaciers in Marie Byrd Land tend to flow towards the peripheral large-scale ice shelves, such as the Ross Ice Shelf. The surrounding marine environment has a significant influence on the distribution of ice shelves. In contrast, the glaciers in Ellsworth Land flow along the mountain range trends and are connected to ice shelves, such as the Ronne Ice Shelf. The ice shelves near the coastline in Ellsworth Land exhibit more complex morphologies due to the influence of fjord topography. For most of the Antarctic continent, the margin zones exhibit a T_B trend of less than 0.15 K.

In Figure 8, the temporal evolution of the T_B trend is depicted monthly, revealing distinct patterns in the western and eastern regions of the study area. A consistent and unwavering warming trend is evident in the west sector, with an increase of 0.15 K per year observed throughout the annual cycle. This homogeneous temperature rise implies a relatively uniform response of the western region to the underlying drivers of T_B change. The linear progression of the trend suggests that the factors influencing T_B in this area, such as atmospheric circulation patterns [33], ocean-ice interactions [34], or local radiative forcing [35], exert a relatively stable influence over time, leading to continuous and predictable warming across all seasons.

Conversely, the eastern region exhibits a more complex and seasonally dependent trend in T_B. During the summer months, particularly in March, the eastern part experiences a warming trend similar to that of the west, with an annual increase of 0.15 K. This warming could be attributed to a combination of factors, including increased solar insolation, changes in cloud cover, or modifications in the heat exchange between the ocean and the atmosphere. However, a stark contrast emerges during winter, especially in July, when the eastern region undergoes a yearly cooling trend of −0.15 K. This seasonal reversal in the T_B trend indicates that the processes governing T_B in the east are susceptible to seasonal variations.

Notably, despite the absence of a discernible long-term trend in T_B over the past decade in the eastern region, there has been a distinct seasonal amplification of temperature extremes. Specifically, the summer months have become progressively warmer while the winter months have grown colder. This seasonal polarization of temperature changes may have significant implications for the local climate system, including alterations in the duration and intensity of the melt-freeze cycle, changes in the stability of ice shelves and sea ice, and potential impacts on the Antarctic ecosystem.

Although we initially posit that the dielectric constant of the ice sheet covering the Antarctic continent has a relatively minor influence on T_B, it is crucial to recognize that the combined effects of z_Teff and T fundamentally govern T_B. At lower temperatures, z_Teff, which represents the depth within the ice from which the microwave radiation contributing to T_B originates, tends to increase. This is because the microwave attenuation in ice is relatively low, allowing the radiation from deeper, warmer layers to reach the surface and contribute more significantly to the observed T_B. Consequently, warmer deep-ice layers can elevate T_B despite low T_s.

Given this complex relationship between T_B and the underlying thermal state of the ice, we opt to employ enthalpy (i.e., the enthalpy above z_Teff calculated from the T profile) rather than relying solely on T or T_eff as the primary variable for analyzing the relationship between energy changes and the climate-induced heating or cooling effects across the Antarctic continent shown in Figure 9.

Upon examination of Figure 9, a distinct pattern emerges: a positive correlation between T_eff and T_B, while z_Teff also affects it. This suggests that the thermal response of the ice sheet to energy inputs becomes less sensitive as the overall temperature level rises, possibly due to the nonlinear nature of heat transfer and phase-change processes within the ice.

Figure 10 further elaborates on this relationship using the regression curve derived from Figure 9. The enthalpy depicted in Figure 10 ranges from approximately 5 × 10⁹ J/m² to −5 × 10⁹ J/m², indicating the diverse energy changes occurring across the Antarctic region.

When comparing these results with the area of T_B increase shown in Figure 7, an interesting discrepancy is observed in the western part of the continent. In this region, the T_B increase is accompanied by a negative enthalpy, implying that despite the rise in T_B, there is a net energy loss within the ice sheet. This could be attributed to various factors, such as changes in ice dynamics, enhanced heat loss to the atmosphere, or modifications in the radiative balance at the ice-air interface.

In contrast, the Antarctic continent’s margin areas exhibit positive enthalpy and T_B increases. This suggests that in these regions, the energy input is sufficient to raise the temperature and increase the overall enthalpy of the ice system. The margin areas are more susceptible to external influences, such as ocean-ice interactions and atmospheric circulation patterns, which may contribute to the observed energy gains and temperature rises.

To further interpret these spatial patterns within the broader context of Antarctic climate change, it is essential to compare our findings with previous observations and analyses. Antarctica plays a crucial role in the global climate system, and understanding its long-term temperature evolution is fundamental to assessing the global energy balance. Current approaches to observing Antarctic climate trends include in situ station records, reanalysis datasets, and satellite remote sensing. Although station observations provide valuable long-term measurements, their spatial distribution is sparse and primarily confined to coastal areas [36], which limits their representation of the continental interior. Reanalysis datasets provide broader spatial coverage and higher temporal continuity; however, inconsistencies among different reanalysis products have led to divergent interpretations of temperature trends across Antarctica [37,38]. Despite these discrepancies, most studies based on long-term station and reanalysis data have revealed a complex spatiotemporal pattern of surface air temperature (SAT) change across the continent.

Consistent with the trends revealed by our passive microwave analysis, significant warming has been observed in the Antarctic Peninsula and West Antarctica since the mid-20th century, while East Antarctica has shown weaker or even cooling trends [39,40,41,42,43]. Additionally, temperature variations within the interior of East Antarctica exhibit spatial patterns distinct from those along the coastal margins of the region [43]. Moreover, some studies have also indicated that Antarctic warming includes narrow coastal areas [44]. These findings are highly consistent with the spatial pattern shown in Figure 7.

Compared with reanalysis and in situ data, satellite remote sensing offers a distinct advantage in monitoring Antarctic climate variability. It provides continuous and spatially extensive coverage throughout the year, directly observing T_B without relying on model-dependent atmospheric corrections. As early as 2002, studies using passive microwave nodules began to investigate climate variability in Antarctica [24]; however, they did not account for variations in penetration depth or effective temperature within the ice sheet. These parameters are crucial for determining the thermodynamic factors that influence Antarctic climate responses. By linking T_B to depth-dependent thermal properties through the τ–z model, our approach establishes a new framework to interpret subsurface heat dynamics and their radiative signatures in microwave observations.

While previous research has emphasized either dynamic processes (atmospheric circulation changes not driven by radiative temperature variations) or thermodynamic processes (changes in sea surface temperature, sea ice, or land surface properties that do not alter large-scale circulation) [43,45,46,47], our findings integrate both perspectives. The comparison between T_B and enthalpy reveals that, in certain interior regions of West Antarctica, an increase in T_B corresponds to a net energy loss, whereas along the continental margins, T_B increases are associated with positive enthalpy gains. This contrast highlights spatially distinct thermodynamic regimes: interior regions are dominated by dynamic ice processes and enhanced radiative heat loss, while coastal zones exhibit greater external energy input from oceanic and atmospheric interactions. These results provide both thermodynamic and dynamic confirmation of the processes shaping Antarctic temperature trends.

It is worth noting that this study still has some deficiencies. The passive microwave satellite used in this study—the SMAP satellite—was launched in 2015 and has so far accumulated only about ten years of observations. Therefore, the results are mainly applicable to short-term climate monitoring of the Antarctic ice sheet. To achieve long-term climate change monitoring, it is necessary to integrate multi-source satellite observations and reanalysis datasets to extend the temporal coverage and improve the reliability of climate trend analyses. Furthermore, to better understand the causes of the inconsistency between the distributions of enthalpy and T_B, various auxiliary factors should be considered, such as sea ice variations, surface albedo, ice-layer temperature, atmospheric circulation characteristics, and ocean–ice sheet interactions. This analysis will help clarify the underlying physical processes governing energy changes in the Antarctic region.

4. Conclusions

This study employs microwave remote sensing and the τ-z model to analyze the thermal dynamics of the Antarctic ice sheet, revealing distinct vertical and regional patterns. The model effectively captures subsurface thermal structures, with the upper ice layer exerting a dominant influence on L-band signals. Correlation analyses demonstrate that effective temperature (T_eff) is more sensitive to subsurface thermal conditions than surface temperature (Ts) or brightness temperature (T_B), particularly at depths ranging from 500 to 2000 m. Despite marginal data gaps, the model’s predicted T_eff exhibits spatially continuous distributions, enhancing its reliability.

Regional T_B trends reveal abnormal warming at ice shelf edges, linked to oceanic heat transfer, atmospheric shifts, and local topography. Monthly T_B variations further indicate persistent warming in western Antarctica, contrasting with seasonal patterns in the east (summer warming vs. winter cooling).

Enthalpy dynamics reveal spatially heterogeneous responses: Western Antarctica exhibits a paradoxical thermodynamic regime where rising temperature coincides with net energy loss, suggesting that advective cooling offsets surface warming. Conversely, coastal regions exhibit direct ocean-ice coupling, driving enhanced melting. These disparities highlight the importance of depth-dependent energy exchanges and subglacial hydrology in determining ice sheet stability.

The findings highlight the limitations of surface-focused analyses and emphasize the need for three-dimensional energy transport models. Accurate predictions of ice shelf evolution, freshwater discharge, and climate feedback require interdisciplinary frameworks integrating vertical thermodynamic processes. This study highlights the need for developing process-based models to capture the dynamic evolution of Antarctic ice sheets in response to climate change.