The Xinjiang Uygur Autonomous Region (73°40′–96°18′ E, 34°25′–48°10′ N) encompasses approximately 1.66×106 km2 in the arid interior of Eurasia. Its terrain is organized into a distinct sequence of six north–south oriented units: the Altai Mountains (N1), Junggar Basin (N2), northern and southern Tianshan Mountains (N3 and S1), Tarim Basin (S2), and Kunlun Mountains (S3) (Fig. 1). This configuration drives extreme contrasts in climate – from the humid alpine zones of the northern mountains to the hyper-arid Tarim Basin – and creates corresponding gradients in snow accumulation and persistence. The regional snowline elevation reflects this variability, ranging from approximately 3200 m in the Altai to 3230–4290 m in the Tianshan (Hu, 2004). As a region containing roughly one-third of China's snow water resources (Marchane et al., 2015; Xuezhi et al., 2000), Xinjiang provides an ideal setting for examining snow–climate interactions across pronounced environmental gradients.

To systematically examine how snow depth (SD) and land surface temperature (LST) respond differently across contrasting climatic and topographic settings, we delineated the Tianshan Mountains into northern and southern slope units based on the mountain ridge line. The northern slope (N3) falls within the mid-temperate arid zone of northern Xinjiang, whereas the southern slope (S1) belongs to the warm-temperate arid zone of southern Xinjiang. This division, combined with the broader regional classification, resulted in six distinct geographical-climatic sub-regions used for subsequent comparative analysis.

The concept of coupling, derived from physics, describes the phenomenon of mutual influence and interaction between two or more systems (Song et al., 2020). Building upon this, the notion of coupling coordination expands the framework to represent how systems can co-evolve toward a more ordered, synergistic state (Song et al., 2020). This approach has been effectively adapted to investigate interdependent systems across various fields, including ecology, geography, and economics (Lai et al., 2020; Zhao et al., 2025).

The Coupling Coordination Degree Model (CCDM) is an analytical framework that quantifies such relationships through two key metrics: the Coupling Degree (CD) and the Coupling Coordination Degree (CCD) (Huang et al., 2020; Liu et al., 2005). The CD measures the strength of association and mutual influence between systems, while the CCD further assesses the degree to which their development is harmonized. In this study, we apply the CCDM to analyze the interaction between SD and LST. Prior to calculation, both SD and LST time series at each grid cell were normalized to the [0,1] range using min-max normalization to eliminate the effects of differing units and magnitudes. The normalization was performed separately for each grid cell across the 20-year study period to preserve spatial heterogeneity in the relative variability of each variable. The CD is calculated as follows: 1C=S×E[(S+E)/2]212 where S and E represent the SD and LST, respectively, and C denotes the coupling degree. In the CCDM framework, CD quantifies the intensity of mutual influence between two subsystems, irrespective of the direction or quality of that exchange; it ranges from 0 to 1, with higher values indicating stronger interdependence. In the context of our SD-LST system, a high CD (>0.8) indicates that temperature changes are closely mirrored by snow depth variations, reflecting efficient energy transfer at the snow surface. A low CD (<0.3) indicates weak or decoupled interaction, where thermal forcing does not translate into detectable snowpack response – either due to snow absence or to other factors overriding the temperature control. However, CD alone does not distinguish whether this interdependence is sustainable or stressful; it only reflects interaction strength.

To assess coordinated development, CCD is introduced, which evaluates both interaction magnitude and mutual promotion/restraint (Huang et al., 2020). In the CCDM framework, CCD assesses the degree of harmonious co-evolution between two subsystems – quantifying not just whether they interact, but whether that interaction is balanced, stable, and mutually adaptive. In our SD-LST system, a high CCD indicates that the snowpack and thermal regime are evolving in a coordinated manner: for example, a deep snowpack that buffers temperature fluctuations and melts gradually under warming, maintaining a stable energy balance. A low CCD indicates maladjustment or system stress – for instance, a thin snowpack that collapses rapidly under thermal forcing, with no buffering capacity remaining to moderate the response. Thus, CCD provides a diagnostic measure of snow-thermal system health that complements the intensity-based information provided by CD. The calculation method is as follows: 2T=α⋅S+β⋅E3D=(C×T)12 where D denotes the CCD, ranging from 0 to 1. T represents the comprehensive evaluation index reflecting subsystem contributions. α and β (both set at 0.5 here) signify subsystem interaction weights. CD and CCD are classified via Meng et al.'s (2024) and Zhang et al.'s (2023) standards (Table 1).

For grid cells where mean snow depth was consistently below 1 cm throughout the study period, these pixels were excluded from the CD, CCD, and lag correlation analyses to avoid spurious results arising from near-zero values. These areas are indicated as snow-free in the relevant figures. For pixels with intermittent snow cover (i.e., snow present in some seasons but not others), the analyses were conducted on a seasonal basis using only the days when snow was present, ensuring that the calculated metrics reflect actual snow-temperature interactions rather than artifacts of snow absence.

To quantify the time-lagged interactions between SD and LST, we employed a time-lagged cross-correlation approach (Wasserman, 2004). This method extends conventional cross-correlation analysis by measuring the linear association between two time series at different temporal offsets (lags), thereby capturing both instantaneous and delayed interactions. The model is applicable in bivariate settings and can be extended to multivariate contexts to account for lagged effects within coupling systems.

In this study, we apply this approach to characterize the dynamic interplay between SD and LST, specifically to identify the time lag at which their correlation is strongest and to evaluate the direction and magnitude of lagged responses. The cross-correlation coefficient R between SD and LST across varying time lags is computed as follows: 4Rk(X,Y)=∑i=1n-k(Xi-Xi‾)(Yi+k-Yi+k‾)∑i=1n-k(Xi-Xi‾)⋅∑i=1n-k(Yi+k-Yi+k‾) where Rk(X,Y) denotes the correlation coefficient sequence between LST (Xi) and SD (Yi) at lag k, where n is the sequence length and k∈[0,n/4] (empirically determined). At k=0, SD responds instantaneously to LST, indicating synchronized evolution. The formula for computing the maximum cross-correlation coefficient and corresponding lag time for each k is as follows: 5R1(k1)=max⁡(Rk(X,Y))6R2(k2)=min⁡(Rk(X,Y))7R=R1K=k1|R1|>|R2|R=nullK=null|R1|=|R2|R=R2K=k2|R1|<|R2| where R1 denotes the maximum correlation coefficient between SD and LST at lag k1, while R2 is the minimum at k2. R and K represent the peak cross-correlation coefficient and corresponding lag time, respectively. Lag time categories are: K=0 (fastest, no delay), 1≤K≤7 (fast), 8≤K≤13 (medium), and 14≤K≤23 (slow). Shorter lags indicate faster SD response to LST, with zero lag implying instantaneous response.

To quantify long-term changes in snow depth (SD), land surface temperature (LST), CD, CCD, and lag times, we applied Sen's slope estimation combined with the Mann–Kendall significance test. Sen's slope estimator calculates the median of all pairwise slopes between data points, providing a robust trend magnitude that is insensitive to outliers and does not assume normality of the data distribution (Sen, 1968). For a time series with n data points, the slope between any two points i and j (i<j) is computed as: 8βij=(xj-xi)/(j-i)

The overall trend slope β is the median of all pairwise slopes: 9β=median(βij)for all i<j

Statistical significance of the observed trends was assessed using the Mann–Kendall test, a non-parametric test for monotonic trends that does not require normally distributed data (Mann, 1945; Kendall, 1975). The test statistic S is calculated as: 10S=∑i=1n-1∑j=i+1nsign(xj-xi) where sign(xj-xi)=1 if xj>xi, 0 if xj=xi, and -1 if xj<xi. For sample sizes n≥8, S is approximately normally distributed, and the standardized test statistic Z is computed to assess significance. A significance level of α=0.05 was used; trends with p<0.05 were considered statistically significant, and p-values between 0.05 and 0.10 were considered marginally significant. All trend analyses were performed on a per-pixel basis and then summarized by sub-region (N1–N3, S1–S3) for reporting.

Figure 2 shows the interannual variations of annual average SD and LST across six sub-regions of Xinjiang over the 20-year study period. The 20-year mean SD (Fig. 2a) exhibits marked spatial heterogeneity, with deeper snowpacks predominantly located in the northern regions. The mean SD values for the six sub-regions were: N1=5.32 cm, N2=2.89 cm, N3=4.25 cm, S1=2.00 cm, S2=0.06 cm, and S3=1.58 cm. The highest mean SD occurred in N1 (5.32 cm), followed by N3 (4.25 cm) and N2 (2.89 cm), while the lowest was in S2 (0.06 cm). Overall, snow accumulation is most pronounced in the northern zones (N1, N3, N2) and the southern alpine zone (S3), showing a clear north-to-south gradient. Maximum accumulation occurs on the northern slopes of the Tianshan Mountains (N3), while the Tarim Basin (S2) remains largely snow-free throughout most of the year.

To statistically verify these visual trends, we applied the Mann–Kendall test combined with Sen's slope estimation (Sect. 3.3). The results show that none of the six sub-regions exhibit statistically significant trends in SD at the 95 % confidence level (p>0.05 for all). Although several regions show directional tendencies – SD declining in N1–N3 and S1–S2 but slightly increasing in S3 – none of these tendencies are statistically robust. The Sen's slopes for SD were -0.039 cmyr-1 (N1), -0.015 cmyr-1 (N2), -0.026 cmyr-1 (N3), -0.031 cmyr-1 (S1), -0.001 cmyr-1 (S2), and +0.016 cmyr-1 (S3), with the largest declining tendency occurring in N1 and the only increasing tendency in S3.

Temporal trends of LST show differentiated variations across the six sub-regions (Fig. 2b). The highest mean annual LST values (>30 °C) occur in the arid Tarim Basin (S2), followed by the Junggar Basin (N2, >25 °C). The remaining mountain-dominated regions (S1, S3, N1, N3) maintain moderate LST regimes ranging between 10 and 18 °C. Temporal analysis indicates a consistent warming trend across all regions except S2, with interannual variability particularly pronounced in the mountainous zones. However, Mann–Kendall test results indicate that none of these LST trends are statistically significant at the 95 % confidence level (p>0.05 for all), with N2,N3,S1 and S2 showing weak increasing tendencies and N1 and S3 showing weak declining tendencies. The Sen's slopes for LST ranged from -0.018 °Cyr-1 (S3) to 0.011 °Cyr-1 (N3), indicating generally weak thermal trends across the region. The absence of significant trends in both SD and LST underscores the importance of using statistical significance tests rather than visual inspection alone to identify robust changes in these highly variable climate variables.

Scatter plot analyses were conducted to quantify the SD-LST interactions across the six sub-regions (Fig. 3). Each panel displays the scatter distribution, linear regression fit, 95 % confidence interval (shaded band), coefficient of determination (R2), and Spearman's rank correlation coefficient (ρ). In five of the six sub-regions (N1, N2, N3, S1, and S3), both Spearman's ρ and R2 indicate statistically significant negative correlations (p<0.01 for ρ; R2 ranging from 0.49 to 0.76, all p<0.001). The majority of data points fall within the confidence intervals, supporting the robustness of the inverse relationship. In contrast, no significant correlation is observed in S2 (Tarim Basin): ρ=-0.0011 (p≈1.0) and R2≈0 (p≈0.98), indicating no linear or monotonic relationship between SD and LST due to limited seasonal snow cover and persistently high LST.

These results demonstrate that in snow-abundant regions of Xinjiang, SD is consistently negatively correlated with LST, though the strength of this relationship varies spatially. However, correlation alone does not elucidate the directionality, lagged responses, or synergistic interactions between the two variables. This highlights the necessity of employing more nuanced analytical frameworks – such as coupling coordination and time-lag models – to better characterize the underlying SD–LST interaction mechanisms across different geographical and climatic contexts.

Our analysis reveals that the spatial patterns of snow–temperature interactions across Xinjiang are governed by a coherent hierarchical control framework (Fig. 12), which is distinctly expressed through the unique climatic and cryospheric characteristics of its three major mountain systems: the Altay (N1), Tianshan (N3, S1), and Kunlun (S3). This integration of scale-dependent controls and regional specificity provides an integrated understanding of the observed heterogeneity.

At the macro-scale, the fundamental contrast between the cold-humid north and the hyper-arid south establishes the baseline potential for strong snow–temperature coupling (Sato, 2005). This is most clearly manifested in the Altay Mountains (N1), where abundant snowfall and a long snow season create a deep, persistent snowpack. This system operates under climate-dominated control, resulting in the highest and most stable coupling degrees observed (CD consistently exceeding 0.8 across all elevations, as shown in Fig. 5; Δ=0.21–0.31, indicating well-matched CD and CCD), alongside the longest winter response lags (14–22 d, Sect. 4.3) – a signature of high thermal inertia. The absence of significant elevational gradients in CD and CCD across N1, combined with consistent lag structures across elevations, suggests that the climatic regime – rather than local topographic or elevational factors – is the primary control. In other words, the snowpack response is uniform across the mountain's vertical extent, a pattern expected under a dominant climatic forcing that operates at the basin scale. This pattern aligns with stable seasonal snow–climate feedbacks typical of high-latitude regions.

The meso-scale control of elevation and topography modifies or even overrides the macro-scale template, particularly in the drier southern regions (Pepin et al., 2015). In the Kunlun Mountains (S3), elevation becomes the dominant, overriding control. The robust correlation between altitude and both coupling and coordination degrees (CD rising from <0.3 at low elevations to >0.7 above 3000 m; CCD improving markedly above 3500 m, as shown in Fig. 7) illustrates a strict elevation-gating mechanism: only above a critical altitude (∼3500 m) does a sufficiently persistent snowpack exist to establish a coordinated interaction with temperature. The lag-elevation relationship further supports this control (autumn lag increasing by 0.8–1.2 d per 1000 m, Sect. 4.3), confirming that snowpack thermal properties are systematically modulated by altitude. The strong correlation between elevation and both CD and CCD indicates that elevation exerts a primary control that cannot be explained by the macro-scale climate alone, which is uniformly hyper-arid across the region; rather, it reflects the elevational control on snow accumulation and persistence, where higher elevations capture more precipitation and sustain lower temperatures.

In the Tianshan Mountains, topography manifests as a sharp intra-mountain contrast. The pronounced north–south asymmetry in coupling and coordination is a direct result of the rain-shadow effect and differential solar radiation, making the south slope (S1) a more sensitive and vulnerable subsystem. The rain-shadow effect reduces precipitation on the southern slope, leading to thinner snowpack with lower cold content and reduced thermal buffering capacity. This directly limits the snowpack's ability to absorb and modulate thermal forcing, manifesting as lower CCD values (0.2–0.4) and greater CD-CCD divergence (Δ up to 0.34) compared to the northern slope. Here, topography amplifies the macro-climatic gradient, creating strong internal heterogeneity. This is supported by the contrasting CD and CCD patterns between N3 and S1: the northern slope maintains higher CCD values (0.5–0.6) and more stable Δ (0.20–0.28 at low elevations), whereas the southern slope exhibits lower CCD (0.2–0.4) and the largest CD-CCD divergence above 2700 m (Δ up to 0.34, Sect. 4.2). The greater solar radiation on the south-facing slope accelerates melt and shortens snow duration, increasing sensitivity to temperature fluctuations – as reflected in the significant spring lag lengthening observed on the southern slope (Sect. 4.3). Lag patterns further reinforce this asymmetry: the southern slope shows significant spring lag lengthening, suggesting heightened sensitivity to seasonal transitions, whereas the northern slope maintains more stable seasonal lag structures. The combination of reduced moisture supply and enhanced radiative forcing makes the southern slope particularly vulnerable to warming. Even moderate temperature increases can trigger rapid snow loss, whereas the northern slope – sustained by greater snowfall and lower radiation – maintains more stable snowpack conditions and higher CCD. This vulnerability is further evidenced by the intensification of the CD-CCD mismatch with elevation on the south slope (Δ increasing from 0.13 at 2700–3000 m to 0.34 at >3800 m), confirming that topographic modulation of snowpack properties is the dominant mechanism underlying the north–south asymmetry.

A high Coupling Degree (CD) reflects strong statistical interdependence between snow depth (SD) and land surface temperature (LST), indicating efficient energy exchange at the snow–atmosphere interface. This is characteristic of thermally responsive snowpacks, as evidenced by the consistently high CD values in the snow-rich Altay Mountains and the high-elevation Kunlun Mountains.

However, a high CD does not guarantee a high Coupling Coordination Degree (CCD). The CD-CCD decoupling observed in the southern and parts of the northern Tianshan reveals a critical state: strong thermal forcing persists as the dominant driver (hence high CD), but the snowpack has lost sufficient buffering capacity to respond sustainably (hence low CCD). The relationship has shifted from coordinated co-evolution – where snowpack properties such as depth, cold content, and albedo modulate the thermal response – to a forced, maladaptive response, where warming drives snow loss with little modulating feedback. Physically, this decoupling manifests as a progressive loss of buffering capacity: the ability to absorb thermal perturbations diminishes as snow depth decreases and snowpack structure deteriorates. Thus, the CD-CCD discrepancy serves not merely as a descriptive metric but as an early warning indicator of system stress, identifying regions where snowpack buffering capacity is eroding under accelerating warming (Hantel and Hirtl-Wielke, 2007).

This decoupling manifests differently across regions, forming a spectrum of system states as revealed by the Δ analysis in Sect. 4.2. At one end, the Altay Mountains represent a well-coordinated state, where the deep, cold snowpack effectively buffers thermal forcing and maintains synchronized SD-LST evolution. At the opposite end, the southern Tianshan above 2700 m exhibits acute system stress, where a marginal snowpack responds quickly to temperature (high CD) but collapses rather than melts gradually (low CCD) – approaching a critical transition. Between these extremes, the northern Tianshan at high elevations shows incipient system stress: high CD but declining CCD indicates that the snowpack retains thermal inertia but is beginning to lose coordination capacity. In contrast, the Kunlun Mountains occupy a distinct position – limited snow cover and weaker thermal forcing yield weak but balanced interactions, representing a low-energy system where CD-CCD separation is less pronounced. This regional differentiation demonstrates that the same high-CD-low-CCD signature can have different physical meanings depending on the regional snowpack and climatic context.

The lag patterns presented in Sect. 4.3 add a temporal dimension to this diagnostic framework. In the Altay Mountains, long and stable winter lags are consistent with a deep, cold snowpack possessing high thermal inertia. In contrast, shorter lags in the Tianshan low-elevation zones suggest reduced thermal buffering capacity. The long-term trends also exhibit seasonal asymmetry: declining autumn lags – particularly in the Tianshan – may indicate accelerated snowpack establishment under autumn cooling, while declining winter lags in the North Tianshan may reflect snowpack thermal degradation under warming winters. This asymmetric interpretation is supported by concurrent regional trends presented by Chen et al. (2015): autumn cooling rates have accelerated over the study period, while winter warming trends have been documented in the same region. These interpretations are inferential – lag time is a statistical metric, whereas thermal inertia and cold content are physical properties we did not directly measure. Direct attribution would require complementary in situ measurements or process-based modeling.

Several mechanisms may explain the observed patterns. First, loss of buffering capacity is most relevant to the Tianshan, where thinning snowpacks lose thermal inertia and latent heat capacity, triggering rapid ablation rather than gradual melt – shifting snow from a climate moderator to a change amplifier (Shengdi et al., 2023). Second, asynchronous response rates help explain why the Altay maintains stable Δ whereas the Tianshan does not: in the Altay, abundant snowfall sustains a deep snowpack that buffers temperature variability, allowing SD and LST to evolve in synchrony; in the Tianshan, the rate of LST increase outpaces stabilizing feedbacks, with snow-albedo feedback likely exacerbating this asynchrony (Flanner et al., 2011). Third, seasonal shifts in interaction mechanisms help interpret the modest CD-CCD divergence in the Kunlun, where limited snowpack and weaker thermal forcing yield less pronounced separation. Pronounced spring lag lengthening indicates a change in energy processing: early ablation is driven by surface heating (short lags), while peak ablation involves energy storage within the snowpack (Zhang et al., 2014), degrading the synchrony essential for high CCD.

The CD-CCD discrepancy is not an analytical artifact but a meaningful indicator. It moves the assessment beyond whether temperature drives snow changes, to evaluate how healthily the snow-climate system is co-evolving. Regions with this decoupling – particularly the southern Tianshan above 2700 m and high-elevation northern Tianshan – are most vulnerable to rapid, potentially irreversible change under continued warming.

The response lag serves as a direct metric of snowpack thermal inertia, reflecting how efficiently energy perturbations propagate through the snow column. The pronounced spatiotemporal heterogeneity in lag times across Xinjiang is fundamentally shaped by regional differences in snowpack characteristics – governed by distinct climatic regimes – and reveals divergent system vulnerabilities.

In the Altay Mountains region (N1), the cold-humid continental climate coupling with abundant winter snowfall sustains a deep seasonal snowpack characterized by high cold content. This results in the longest and most stable winter response lags observed across the study area (14 to 22 d), serving as a direct manifestation of its strong thermal inertia. The minimal interannual variation in these seasonal lags further indicates that snow depth and cold content remain the dominant controls, effectively buffering the system against abrupt shifts in melt timing. This high-inertia regime corresponds closely with the region's consistently high coupling coordination, reflecting a resilient snow–climate system in which temperature forcing and snow depth response remain in a state of relative equilibrium.

The Tianshan Mountains (N3 and S1) display a pronounced north–south asymmetry in lag patterns, which originates from fundamentally contrasting snowpack regimes (Lie-qun et al., 2013). Influenced by greater moisture availability, the northern slopes maintain a moderately deep and seasonally persistent snowpack, resulting in intermediate yet stable lag times. In contrast, the southern slopes experience a warmer and drier climatic regime, supporting only a shallower, more intermittently distributed snow cover. Notably, the significant lengthening of spring lags observed on the south slope suggests a possible increase in snowpack cold content – potentially linked to enhanced winter accumulation at higher elevations – or a shift in the dominant spring melt energy from sensible to radiative heating, a process that requires more time to offset the snowpack's energy deficit. This evolving dynamic indicates that the south slope is undergoing a regime transition, wherein its already limited snowpack is growing more sensitive to variations in winter precipitation and spring radiative forcing, thereby intensifying the coupling-coordination stress documented across this region.

Under hyper-arid climatic conditions, the snowpack in the Kunlun Mountains (S3) is sparse, shallow, and exhibits strong elevation dependence. At lower elevations, snow cover is transient, resulting in near-zero lag times. Only above approximately 3500 m does a thin yet seasonally persistent snowpack develop, displaying measurable lag responses. The relatively stable seasonal lags, coupling with an observed improvement in coordination, indicate that at these highest elevations the snowpack has attained a fragile yet stable equilibrium with the extreme environment. The existing snow depth is just sufficient to provide the necessary thermal inertia and sustain coordinated thermal exchange; however, any further warming or aridification could push the system below the persistence threshold, leading to rapid decoupling.

These regional patterns underscore that lag dynamics are not merely statistical outcomes but are emergent properties of snowpack structure under specific climatic forcing. The Altay's deep snow provides robust buffering, the Tianshan's asymmetric snowpack leads to divergent sensitivity, and the Kunlun's marginal snow exhibits threshold-dependent behavior. The lengthening spring lags in the Tianshan south slope are particularly telling: they indicate a system where changes in snow accumulation or melt energy are altering the fundamental timing of hydrological response, potentially increasing the risk of abrupt meltwater release. This regional synthesis clarifies that “one-size-fits-all” models of snow–temperature interaction are inadequate; future projections must account for these intrinsically different snowpack regimes and their unique lag-response sensitivities to climate change.