Ice-related flooding in the lower Yellow River driven by atmospheric teleconnections over the past 160 years

Abstract

Ice-jam floods are a unique yet understudied hydrological hazard, occurring in cold-region rivers when upstream thawing and downstream freezing create ice blockages. Despite their severe impacts, their atmospheric drivers and future trends remain unclear. Using a 160-year documentary record, historical reanalysis datasets, and statistical modeling, we examine the climatic and hydrological controls of ice-jam floods in the lower Yellow River, one of the world’s most flood-prone rivers. Our findings show that ice-jam floods are strongly influenced by large-scale atmospheric teleconnections, including the Arctic Oscillation, Siberian High, and Ural Blocking, which regulate regional thermal contrasts and cold-air intrusions. Over the past century, ice-jam flood frequency has declined, with hot spots shifting toward the river estuary due to weakening upstream-to-downstream temperature gradients under climate warming. Projections using bias-corrected CMIP6 multimodel ensemble indicate a continued decline in ice-jam flood occurrences by 2100. Our study bridges historical and future perspectives, emphasizing the need for adaptive flood management as climate change shifts hydrological risks worldwide.

Climate warming shifted ice-jam hot spots and reduced flood frequency in the Yellow River, demanding adaptive water strategies.

INTRODUCTION

Climate change is amplifying the global hydrological cycle, driving more frequent and severe floods that pose critical challenges for large rivers worldwide (1, 2). These complex fluvial systems, often spanning diverse climatic and geographic regions, are particularly vulnerable to flood events due to their intricate hydrological dynamics and extensive human use (3). The socioeconomic consequences of river floods, ranging from catastrophic property damage to disruptions in livelihoods and loss of life, are further magnified by the critical role they play in supporting agriculture, transportation, and urban settlements (4). As the climate continues to warm, understanding the drivers of flood variability and intensity in large river systems, including the interplay between natural climatic forces and anthropogenic influences, is essential for developing adaptive strategies and mitigating future risks (5).

Ice-jam floods, a localized but potentially highly destructive hazard, represent a critical component of this challenge (6). Predominantly occurring in cold regions, these events usually arise during late winter and early spring, when a contrasting thermal regime within a river basin, with upstream sections thawing while downstream reaches remain frozen, prevails (7, 8), thereby leading to the formation of ice blockages. These obstructions impede river flow, causing water levels to rise rapidly and often resulting in sudden and devastating downstream flooding. The localized impacts, coupled with the challenges of predicting the timing and extent of ice jams, make these events particularly hazardous in mid-to-high latitudes (9, 10). Despite their societal impact, research on ice-jam floods remains limited (11, 12), leaving critical knowledge gaps in understanding their dynamics, climatic influences, and future implications.

The lower Yellow River, historically plagued by devastating floods (13), provides an ideal case study for investigating the dynamics of ice-jam floods. This river system is shaped by unique geomorphological, climatic, and anthropogenic factors that exacerbate ice-jam risks. Frequent avulsions over the last millennium have altered the course of the lower Yellow River (14, 15), most notably in 1855 CE, when it shifted to a northerly route into the Bohai Sea (Fig. 1). This shift, combined with its exceptionally high sediment load that elevates the riverbed and reduces channel capacity (16), has created conditions conducive to ice-jam floods. In addition, the regional climatic conditions, marked by frequent cold air outbreaks associated with the Siberian High (SH) (Fig. 1), may enlarge the pre-existing upstream-to-downstream temperature gradient and thus foster ice-jam formation, amplifying the perceived flood risk during late winter and early spring.

Fig. 1. Atmospheric circulation and near-surface temperature patterns conducive to ice-jam formation in the lower Yellow River during late winter and early spring.

(A) February–March mean sea-level pressure (shading) and 850-hPa winds (vectors), highlighting the dominant influence of the Siberian High (SH) on regional circulation patterns linked to ice-jam flood dynamics. (B) February–March normalized near-surface air temperature distribution, with zonal and meridional means being removed to highlight regional deviations. Blue circles mark documented ice-jam flood events from 1855 CE to the present, while blue dashed lines depict the historical main course and floodways of the lower Yellow River from 1128 to 1855 CE. Light blue boxes indicate the upstream (113.50°E to 115.50°E, 34.50°N to 35.50°N) and downstream (117.50°E to 119.50°E, 37.00°N to 38.00°N) regions used for temperature gradient calculations.

Despite extensive research on summer floods driven by extreme monsoonal rainfall (17, 18), ice-jam floods in the lower Yellow River remain relatively understudied. Examining the changes in freeze and breakup dates of the Yellow River over the past five decades highlights the crucial role of temperature in ice phenology (19), but the connection of ice-jam occurrences with atmospheric drivers remains poorly understood. Furthermore, while climate change is expected to alter river ice dynamics, the long-term response of ice-jam floods to warming remains uncertain. In this study, we integrate historical records, atmospheric reanalysis datasets, and climate model projections to comprehensively examine the past, present, and future of ice-jam flooding in the lower Yellow River. We specifically aim to: (i) quantify the historical relationship between ice-jam floods and large-scale atmospheric teleconnections, (ii) assess long-term trends in ice-jam frequency and spatial distribution, and (iii) project future flood dynamics under different warming scenarios in climate models. By bridging historical analysis with future climate projections, our findings contribute to a broader understanding of ice-related river flooding and provide actionable insights for flood risk mitigation in cold regions worldwide.

RESULTS

Timeline of historical ice-jam flood events

The Yellow River, colloquially referred to as the “Mother River” of China, has a long and complex history intertwined with human civilization (20). However, this history is also marked by a legacy of recurrent and devastating floods, particularly in its lower reaches. The lower Yellow River, extending 786 km from Zhengzhou in Henan Province to its estuary in Shandong Province, is a highly dynamic section with approximately 1500 levee breaches and 26 occasions of major course displacement occurring during the past two millennia (18). Ice-jam regimes on the lower Yellow River did not emerge until 1855 CE, when the river breached its levee at Tongwaxiang in Henan Province and diverted from the Hui River catchment onto the North China Plain (14). This event consequently created a natural thermal contrast along the river (Fig. 1), making it susceptible to ice-jam floods during the spring thaw while downstream reaches remain frozen. Ice-jam floods, accompanied by the inherent risks of levee breaches and channel avulsions as well as the ever-present threat of summer flooding, have had profound societal and ecological implications throughout modern Chinese history (21).

Historical timeline of ice-jam flood events (Fig. 2A), including levee breaches and overtopping in the lower Yellow River, was compiled from official documents dating back to 1855 CE (data S1). Our compilation relied exclusively on authoritative sources, including imperial annals, treatises on statecraft addressing hydraulic works and natural anomalies during the Qing Dynasty (1644–1911 CE) and event chronicles during the Republic of China (1912–1949 CE) and the People’s Republic of China (1949 CE–present). Because these documents were prepared for central government review, they are regarded as accurate and comprehensive in their reporting (22). Geographical coordinates of nearby villages were used to represent the spatial locations of ice jams. For historical place names that are no longer in use, modern equivalents were identified using cross-references from the Encyclopedic Dictionary of Ancient and Modern Chinese Geographical Names (23).

Fig. 2. Temporal and spatial variability of ice-jam floods in the lower Yellow River highlighting the complex interplay between climate and river ice conditions.

(A) Timeline of ice-jam flood events from 1850 to 2010 CE. (B) February–March mean near-surface temperature anomalies (ΔT) relative to the 1981–2010 mean (20CR v3). (C) Freezing degree days (FDDs). (D) Thawing degree days (TDDs). (E) Freeze-thaw cycle (FTC). (F) Ice-jam duration (IJD). (G) Kernel density map of ice-jam flood locations before 1900 CE. (H) Kernel density map of ice-jam flood locations after 1900 CE. Data were smoothed using a 21-point moving-mean filter to highlight the trend. Blue dashed lines depict the historical main course and floodways of the lower Yellow River from 1128 to 1855 CE.

Changes in river thermal conditions for ice-jam formation

Ice-jam flood in the lower Yellow River usually occurs in the cold season, spanning late winter and early spring with the highest frequency in February (fig. S1A), primarily associated with overall thermal conditions of the river basin (see the Materials and Method for details) and influenced by regional temperature variations. During this period, minimum near-surface air temperatures fall below 0°C, while maximum near-surface air temperatures remain above 0°C, facilitating freeze-thaw cycles (fig. S1B). However, the primary driver of these events is the pronounced temperature gradient between upstream and downstream sections (fig. S1C). For instance, in late winter and early spring, warmer temperatures upstream cause ice to break down and drift downstream. This ice then encounters colder downstream sections, where it can refreeze up and contribute to the formation of ice jams.

Our results reveal notable temporal and spatial dynamics of ice-jam floods in the lower Yellow River over the past 160 years (Fig. 2). The timeline of ice-jam flood events demonstrates episodic flood-rich and flood-poor periods, with an overall declining trend that aligns with rising February–March mean temperatures (Fig. 2B). This warming trend is corroborated by the reduction in freezing degree days (Fig. 2C) and the increase in thawing degree days (Fig. 2D), indicating milder late winters and earlier spring thaws. Furthermore, the frequency of freeze-thaw cycles (Fig. 2E) and ice-jam duration (Fig. 2F) also show a decreasing trend, reflecting reduced ice-jam flood occurrences under warming climatic conditions. Our results show that ice-jam sites have progressively shifted toward the lower reaches of the river over time (fig. S2A), with a migration rate of 86.06 km/K of warming (fig. S2B). Kernel density estimate (see Materials and Method for details) further indicates that, before 1900 CE, ice-jam floods were concentrated in the middle reaches of the lower Yellow River (Fig. 2G), consistent with colder conditions and a wider distribution of events. After 1900 CE, hot spots migrated markedly toward the river estuary (Fig. 2H), demonstrating the sensitivity of ice-jam dynamics to climatic warming and their dependence on thermal thresholds within the river system.

DISCUSSION

Climatic drivers of ice-jam floods

To understand the atmospheric and climatic conditions contributing to ice-jam formation in the lower Yellow River during late winter and early spring, we conducted composite analyses of February–March near-surface temperatures and 850-hPa winds using the EKF400 reanalysis datasets (24). The results reveal distinct atmospheric patterns during flood and non-flood years (Fig. 3). During flood years, a Warm Arctic-Cold Eurasia (WACE) pattern dominates (25), characterized by anomalously warm temperatures in the Arctic and colder-than-average conditions over Eurasia (Fig. 3A). This pattern is usually accompanied by weakened zonal winds, which facilitate cold-air outbreaks over North China (26). These cold-air intrusions intensify the temperature gradient between upstream and downstream river sections, fostering conditions favorable for ice-jam floods. Conversely, non-flood years are associated with a Cold Arctic-Warm Eurasia pattern (27), marked by warmer-than-average conditions across Eurasia and strengthened zonal winds (Fig. 3B). These factors inhibit the southward penetration of cold air, thereby limiting ice formation upstream and decreasing the likelihood of ice jams.

Fig. 3. Dynamical climate characteristics of ice-jam floods in the lower Yellow River over the past 160 years.

(A) Composite February–March mean near-surface temperature and 850-hPa winds anomalies (EKF400 v2) during flood years. (B) Composite February–March mean near-surface temperature and 850-hPa winds anomalies (EKF400 v2) during non-flood years. (C) Biserial correlation of ice-jam flood timeline with February–March mean sea level pressure anomalies (EKF400 v2). (D) Biserial correlation of ice-jam flood timeline with February–March mean 200-hPa zonal wind anomalies (EKF400 v2). Light purple box indicates the lower Yellow River basin (113.50°E to 119.50°E, 34.50°N to 38.00°N), and dots show regions of significance at the 0.05 level.

Statistical analyses further corroborate these findings, emphasizing the role of surface atmospheric dynamics in driving ice-jam flood events. A significant correlation between ice-jam floods and February–March mean sea level pressure anomalies is observed (Fig. 3C). Flood years are associated with anomalously strong surface high-pressure systems that cover large portions of Eurasia, such as the SH. The clockwise circulation around these large-scale high-pressure systems drives cold, dry air masses southward over the lower Yellow River basin. This process amplifies the pre-existing temperature gradient between upstream and downstream river sections (28), consequently creating an ideal environment for ice-jam formation. The prominence of these high-pressure anomalies highlights the critical role of surface atmospheric patterns in modulating climate conditions in the river basin during late winter and early spring.

Upper-level atmospheric dynamics also play a crucial role in shaping ice-jam flood events. February–March mean 200-hPa zonal wind anomalies show strong correlations with flood occurrences (Fig. 3D). Negative correlations in key regions indicate that weakened upper-level zonal winds are closely linked to ice-jam floods. These weakened westerly winds, driven by the intensified Ural Blocking (UB), may enhance the WACE pattern (29, 30), which in turn allow for colder conditions to prevail in the lower Yellow River basin. The interplay between surface-level pressure systems and upper-level atmospheric teleconnections implies the complexity of the climatic mechanisms driving ice-jam floods (31). Together, these findings provide a comprehensive understanding of the combined effect of large-scale atmospheric drivers on ice-related hydrological processes (7), connecting broader climate dynamics to localized flood risks.

Decadal-scale variability of ice-jam floods linked to atmospheric teleconnections

To investigate the temporal variability of key atmospheric teleconnections and their causal relationships with ice-jam conditions in the lower Yellow River, we calculated flood frequency (see Materials and Method for details) and compared it with those of February–March atmospheric and thermal extremes (see the Materials and Method for details) from the EKF400 reanalysis dataset (24). Notably, the occurrence rates of ice-jam floods reveal a long-term decreasing trend since the late 19th century (Fig. 4A), consistent with the frequency of atmospheric extremes such as the anomalously intensified SH events (Fig. 4B), UB (Fig. 4C), and negative Arctic Oscillation (AO) phases (Fig. 4D) as well as the extremely weakened westerly jet stream (Fig. 4E). This trend reflects broader climatic shifts that have potentially modulated regional climate (Fig. 4F) and thermal conditions of the river (Fig. 4G) necessary for ice-jam formation. Superimposed on this decline are pronounced decadal-scale variability, with peaks in ice-jam flood occurrence rate aligning with those of atmospheric extremes. The heightened teleconnection activity may have reduced the strength of the westerly jet stream (32, 33), which in turn created colder-than-normal spring condition and enhanced thermal contrasts between the upstream and downstream sections of the river, collectively fostering conditions conducive to ice-jam formation.

Fig. 4. Interplay between February–March mean atmospheric teleconnection patterns and ice-jam floods in the lower Yellow River.

(A) Ice-jam flood frequency (FF). (B) Frequency of extremely strong SH. (C) Frequency of extremely intense UB. (D) Frequency of anomalously negative phase of AO. (E) Frequency of extremely weak westerly jet stream (JS). (F) Frequency of extremely cold spring (CS). (G) Frequency of anomalously large upstream-to-downstream temperature contrast (TC). (H) Structural equation model depicting the influence of teleconnection patterns on ice-jam floods through modulation of the jet stream, cold air outbreak, and river thermal conditions. Ligh dark arrows denote the loading of interpretive variables (rectangles), while heavy red arrows denote the effect of latent variables (ovals). (I) Violin plots showing the unique contribution of the teleconnection patterns to ice-jam flood variations.

Based on structural equation modeling (see the Materials and Methods for details), we quantified the relationships among teleconnection patterns, atmospheric processes, and ice-jam flood occurrence (Fig. 4H). The goodness-of-fit (0.849) assessment validates the ability of our model to accurately represent the complex dynamics underpinning ice-jam floods. The model suggests the SH, UB, and AO as key predictors of teleconnection activity at decadal scales. These teleconnections synergistically regulate the strength of the westerly jet stream (34), which in turn influence cold-air intrusions to the lower Yellow River basin and ice-jam conditions favorable for river flooding. Furthermore, the model reveals robust causal pathways, such as the link between cold-air intrusions and river flooding through changing ice-jam conditions, highlighting the critical role of these atmospheric processes in regulating downstream climate and hydrology (35).

We further quantified the unique contributions of teleconnection patterns to ice-jam flood occurrences using dominance analysis (see the Materials and Method for details). The AO emerges as the dominant driver (Fig. 4I), accounting for ~40% of the variability in flood frequency, likely due to its extensive influence on atmospheric circulation at mid- and high latitudes (36). The SH contributes around 35%, while the UB accounts for 25%, highlighting their substantial, albeit secondary, roles. This breakdown reveals the intricate interplay of teleconnections in shaping thermal and atmospheric conditions conducive to ice-jam floods (37). The long-term decreasing trend in these large-scale atmospheric drivers, combined with their decadal-scale variability, reflects the changing dynamics of the climatic and hydrological system over the past 160 years.

Future of ice-jam floods under different warming scenarios

Our analyses reveal a threshold response of ice-jam floods to near-surface temperature and hydrological conditions during the late winter and early spring (Fig. 5A). To evaluate the projected impact of future climate changes on ice-jam flood dynamics, we developed a probabilistic model using the maximum entropy method (see the Materials and Methods for details), which quantifies the probability of ice-jam flood occurrence as a function of February–March mean upstream-to-downstream temperature gradient and streamflow at the Huayuankou gauging station. The model reveals that ice-jam floods are most likely to occur under conditions of high-temperature gradient and streamflow (Fig. 5B), emphasizing the critical role of thermal contrasts and streamflow dynamics in driving these events. Observed data show a peak in ice-jam flood frequency in the mid-20th century, followed by a sharp decline after the 1980s, which is well captured by the model simulations (Fig. 5C).

Fig. 5. Historical and projected changes in ice-jam flood frequency in the lower Yellow River driven by temperature and streamflow.

(A) Temporal variations in February–March upstream-to-downstream temperature gradient and streamflow (Q) at the Huayuankou gauging station from 1950 to 2014 CE (historical period), with vertical lines denote ice-jam flood events. (B) Maximum entropy model depicting the probability of ice-jam flood occurrence as a function of temperature gradient and streamflow (Q). (C) Comparison of observed and modeled ice-jam flood frequencies during the historical period with future projections under three contrasting shared socioeconomic pathway (SSP) scenarios extending to 2100 CE.

We analyzed future projections of near-surface air temperature under three shared socioeconomic pathway (SSP) scenarios (i.e., SSP1-2.6, SSP2-4.5, and SSP58.5) that represent different socioeconomic development trajectories and their corresponding climate change impacts from 10 models (table S1) of the Coupled Model Intercomparison Project Phase 6 (CMIP6) (38). After correcting for model biases (see the Materials and Methods for details), we used the February–March mean upstream-to-downstream temperature gradients to estimate the probability of ice-jam flood occurrences through the end of the 21st century. Streamflow levels were assumed to remain constant, given that the flow of the lower Yellow River has been fully regulated since the Xiaolangdi Dam began operation in 2000 CE (39). To simulate flood events, we used a Monte Carlo approach. Using the calculated probabilities, we generated 10,000 timelines of potential ice-jam flood events through a Bernoulli process, where 1 represented the occurrence of a flood event and 0 indicated its absence. These binary time series were subsequently used to estimate mean flood frequency.

Future projections indicate a continued low frequency of ice-jam floods across all scenarios, with notable differences (Fig. 5C). Under SSP1-2.6, flood occurrences show a modest increase toward the late 21st century, suggesting that limited warming may still permit ice formation under specific conditions. The SSP2-4.5 scenario projects a relatively stable but low occurrence rate, while SSP5-8.5 exhibits the lowest probability of ice-jam occurrences, indicating that severe warming would largely suppress ice-jam floods due to diminished winter ice formation. Overall, these findings suggest that future climate warming will reshape the ice-jam flood regime in the lower Yellow River basin, with a substantial decline in their frequency. However, occasional events may still occur under moderate warming scenarios.

Our study advances the understanding of ice-jam flood dynamics by elucidating their strong coupling with large-scale atmospheric teleconnections and demonstrating how climate change is fundamentally reshaping their spatial and temporal characteristics. In contrast to previous research (19), which has primarily focused on localized hydrological and climatic conditions, this work establishes a direct linkage between ice-jam flood occurrences and large-scale atmospheric circulation patterns. By integrating historical records with climate projections, we provide compelling evidence that climate warming is not only driving a long-term decline in ice-jam flood frequency but also shifting the geographic distribution of hotspots downstream. These variations highlight the sensitivity of ice-jam flood dynamics to changing thermal regimes. More broadly, this research enhances the understanding of cryospheric hazards in riverine environments under a warming climate, thereby providing a transferable framework for evaluating ice-jam flood risks in cold-region river systems worldwide.

Policy implications for cold-region river management

Our findings hold important implications for managing ice-related floods along the Yellow River and beyond. The Yellow River serves as an exemplary case, illustrating the intricate interplay between thermal gradients and large-scale atmospheric teleconnections that govern ice-jam flood dynamics (7, 9). While hydraulic infrastructure, such as the Xiaolangdi Dam, has enhanced streamflow regulation and mitigated certain flood risks, our results reveal the predominant influence of climate-driven thermal dynamics. This highlights the necessity for climate-informed water resource management strategies to bolster the resilience of the Yellow River basin to future flood events. In addition, the observed decline in ice-jam flood occurrences presents both opportunities and challenges. On one hand, it offers a promising outlook for reduced immediate risk from ice-related floods; on the other hand, it signals potential shifts in river ice dynamics, sediment transport, and broader hydrological regimes. This evolving risk landscape necessitates the recalibration of existing flood management strategies to align with changing climatic conditions (40), ensuring their effectiveness in the long term. Furthermore, this trend provides an opportunity to reallocate resources to address emerging vulnerabilities (41), such as optimizing reservoir operations, restoring river ecosystems, and developing climate-resilient infrastructure to counteract the impacts of non-ice–related flooding caused by intensified rainfall or altered precipitation patterns in this historically flood-prone region (42).

The insights into ice-jam flood dynamics derived from the Yellow River have broader relevance for other cold-region rivers facing similar challenges (43). Ice-jam floods are a global phenomenon, affecting rivers such as the Amur, Lena, Mackenzie, and others in high-latitude and continental-climate regions (44). Climate change is amplifying variability in winter temperatures, intensifying freeze-thaw cycles, and thereby altering the likelihood and severity of ice-jam floods (45). Understanding the mechanisms driving these floods in the Yellow River provides valuable lessons for managing ice-related flooding in similar contexts, particularly in regions with pronounced continental climates. As warming continues, these regions may experience a paradoxical scenario: declining risks of ice-jam floods but heightened vulnerability to alternative flood mechanisms (46), such as extreme precipitation and rapid snowmelt. The case study of the Yellow River emphasizes the need for adaptive management strategies to address this dual challenge. Key strategies may include optimizing reservoir operations, implementing improved floodplain zoning, and investing in climate-resilient infrastructure. These measures can reduce vulnerabilities and enhance preparedness, offering a blueprint for addressing the complex and evolving risks posed by climate change to cold-region rivers globally.

MATERIALS AND METHODS

Calculating river thermal indices

To quantify the duration and intensity of ice-jam conditions during late winter and early spring (i.e., February–March), we calculated several thermal indices using daily maximum and minimum near-surface air temperatures from the Twentieth Century Reanalysis (20CR V3) dataset (47, 48). These indices include freezing degree days (FDDs), thawing degree days (TDDs), freeze-thaw cycle (FTC), and ice-jam duration (IJD). Daily average temperature (T_avg), calculated as the mean of daily maximum and minimum temperatures, is used to determine FDD and TDD. Specifically, for days with T_avg < 273.15 K, the FDD contribution is −T_avg, while the TDD contribution is T_avg; otherwise, both are 0. The total FDD and TDD are the sum of these daily contributions, representing the cumulative intensity of freezing and thawing conditions, respectively. FTC is calculated by counting the number of days where the upstream daily maximum temperature (T_max) exceeds 273.15 K while the downstream minimum temperature (T_min) remains below 273.15 K. Similarly, IJD is determined by counting the number of days when the upstream T_avg is above 273.15 K and the downstream T_avg is below 273.15 K.

Kernel density estimate of ice-jam sites

Adaptive kernel density estimation was conducted to show the spatial distribution of ice-jam sites along the lower Yellow River before and after 1900 CE. This method calculates the density of documented ice-jam flood events based on their geographical coordinates, with the locations smoothed using a Gaussian kernel function (49). The bandwidth parameter was estimated by iterative adjustment to balance localized detail and broader spatial trends. The resulting density map identifies hot spots of ice-jam activity, providing insights into spatial clustering and distribution patterns of these events.

Calculating ice-jam flood frequency

The ice-jam flood events are expressed as a binary time series, $x_t={\displaystyle {\sum }_{i=1}^N}\mathrm{\delta }(t-t_i)$ , where N denotes the total number of flood events occurring at times t_i, $i=1,2,\cdots ,N$ , within the time range $t\in [1850,2010]$ CE. Here, δ (⋅) represents the Dirac delta function defined as

$$\mathrm{\delta }(t-t_i)=\{\begin{array}{cc}1,\hfill & t=t_i\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array}$$ (1)

To estimate the occurrence rate of ice-jam floods, λ(t), the binary time series, x_t, is convolved with a Gaussian kernel function, leading to

$$\widehat{\mathrm{\lambda }}\left(t\right)=\frac{1}{N}{\displaystyle {\int }_{-\infty }^{\infty }}\mathrm{\delta }(t-t_i)\frac{1}{\sqrt{2\mathrm{\pi }}h}\text{exp}(-\frac{{\mathrm{\tau }}^2}{2h^2})d\mathrm{\tau }$$ (2)

where h = 31 year is the bandwidth of the kernel function. The kernel function smooths the binary time series, providing a continuous estimate of flood occurrence rates over time. In addition, a bootstrap approach was used to account for statistical variability. Flood events were resampled through random permutation with replacement, repeated 10,000 times. For each iteration, the convolution integral (Eq. 2) was recalculated, allowing the estimation of the mean and the 95% confidence interval of flood frequency.

Calculating the frequency of atmospheric extremes

We first calculated February–March mean indices of key atmospheric teleconnections, including the SH, UB, AO, and westerly jet stream using the EKF400v2 paleo-reanalysis products (50). The SH index was derived from the monthly sea level pressure anomalies over the core of the SH (80°E to 120°E, 40°N to 65°N). We applied the method proposed by Tibaldi and Molteni (51) to detect atmospheric blocking, characterized by stagnant or meandering flow associated with high-pressure ridges, over the Ural region (40°E to 80°E) using the 500-hPa geopotential height field. For each longitude, meridional gradients were calculated between a central latitude at 60°N and latitudes 10° to the north and south. A blocking event was identified when the northern gradient was ≥−10 and the southern gradient was ≤0. The blocking index was then derived as the fraction of longitudes within the Ural sector that satisfied these criteria. Empirical orthogonal function (EOF) analysis was performed over the Northern Hemisphere (0°E to 360°E, 20°N to 90°N) using the 850-hPa stream function (Supplementary Text). The first EOF mode (fig. S3), which explains the largest variance in the stream function anomalies, was used as the AO index. The westerly jet stream index was derived by averaging the 200-hPa zonal wind speed anomalies over the climatological core of the East Asian westerly jet stream (80°E to 120°E, 50°N to 70°N). We then identified extreme atmospheric variability using a percentile-based thresholding approach. Events were classified as instances of an extremely strong SH or UB when their respective indices exceeded the 90th percentile of their monthly index distributions. Conversely, anomalously negative AO phases or weak westerly jet stream events were defined by indices falling below the 10th percentile. The frequency of these atmospheric extremes, along with their associated uncertainty, was lastly calculated using Eq. 2.

Calculating the frequency of thermal extremes

We first calculated indices for cold spring conditions and upstream-to-downstream temperature contrasts using the EKF400v2 paleo-reanalysis products (50). The cold spring index was derived by averaging the February–March mean near-surface air temperature anomalies over the lower Yellow River basin (113.50°E to 119.50°E, 34.50°N to 38.00°N). The thermal contrast index was determined by calculating the difference in areal-averaged February–March mean near-surface air temperature anomalies between the upstream section (113.50°E to 115.50°E, 34.50°N to 35.50°N) and the downstream section (117.50°E to 119.50°E, 37.00°N to 38.00°N). We then identify thermal extremes following a percentile-based thresholding approach. This method better captures the rarity and intensity of these events than SD-based thresholds. Extremely cold spring events were defined as those with indices falling below the 10th percentile, while anomalously large temperature contrast events were characterized by indices exceeding the 90th percentile. Last, the frequency of these thermal extremes, along with their associated uncertainties, was computed using Eq. 2.

Structural equation modeling and dominance analysis

We applied structural equation model (SEM) to evaluate the impact of key atmospheric teleconnection patterns on ice-jam floods using the partial least squares method (52). This framework incorporated seven predictive variables and five latent variables. The SH, UB, and AO served as predictors for teleconnection patterns, while indices representing the jet stream, cold spring, upstream-to-downstream thermal contrast, and flood frequency were used to characterize westerly strength, cold air intrusion, ice-jam conditions, and river flooding, respectively. The relationships among these latent variables were quantified through correlation coefficients, and the overall performance of the model was evaluated using the goodness-of-fit metric, allowing us to assess the significance and robustness of the model. To further isolate the contribution of individual teleconnection patterns, we conducted dominance analysis through multiple regression (53). This approach quantified the relative importance of SH, UB, and AO in influencing ice-jam floods by calculating their unique and marginal effects using Shapley regression.

Modeling ice-jam flood dynamics

We developed a maximum entropy (MaxEnt) model to simulate the occurrence of ice-jam flood events as a function of temperature and hydrological conditions. This approach is particularly well-suited for handling presence-only data. The probability of an ice-jam flood event, p, is expressed as

$$f(∆T,Q)=\frac{\text{exp}({\mathrm{\beta }}_0+{\mathrm{\beta }}_1∆T+{\mathrm{\beta }}_{2}Q)}{1+\text{exp}({\mathrm{\beta }}_0+{\mathrm{\beta }}_1∆T+{\mathrm{\beta }}_{2}Q)}$$ (3)

where ΔT represents the upstream-to-downstream temperature gradient; Q denotes streamflow; and β₀, $\mathrm{\beta }$₁, and $\mathrm{\beta }$₂ are model parameters. Optimal parameter estimates were derived by maximizing the entropy of simulated versus historical flood events during the period 1950–2014 CE. The performance of the MaxEnt model was evaluated using the receiver operating characteristic curve (Supplementary Text). The high area under the curve (AUC) value of 0.92 indicates that the model demonstrates excellent predictive capability, with minimal false-positive and false-negative rates compared to a random classifier (fig. S4).

Correcting for biases of projected temperature in CMIP6 models

To account for biases in projected temperature data from CMIP6 models (54–63), we applied corrections using the Berkeley Earth dataset (1950–2014 CE) as a reference (64). The quantile mapping method was used for bias correction, following established protocols (65). First, the CMIP6-simulated (1950–2014 CE) and projected (2015–2099 CE) monthly temperature data were downscaled to match the spatial resolution of the Berkeley Earth data (1° × 1°) using conservative interpolation. At each grid point, the observed, simulated, and projected temperature gradients were fitted to a four-parameter Beta distribution (66). Analysis revealed that both the simulated (1950–2014 CE) and projected (2015–2099 CE) CMIP6 temperature gradient distributions deviated from the observed Berkeley Earth data (fig. S5), indicating potential model biases. For a given projected temperature gradient, x_p, the bias-corrected value, ${x\prime }_{\mathrm{p}}$ , was calculated as

$${x\prime }_{\mathrm{p}}=x_{\mathrm{p}}+F_{\mathrm{o}}^{-1}\left[F_{\mathrm{p}}\left(x_{\mathrm{p}}\right)\right]-F_{\mathrm{s}}^{-1}\left[F_{\mathrm{p}}\left(x_{\mathrm{p}}\right)\right]$$ (4)

where F_p represents the cumulative distribution function of projected temperature gradients and $F_{\mathrm{o}}^{-1}$and $F_{\mathrm{s}}^{-1}$ are the quantile functions of the observed and simulated temperature gradients, respectively. This approach ensures consistency between the simulated and observed temperature distributions while preserving the projected trends.

Supplementary Materials

The PDF file includes:

Supplementary Text

Figs. S1 to S5

Table S1

Legend for data S1

Other Supplementary Material for this manuscript includes the following:

Data S1