Assessing the onset of spring water-level rise in snowmelt-dominated rivers of northeastern Russia using machine learning

Abstract

The timing of the initial spring water-level rise represents a key indicator of seasonal hydrological transition in snowmelt-dominated river systems of high-latitude regions. This study evaluates the capability of ensemble machine learning (ML) models to estimate the onset date of the spring water-level rise in Arctic–subarctic rivers of the Anadyr–Kolyma basin district in northeastern Russia using a station-year dataset for the period 2008–2022, combining hydrological observations with meteorological and basin-related predictors. Five regression algorithms were tested using grouped cross-validation by year. CatBoost achieved the highest predictive accuracy with an out-of-fold mean absolute error of 4.54 days, RMSE of 9.79 days, and , slightly outperforming ExtraTrees (MAE 4.66 days) and RandomForest (MAE 4.70 days). Spatial analysis shows that most gauging stations exhibit prediction errors within 0.5–3 days, whereas errors exceeding 10 days occur mainly in small or topographically complex basins with limited observational coverage. Model interpretation using SHapley Additive exPlanations (SHAP) and partial dependence (PDP) analysis indicates that predictors describing thermal forcing during late winter and early spring dominate the model response, with positive degree days during March–April, the first thaw day, and indicators of rapid water-level rise providing the largest contributions. The onset of spring water-level rise in the studied Arctic–subarctic river systems is primarily associated with the interaction between temperature-driven snowmelt processes and the early hydrological response of the river network, whereas precipitation and spatial descriptors exhibit comparatively smaller contributions. These statistical relationships are conditioned on the 2008–2022 period and may vary under different climatic conditions or longer observational records, which should be considered when applying the model for prediction.

Introduction

The timing of spring flood initiation represents one of the key hydrological characteristics of river systems in cold and high-latitude regions ¹. In basins dominated by seasonal snow accumulation, the transition from winter low-flow conditions to the rising limb of the spring water level hydrograph. ^2,3. This transition is influenced by a combination of atmospheric forcing, snowpack dynamics, river ice conditions, and basin-scale hydrological responses. Variations in the timing of spring runoff affect river navigation⁴, water resource management, ecosystem processes, and flood risk, with strong relevance for northern regions where snowmelt-driven floods represent the dominant hydrological event of the year. Recent analysis of spring freshet generation in snow-dominated catchments has further shown that the timing and magnitude of spring flood response, typically analyzed in terms of discharge, depend on the combined effects of snow accumulation, snowmelt dynamics, antecedent basin conditions, and rainfall inputs⁵.

In many northern river systems the spring flood is closely linked to the evolution of river ice and the rapid release of snowmelt runoff during the late winter–spring transition ^6,7. Air temperature controls the onset of snowmelt through the accumulation of positive degree days, while precipitation and snow water equivalent influence the magnitude and rate of runoff generation ^8,9. At the same time, river ice breakup alters channel hydraulics and can modify the propagation of meltwater through the river network. The combined influence of these processes often leads to rapid and spatially coherent increases in water level during the early stages of the spring flood ¹⁰. For large northern rivers, the forecasting of spring high water is additionally complicated by ice-jam formation, backwater effects, and spatial heterogeneity of melt conditions across the basin^11,12.

Predicting the timing of spring flood initiation remains challenging because it depends on multiple interacting processes that vary across spatial scales and hydrological regimes ¹³. Physically based hydrological models such as the Snowmelt Runoff Model (SRM) ^14,15, the Hydrologiska Byråns Vattenbalansavdelning model (HBV) ^16,17, the Soil and Water Assessment Tool (SWAT) ^18,19, and the Variable Infiltration Capacity model (VIC) ^20,21 have been widely used to simulate snowmelt and runoff generation in cold regions. These approaches represent key processes such as snow accumulation and melt, soil moisture dynamics, and runoff routing, but they require detailed, spatially explicit information on basin characteristics, cryospheric state, and meteorological forcing, including channel geometry, snowpack properties, distributed precipitation fields, and parameter calibration against discharge observations. In large or remote northern basins such information is often sparse, uncertain, or not consistently available.

At the same time, it is important to note that a substantial body of Russian and Soviet hydrological research has historically relied on high-quality in situ observations and empirical relationships to describe and predict river ice and spring flood processes, often without the use of complex numerical models. Even where physically based models are successful, their application may be limited by data availability, parameter uncertainty, and the difficulty of representing nonstationary climate and land-surface conditions ²². For example, recent modelling of runoff in northern China has shown that changes in temperature, precipitation, and permafrost-related processes can substantially modify seasonal runoff structure and spring melt behaviour²³.

Data-driven approaches provide a complementary alternative by relying on aggregated and observationally available predictors (e.g., station-level water levels, temperature, and precipitation summaries), without requiring explicit specification of channel geometry, spatially distributed snowpack properties, or calibrated process parameters. While such approaches also depend on data availability, they relax the need for detailed spatial parameterization and can be applied more consistently across heterogeneous basins. This makes them suitable for identifying empirical relationships in regions where process-level information is incomplete and observational data are unevenly distributed.

Machine learning (ML) methods have been applied to hydrological prediction problems, including snow cover reconstruction, runoff simulation, river flow forecasting, flood prediction, and hazard assessment^24–27. Ensemble learning algorithms are widely used in such settings due to their ability to model nonlinear relationships and interactions among meteorological, hydrological, and spatial predictors, as well as their robustness on structured tabular data. In snow-related applications, gradient boosting methods have been shown to reproduce both snow accumulation and melt periods with stable performance²⁴.

In this study, CatBoost ²⁸ is selected as a representative gradient boosting method because it is specifically designed for heterogeneous tabular datasets and provides stable performance under relatively small sample sizes and mixed feature types. In particular, CatBoost incorporates ordered boosting and built-in regularization mechanisms that reduce overfitting and improve generalization in the presence of correlated predictors and uneven data distribution across stations. These properties are relevant for the station-year dataset considered here, which combines hydrological, climatic, and derived features with varying temporal coverage.

In river forecasting studies, ML models have been used for spring flood prediction ^29,30 in northern Russia²⁶, daily flow forecasting in snowmelt-affected basins²⁷, and hybrid flood prediction systems combining ML with physically based snowmelt-runoff modelling¹¹. Deep learning approaches have also been applied to runoff simulation in mountain basins where snow cover and elevation-dependent climatic forcing play a substantial role²⁵. However, such approaches typically require larger training datasets and more complex model tuning, which may limit their applicability in data-sparse northern regions.

At the same time, recent hydrological studies rely not only on predictive performance but also on model interpretability. Methods such as SHapley Additive exPlanations (SHAP) and partial dependence analysis make it possible to quantify the contribution of individual predictors and to examine nonlinear predictor–response relationships. Such approaches have already been used to identify dominant environmental controls in interpretable ML studies of hydrological and environmental systems^31,32. For spring flood and snowmelt applications, interpretable analysis is especially relevant because the modeled response is governed by coupled thermal, cryospheric, and hydrological processes rather than by a single forcing factor.

However, the application of ML methods specifically to the prediction of spring flood onset in Arctic–subarctic river systems remains limited. Many existing studies focus on runoff magnitude, daily discharge, or peak flow forecasting rather than on the timing of the initial water-level rise^33,34, which represents an earlier phase of the hydrological response and is directly linked to the onset of snowmelt-driven channel activation. This distinction is hydrologically relevant because the first sustained rise in water level marks the transition from winter conditions to active spring runoff^35,36 and may provide useful information for operational forecasting, flood preparedness, and analysis of climate-related changes in seasonal flow regimes.

The present study investigates the use of ML models to predict the onset date of the spring water-level rise in snowmelt-dominated rivers of the Anadyr–Kolyma basin district in northeastern Russia. This region includes Arctic and subarctic river systems characterized by strong seasonal snow accumulation, prolonged ice cover, and marked spatial heterogeneity of basin conditions. A station-year dataset combining hydrological observations with meteorological and basin-related predictors is used to train and evaluate several regression algorithms. The objectives of the study are threefold: (i) to compare the predictive performance of a suite of ML models, including ensemble-based methods, for estimating the timing of the spring water-level rise; (ii) to analyse the spatial distribution of prediction errors across river basins; and (iii) to interpret the contribution of individual predictors using SHAP and partial dependence analysis in order to identify the dominant controls on flood initiation.

Materials and methods

Physical–geographical and climatic characteristics of the study region

The study region occupies the northeastern part of Russia within approximately – N and – E. The territory includes Chukotka Autonomous Okrug ^37,38, the Kamchatka Peninsula ^39,40, Magadan Oblast ^41,42, and the northeastern part of the Republic of Sakha (Yakutia) ^43,44. The region extends from the Arctic coast of the East Siberian Sea to the Pacific margins of the Bering Sea and the Sea of Okhotsk. River systems drain toward both the Arctic Ocean and the North Pacific. A total of 124 hydrological stations were considered in this study.

The hydrological stations considered in this study are located within the Anadyr–Kolyma basin district ^45–47, one of the twenty officially defined basin districts of the Russian Federation established under Article 28 of the Water Code of the Russian Federation. This basin district corresponds to hydrological unit code 19 and covers river systems draining into the East Siberian Sea, the Chukchi Sea, the Bering Sea, the Sea of Okhotsk, and the Pacific Ocean in northeastern Russia.

The district includes several major river basins such as the Kolyma ^48,49, Anadyr ^50,51, Kamchatka ^52,53, and Penzhina ⁵⁴ rivers, together with numerous medium and small rivers of Chukotka and the Kamchatka Peninsula. These river systems represent a range of Arctic and subarctic hydrological regimes ⁵⁵ characterized by strong seasonality of runoff, prolonged winter ice cover, and a dominant contribution of snowmelt to annual discharge.

Relief, permafrost, and river network structure

Mountain systems dominate the regional relief. Major orographic units include the Chersky Range, the Verkhoyansk–Kolyma highlands, and the volcanic ranges of the Kamchatka Peninsula. Elevations frequently exceed 1000–2000 m. River valleys are narrow and deeply incised within mountainous terrain, while coastal zones and intermountain depressions contain wider floodplains. The spatial distribution of the river network and hydrological observation stations within the study region is shown in Fig. 1. The map illustrates the main river systems draining toward the East Siberian Sea, the Sea of Okhotsk, and the Bering Sea, together with the locations of long-term hydrological monitoring sites used in this study. The analysis is performed at the river basin level, whereas the longitude bounds are used solely for map visualization.

Fig. 1.

Study region in northeastern Russia (52–70N, 145–180E) including Chukotka, Magadan Oblast, the Kamchatka Peninsula, and northeastern Yakutia. Blue lines represent the river network, and black circles indicate hydrological observation stations used for runoff analysis. (created using ArcGis 9.3.1).

Permafrost occurs across most of northeastern Siberia in continuous and discontinuous forms. Frozen ground restricts infiltration and promotes surface and shallow subsurface runoff. Groundwater discharge during winter produces extensive icing fields (aufeis) in many valleys. These ice bodies form through successive freezing of groundwater emerging at the surface during the cold season. Individual icing fields may reach several square kilometres in area and persist until early summer.

Aufeis formation modifies channel morphology and drainage structure. Groundwater-fed ice accumulation forces water to redistribute across valley floors, generating multiple shallow channels and reticular drainage patterns. In several mountain regions of northeastern Siberia, the additional channel length associated with icing systems reaches tens of kilometres⁵⁶. These processes occur frequently in the Verkhoyansk–Kolyma mountain system and in parts of Chukotka.

Climate and hydrological regime

The climate of northeastern Russia within the domain 52– N and 145– E corresponds to subarctic and arctic continental regimes with maritime influence along the Pacific sector. Thermal conditions are controlled by strong seasonal contrasts in solar radiation and by the interaction between continental air masses and the adjacent North Pacific circulation.

Winter conditions are severe across inland regions of northeastern Siberia. Mean January air temperatures over continental sectors of Yakutia and the interior parts of the Magadan region typically range from approximately C to C. In contrast, coastal areas of Kamchatka and the Sea of Okhotsk experience milder winter conditions due to maritime moderation, where January temperatures frequently remain between C and C. Summer conditions remain relatively cool across the entire region. Mean July temperatures generally vary from about C in northern coastal areas to 12–C in southern continental valleys.

The seasonal structure of temperature and precipitation over a 15 year climatology (2008–2022) is illustrated in Fig. 2. Monthly climatological curves are shown separately for continental and ocean-influenced grid cells. The curves also highlight two individual years, 2008 and 2022, relative to the range of interannual variability.

Fig. 2.

Seasonal evolution of near-surface climate conditions averaged over continental and ocean-influenced grid cells within the study region. (a) Monthly air temperature at 2 m showing strong continental cooling in winter and moderate summer warming. Winter temperatures over continental sectors frequently drop below C, while maritime sectors remain substantially warmer. (b) Monthly precipitation totals illustrating the seasonal maximum during summer and early autumn, particularly over maritime sectors influenced by Pacific moisture transport. Shaded envelopes represent the interannual variability range across the full period 2008–2022, while highlighted curves correspond to the individual years 2008 and 2022.

Annual precipitation varies substantially across the region due to the strong influence of topography and oceanic moisture transport. Mountain systems of Kamchatka and the coastal ranges surrounding the Sea of Okhotsk ⁵⁷ receive approximately 800–1200 mm of precipitation annually. In contrast, interior continental regions of northeastern Siberia typically receive only about 200–400 mm per year. A large fraction of precipitation occurs as snowfall during the cold season and forms a seasonal snowpack that persists throughout winter and early spring.

The spatial structure of the main climatic variables is illustrated in Fig. 3. The figure shows air temperature at 2 m, total precipitation, near-surface wind speed and direction, and surface pressure for representative winter and summer months in three different years.

Fig. 3.

Spatial distribution of key climatic variables across northeastern Russia derived from NASA POWER reanalysis data. Panels show winter and summer conditions for three representative years: (a) January 2008, (b) August 2008, (c) January 2016, (d) August 2016, (e) January 2022, and (f) August 2022. Each panel includes air temperature at 2 m, precipitation, 10 m wind speed and direction, and surface pressure. Maps were generated by the authors using Python 3.11.

The hydrological regime of rivers in the region reflects the strong seasonal climate forcing and the widespread presence of permafrost. Most basins exhibit a predominantly nival runoff regime. Snow accumulation during winter is followed by rapid melt during late spring and early summer, producing the annual flood peak in May–June for southern basins and in June–July for northern catchments.

During winter, river discharge remains minimal because of extensive river ice cover and reduced groundwater exchange in frozen soils. Ice formation typically begins in October or November and persists until late spring. Break-up of river ice coincides with the onset of snowmelt floods and often contributes to short-term increases in water levels due to ice jams ²².

Hydrological observations from the Northern Okhotsk Sea region indicate detectable long-term changes in river runoff characteristics. Mean annual runoff has increased in several basins during recent decades, with reported increases ranging from approximately 5–37%. These changes correspond with increased precipitation and with the degradation of ground ice in permafrost deposits^58,59. River water temperatures also show positive trends during the late twentieth and early twenty-first centuries. Observations from more than two hundred hydrological stations indicate anomalies of up to C relative to earlier observation periods⁶⁰.

Volcanic landscapes of Kamchatka ⁶¹ and the northern Okhotsk Sea region strongly influence river morphology, sediment transport, and channel dynamics. Volcanic edifices supply large volumes of unconsolidated pyroclastic material and weathered volcanic rocks to surrounding drainage basins. These materials are mobilized during snowmelt floods and intense rainfall events, producing high suspended sediment concentrations and widespread braided channel patterns.

Representative landscapes of river systems in volcanic terrains of northeastern Russia are shown in Fig. 4. The images illustrate the interaction between volcanic relief, large sediment supply, and fluvial channel morphology.

Fig. 4.

Examples of river systems in volcanic and mountainous landscapes of northeastern Russia. (a) Typical Kamchatka peninsula volcanic landscape. (b) Braided tributary of the Kamchatka River with gravel bars and multiple shallow channels formed under conditions of high sediment supply. (c) The main channel of the Kamchatka River within the Central Kamchatka depression, characterized by a wide valley and relatively low channel slope; flow direction is from south to north. (d) The Arman River with the Khasyn tributary in the northern Okhotsk Sea basin. Mountain catchments of the Okhotsk region generate large sediment fluxes and form wide braided channels that deliver suspended and bedload material to coastal marine environments.

Representative examples of long-term water-level variability along the Kolyma River are shown in Fig. 5. The panels illustrate multi-year hydrographs from several gauging stations distributed along the main river channel and demonstrate the typical seasonal dynamics associated with the spring flood period. The data represent daily water levels based on available observations for the period 2008–2022.

Fig. 5.

Interannual variability of water level at hydrological posts along the Kolyma River. Each panel shows the envelope of observed water levels across years with curves from the first and last observation periods.

Data aggregation and predictive modeling

Data sources and integration

The workflow combines three primary data sources at the gauging-station level obtained from the hydrological observation network operated by the Federal Agency for Water Resources of the Russian Federation (Rosvodresursy) ⁶². The first source is a station metadata table containing station identifiers, river names, drainage area, distances along the river network, gauge zero level, vertical datum information, and geographic coordinates. The second source consists of annual hydrological reports provided in spreadsheet format, from which daily water-level observations and qualitative annotations describing river conditions (e.g., ice cover, ice breakup, and open-water periods) are extracted. The third source comprises daily climate datasets obtained from the NASA POWER (Prediction Of Worldwide Energy Resources) database ⁶³, providing near-surface meteorological variables at a spatial resolution of approximately latitude–longitude grid (about 50 km at the equator) for the period 2008–2022, used to characterize atmospheric forcing during the snowmelt and spring flood formation periods (Fig. 6).

Fig. 6.

Workflow of data integration, feature construction, and ML modeling used to predict the onset of the spring water-level rise.

Let i denote a gauging station, t the year, and d the day of year. After parsing, the daily hydrological record is represented as

where is the observed water level and is the raw state annotation. The daily climate record is represented as

where T is air temperature, P is precipitation, and R is shortwave radiation, with additional meteorological variables retained when available. Station metadata are denoted by

where and are latitude and longitude, is drainage area, is distance from source, is distance to mouth, is gauge zero, and is a river identifier.

All datasets are linked by a normalized station code. Geographic coordinates from the climate headers are used only to fill missing coordinates in the metadata table. The merged daily dataset is therefore defined as

Parsing of hydrological state codes

The hydrological reports contain symbolic river-state annotations. These annotations are tokenized and mapped to a set of binary indicators describing stable ice conditions, breakup conditions, ice-jam occurrence, complete freezing, and channel drying. For a given raw annotation , the parser produces

where each component is binary. Stable ice is assigned when the token list contains any symbol from the predefined stable-ice set or when the river is marked as frozen. Breakup and jam conditions are defined analogously from dedicated symbol sets. Several non-informative marks are ignored during tokenization.

This transformation converts heterogeneous textual field notes into categorical variables suitable for subsequent aggregation and modeling.

Completion of daily hydrographs

Daily hydrological records are completed separately for each station-year pair. For each (i,t), a full calendar sequence

d = 1,2,… ,365

is created. Missing days in the water-level series are filled by interpolation followed by forward and backward propagation:

where denotes linear interpolation with boundary filling. Missing state variables are replaced with neutral values, i.e. empty strings for textual fields and zeros for binary flags. This step yields a complete station-year hydrograph on a uniform daily grid.

In practice, missing data are concentrated in the cold-season periods, typically before the onset of spring melt (January–April) and after freeze-up (November–December), when hydrometric observations are often unavailable or incomplete due to ice cover, reduced accessibility, and potential damage to measurement equipment during freeze-up and breakup events. The proportion of infilled values varies across stations and years, but is generally highest during these periods and minimal during the open-water season.

Derived hydrological and climatic features

Feature construction is performed at the station-year level. For each (i,t), the water-level series is smoothed by a centered rolling mean with window size w=5:

where is the local 5-day window centered at day d, truncated at the boundaries. The choice of a 5-day window is not based on a formal standard, but is adopted as a pragmatic smoothing parameter to reduce high-frequency variability while preserving the timing of the spring water-level rise; alternative window sizes were not iteratively optimized and are left for future sensitivity analysis. The use of daily water-level data is motivated by the need to resolve the timing of onset events, which occur at sub-monthly scales, whereas climate variables are aggregated to monthly summaries to represent broader seasonal forcing and to reduce noise in the predictor set.

The winter baseline level is estimated from the first 90 days of the year:

The corresponding winter variability is

Short-term and medium-term water-level rises are then defined as

and the corresponding annual maxima are retained:

The annual amplitude relative to the winter baseline is

with a lower bound of 1.0 imposed in the implementation to avoid degenerate thresholds.

Monthly climate summaries are computed for March, April, and May. These include mean air temperature in March and April, cumulative precipitation in April and May, positive degree days during March–April,

and cumulative shortwave radiation during March–April,

The first thaw day is defined as the first day of a sequence of at least k=3 consecutive days with positive air temperature:

This definition is used as a simple and robust indicator of sustained thaw conditions; alternative thresholds (e.g., sub-zero criteria) have been proposed in the literature and are noted as a potential direction for future sensitivity analysis.

The state-code variables are aggregated into annual descriptors, including the last day with stable ice, the first day with breakup, the total number of stable-ice days, the total number of transition days, and an annual ice-jam flag:

Definition of the target variable

The prediction target is the onset day of the spring water-level rise, denoted by

Its extraction combines hydrograph morphology and river-state annotations.

The hydrometric dataset used in this study consists of daily mean water-level observations; higher temporal resolution data (e.g., hourly or sub-daily records) are not available for the majority of stations. As a result, short-term fluctuations and rapid water-level increases associated with ice-jam events may be smoothed in the daily series, and the detected onset should be interpreted as a daily-scale approximation of the underlying process.

First, the search is restricted to the interval

d ∈ [90, 220].

Within this interval, a candidate onset day is identified from the smoothed hydrograph. Let

be the first difference, and let denote its 5-day rolling mean. A day d is considered a hydrological onset candidate if three conditions are satisfied:

and

where α =0.15, β =0.02, and γ =1.0. The first condition requires the level to exceed a fraction of the annual amplitude above the winter baseline. The second requires sustained positive slope, and the third requires net growth over the following 5 days.

Independently, the first breakup day

is extracted from the parsed state sequence.

The final target is determined by combining both sources. If only one of the two candidates exists, that value is used. If both exist, the target is defined as

where is the first hydrological onset candidate. This rule prevents the target from being placed substantially earlier than the first observed breakup signal while preserving the hydrograph-based rise detection.

For reference, the annual peak day and annual peak water level are also recorded:

Station-year learning table

After aggregation, each station-year sample is represented by a feature vector

where contains the climatic summaries, contains the hydrograph descriptors, and contains the ice-state features. The corresponding response variable is .

Rows with undefined target values are excluded from modeling. The final table is sorted by station and year and exported in spreadsheet, CSV, and parquet formats.

Regression model

The onset day is predicted using gradient boosting on decision trees implemented through CatBoost regression ²⁸. The selected predictor set includes station descriptors, climate summaries, hydrograph-based metrics, and ice-regime variables. Formally, the model estimates a nonlinear mapping

where f(· ) is learned from the station-year dataset. The river identifier is retained as a categorical predictor, whereas all remaining predictors are treated as numerical variables.

Missing numerical values are imputed within each training fold by the median of the corresponding training subset:

Missing river identifiers are assigned the category unknown.

The CatBoost regressor is trained with 500 boosting iterations, tree depth 6, learning rate 0.05, and the mean absolute error as both loss and evaluation metric. This configuration is consistent with the objective of predicting onset timing in units of days.

Grouped cross-validation by year

To reduce temporal leakage, model evaluation is performed with grouped cross-validation in which the grouping variable is the calendar year, where temporal leakage refers to the unintended use of information from future time periods (e.g., the same year) during model training, leading to overly optimistic performance estimates. Let be the set of unique years. The dataset is partitioned by GroupKFold ⁶⁴ so that all station-year observations belonging to the same year are placed entirely in either the training or the test subset for a given fold. If the number of unique years is , the number of folds is

For fold k, the model is trained on the union of years assigned to the training subset and tested on the held-out years. This yields out-of-fold predictions for all valid samples.

Evaluation metrics

Predictive performance is summarized using mean absolute error ⁶⁵, root mean squared error ⁶⁶, and the coefficient of determination ⁶⁷:

These metrics are first computed separately for each fold, where each fold corresponds to a held-out calendar year, and then for the combined out-of-fold predictions over the entire dataset. In addition, the absolute error for each station-year observation is stored:

The grouped evaluation design makes the reported accuracy reflect the ability to generalize across years rather than merely across stations within the same hydrological season.

Implementation output

The pipeline produces five levels of output: station metadata, raw daily hydrological observations, completed daily hydrological series, daily climate records, and the merged station-year machine-learning table. The modeling stage further exports fold-wise cross-validation metrics (i.e., performance computed for each held-out year) and out-of-fold predictions (i.e., predictions generated for observations not used during model training) for each station-year sample. This structure preserves traceability from the final prediction target back to the original daily records and intermediate derived variables.

Results

Comparison of regression models

The predictive performance of five regression models was evaluated using grouped cross-validation by year. Figure 7 summarizes the out-of-fold results in terms of mean absolute error, root mean squared error, and coefficient of determination.

Fig. 7.

Comparison of regression models for predicting the onset day of spring water-level rise.

Among the tested methods, CatBoost achieved the best overall performance with an out-of-fold MAE of 4.54 days, RMSE of 9.79 days, and . ExtraTrees ⁶⁸ ranked second with MAE of 4.66 days and RMSE of 10.00 days, followed by RandomForest ⁶⁹ with MAE of 4.70 days and RMSE of 10.17 days. XGBoost produced comparable results, with slightly higher MAE than the tree-ensemble baselines, whereas LightGBM showed the lowest predictive accuracy among the evaluated models.

The fold-wise results indicate that CatBoost remained competitive across all validation splits and yielded the best aggregate trade-off between absolute error, squared error, and explained variance. Its advantage over the other models was moderate rather than large, which suggests that the predictive structure of the station-year dataset is captured reasonably well by several ensemble methods. Nevertheless, CatBoost provided the most accurate and most stable out-of-fold estimates overall and was therefore selected as the main model for subsequent analysis.

The relative differences between models were smaller for MAE than for , indicating that the main distinction between methods was not only the typical absolute deviation in days, but also the ability to reproduce interannual variability in the onset date. It should be noted that values are generally moderate in this setting and are not the primary evaluation metric, as the prediction task focuses on timing errors expressed in days; therefore, MAE provides a more direct and interpretable measure of performance. In this context, CatBoost and ExtraTrees preserved more variance of the target variable than the remaining approaches. LightGBM yielded the weakest results in all three metrics, which may reflect lower robustness of the selected configuration for the present feature set and sample structure.

Spatial distribution of prediction errors

The spatial distribution of prediction errors for the predicted onset of the spring water-level rise is shown in Fig. 8. Panel (a) presents the station-level mean absolute error (MAE) mapped at the geographic locations of hydrological gauges, while panel (b) summarizes error statistics aggregated at the river level.

Fig. 8.

Spatial distribution of prediction errors for the estimated onset of the spring water-level rise. (a) Station-level mean absolute error (MAE) mapped at hydrological gauge locations. (b) River-level aggregation of prediction errors represented as a treemap, where the area of each block is proportional to the product of MAE and łog (1+n), with n denoting the number of station-year observations available for the corresponding river basin. Color intensity indicates the magnitude of MAE in days. (Map was generated by the authors using Python 3.11.).

At the station scale, the majority of gauges exhibit relatively low prediction errors, typically within the range of 0.5–3 days. These stations are distributed across the study region and include both coastal and inland catchments. As visible in Fig. 8a, many stations located along the central and eastern parts of the region show MAE values close to one day, indicating that the model captures the timing of the initial flood rise with high temporal accuracy. This level of performance is consistent with the characteristic hydrological response of snowmelt-driven rivers, where the transition from winter low flow to the spring rising limb is often associated with a relatively rapid and coherent hydrometeorological signal.

Higher prediction errors are observed at several stations located in the western mountainous part of the region and in a few isolated northern basins. In these locations the MAE reaches values between approximately 7 and 16 days (Fig. 8a). Such discrepancies can be associated with local hydrological and geomorphological conditions, including complex snow accumulation patterns, delayed melt due to elevation gradients, or the influence of river ice processes that modify the relationship between meteorological forcing and observed water level dynamics. In addition, some stations correspond to short observational records or isolated gauges with limited training data, which can increase model uncertainty.

The aggregation of errors at the river scale (Fig. 8b) reveals systematic differences among catchments. Large river systems with numerous stations, such as the Kolyma basin, show relatively low average errors (approximately 3 days) despite a large number of observations. This suggests that the model generalizes well for major river systems with consistent hydrological regimes and sufficient training samples. Similarly, several medium-sized basins (e.g., Bokhapcha, Ola, and Kulu) exhibit mean errors in the range of 3–4 days. Here, the distinction between large and medium river systems is based on relative basin representation in the dataset, primarily reflected by the number of associated stations and station-year observations, rather than on an explicit classification by drainage area.

In contrast, the largest errors are observed for small rivers represented by only a few stations or short observational series. Examples include Mukhtuya and Kontaktovy rivers, where MAE exceeds 9–15 days. The treemap representation in Fig. 8b highlights this pattern by scaling the area of each river block proportionally to the product of MAE and the logarithm of the number of observations, thereby emphasizing both prediction difficulty and data availability. This pattern reflects the reduced statistical support available for model training in sparsely observed basins and should be interpreted as a data limitation rather than a model-specific deficiency. The period 2008–2022 represents the complete available time series for the majority of stations used in this study.

The spatial analysis indicates that prediction accuracy is strongly influenced by hydrological similarity and data density. River systems with extensive observational coverage and relatively homogeneous snowmelt-driven regimes tend to exhibit stable and low prediction errors, whereas smaller or hydrologically complex basins ⁷⁰ show larger variability in prediction performance. These results suggest that the proposed modeling framework effectively captures large-scale hydrometeorological controls on spring flood initiation while remaining sensitive to local hydrological processes and data limitations.

Model interpretation using SHAP

To interpret the contribution of individual predictors to the model output, SHapley Additive exPlanations (SHAP) ^71–73 were applied to the trained CatBoost model. SHAP values provide a unified framework for explaining ML predictions by quantifying the contribution of each feature to the final model output for every observation. The method is based on cooperative game theory and evaluates how much each predictor changes the prediction relative to the average model response.

For a given observation, a positive SHAP value indicates that the feature shifts the prediction toward later dates of the hydrological event, while negative values shift the prediction toward earlier occurrence. The magnitude of the SHAP value reflects the strength of the contribution.

Figure 9 summarizes the global and local interpretation of the model.

Fig. 9.

SHAP analysis of the CatBoost model predicting the timing of the hydrological event. (a) SHAP beeswarm plot showing the distribution of SHAP values for all predictors and observations. (b) Global feature importance based on mean absolute SHAP values. (c–j) SHAP dependence plots illustrating the relationship between selected predictors and their contribution to the model output. The most influential predictors describe thermal conditions during late winter and early spring (first rise candidate day, positive degree days, first thaw day) together with indicators of rapid water level rise and winter hydrological variability.

The SHAP beeswarm diagram (Fig. 9a) shows the distribution of SHAP values for all observations and predictors. Each point corresponds to a single observation. Color indicates the value of the feature, where blue represents low values and red represents high values. The horizontal position of the point shows the contribution of the feature to the model output. Predictors are ordered by their importance, measured as the mean absolute SHAP value.

The bar chart (Fig. 9b) shows the global importance ranking of the predictors. Features with larger mean absolute SHAP values have a stronger overall influence on the predicted timing of the hydrological event.

The dependence plots (Fig. 9c–j) illustrate how the SHAP value of a feature varies with the feature value itself. These plots reveal nonlinear relationships between predictors and model output and help identify threshold behaviour.

The most influential predictors include the first rise candidate day, positive degree days during March–April, and the first thaw day. These variables reflect the thermal conditions during the transition from winter to spring and control the onset of snowmelt processes in the river basin. Earlier thawing and higher accumulated positive temperatures shift the predicted event toward earlier dates.

Hydrological variables describing short-term water level dynamics also contribute to the model predictions. The maximum water level rise over 7 and 14 day intervals indicates rapid snowmelt runoff and channel response during the spring flood. Increased variability of winter water levels is associated with unstable ice conditions and possible ice movement prior to the breakup period.

Precipitation during April and May has a secondary influence on the prediction. Higher precipitation totals contribute to increased snowpack water equivalent and enhanced runoff generation during the melt period. It should be noted that the NASA POWER dataset used in this study does not explicitly distinguish between snowfall and rainfall, and precipitation is treated as a combined variable, which may introduce additional uncertainty in interpreting its role during the transition season.

Spatial variables such as river longitude, latitude, and distance along the river network have comparatively smaller contributions. These predictors primarily reflect regional differences in climate and basin characteristics rather than direct hydrological controls ⁶.

SHAP analysis demonstrates that the model predictions are primarily controlled by variables describing thermal forcing during the late winter and early spring period, together with indicators of rapid water level rise associated with snowmelt-driven runoff.

Partial dependence analysis of predictors controlling flood peak onset

To investigate how individual predictors influence the modeled timing of the spring flood peak, partial dependence plots (PDPs) ⁷⁴ were calculated for the most influential variables identified by the CatBoost model (Fig. 10). These plots represent the marginal effect of each predictor on the predicted onset date of the spring flood peak (day of year, DOY) while averaging over the distribution of the remaining variables in the dataset.

Fig. 10.

Partial dependence plots showing the influence of key hydrometeorological and ice-regime predictors on the modeled timing of the spring flood peak (day of year, DOY). Each panel represents the marginal response of the CatBoost model to variation of a single predictor while averaging over the remaining variables. The predictors include (a) baseline winter water level, (b) first river-ice breakup day, (c) first candidate day of rapid water-level rise, (d) first thaw day, (e) positive degree days accumulated during March–April, (f) total precipitation in April, (g) maximum 14-day increase in water level, and (h) mean air temperature in April. The relationships highlight the combined influence of antecedent hydrological conditions, thermal forcing, and spring precipitation on the timing of peak flow onset.

Hydrological state variables exhibit a clear influence on the predicted flood timing. The baseline winter water level (Fig. 10c) shows a nonlinear relationship with the predicted onset date, suggesting that higher antecedent water levels are in some cases associated with earlier spring flood initiation. This relationship should be interpreted with caution, as it may reflect multiple competing mechanisms, including winter storage conditions, ice cover characteristics, and channel hydraulic state. In particular, higher freeze-up water levels may also correspond to increased channel conveyance capacity during breakup, potentially moderating the response in some systems. These results therefore indicate a statistical association rather than a single deterministic physical mechanism.

Ice regime indicators ⁷⁵ demonstrate a strong control on flood timing. The first breakup day of river ice (Fig. 10d) and the first candidate day of rapid water level rise (Fig. 10e) both exhibit steep responses in the predicted DOY range. These variables represent key transition points in the seasonal evolution of river ice processes. Earlier ice breakup and earlier hydrological response are consistently associated with earlier flood peak onset, highlighting the importance of ice-controlled hydraulic conditions in high-latitude river systems.

Thermal forcing variables are reflected in the model response. The first thaw day (Fig. 10f) and the accumulated positive degree days during March–April (Fig. 10g) show systematic relationships with the modeled flood timing. Increasing positive degree days correspond to earlier predicted flood onset, reflecting the influence of air temperature on snowmelt intensity and the timing of snowpack depletion in cold-region basins. While cumulative shortwave radiation is also included as a predictor, temperature-based metrics show a more stable relationship with onset timing. This may be related to the fact that air temperature integrates multiple energy flux components, whereas radiation is aggregated at a monthly scale and may smooth rapid seasonal transitions.

Precipitation and short-term hydrological response indicators contribute additional variability to the predicted flood timing. Total precipitation in April (Fig. 10h) shows a tendency toward earlier peak onset under higher precipitation amounts, which may reflect rainfall contributions during the snowmelt period, particularly in maritime-influenced areas such as the Kamchatka Peninsula and coastal basins, where rain-on-snow events are more likely than in continental interiors. Similarly, the maximum 14-day water level rise (Fig. 10i) represents the intensity of hydrological response during early melt conditions and is associated with accelerated flood development.

Mean air temperature in April (Fig. 10j) exhibits a clear monotonic influence on predicted flood onset. Warmer spring temperatures correspond to earlier predicted peak timing, consistent with the thermally driven acceleration of snowmelt processes. Together, these relationships demonstrate that the timing of spring flood peaks in the study region is controlled by a combination of antecedent hydrological state, river ice dynamics, and spring thermal forcing.

Discussion

The results indicate that ensemble ML approaches can reproduce the timing of the initial spring water-level rise with relatively low prediction error, on the order of a few days (mean absolute error approximately 4.5–4.7 days and RMSE below 10 days), when hydrometeorological and hydrological predictors are combined. Among the evaluated models, CatBoost yielded the lowest mean absolute error and root mean squared error under grouped cross-validation by year. The differences between CatBoost, ExtraTrees, RandomForest, and XGBoost were moderate, suggesting that the predictive structure of the station-year dataset can be captured by several tree-based ensemble algorithms. The slightly higher coefficient of determination obtained by CatBoost indicates a stronger ability to represent interannual variability in the timing of flood initiation.

The spatial distribution of prediction errors reflects differences in hydrological regime and observational coverage across river basins. Rivers represented by a larger number of station-year observations tend to exhibit lower prediction errors, which is consistent with the greater availability of training samples for these systems. Major river basins with relatively homogeneous snowmelt-driven regimes show mean errors of only a few days. Larger deviations occur mainly in smaller basins or in regions with complex topographic conditions. In mountainous areas, snow accumulation and melt processes may vary substantially with elevation and local microclimate, which can reduce the representativeness of basin-scale predictors derived from station-level observations ⁷⁶.

Model interpretation based on SHAP analysis and partial dependence plots indicates that predictors associated with thermal forcing during the late winter and early spring period explain a substantial fraction ⁷⁷ of the model output. Positive degree days accumulated during March–April and the first thaw day are among the highest-ranked predictors, which reflects the role of air temperature in controlling the transition from frozen to melt conditions in snow-dominated catchments. Earlier thawing and higher accumulated positive temperatures correspond to earlier predicted onset of the spring water-level rise. This behaviour is consistent with the established mechanism of snowmelt-driven runoff generation in high-latitude river systems.

Variables related to river ice dynamics also contribute strongly to the model predictions. The first breakup day and the first candidate day of rapid water-level rise represent hydrological transition points associated with the weakening and movement of river ice. Changes in ice cover influence hydraulic resistance and channel conveyance, which in turn affects the timing of water-level response to snowmelt runoff ⁷⁸. The presence of these variables among the most influential predictors indicates that river ice processes play a measurable role in determining the onset of spring water-level rise in the study region.

Hydrological indicators describing short-term water level dynamics provide additional explanatory information. The maximum increase in water level over short time windows reflects the early response of the channel network to meltwater inputs and basin storage release. These variables capture the transition from winter low-flow conditions to the rising limb of the spring hydrograph. Precipitation during the melt period exhibits a secondary influence, suggesting that rainfall contributions during spring can modify runoff generation but do not represent the dominant control on the timing of the initial flood rise.

Several limitations of the present analysis should be considered. The observational dataset contains an uneven spatial distribution of gauges and record lengths, with some river systems represented by dense monitoring networks and others by only a few stations. The period of investigation (2008–2022) provides up to 15 years of observations per station, although the effective record length varies due to data gaps and station availability. This heterogeneity affects the balance of training samples across basins and may influence model generalization. Missing daily water-level values were infilled using interpolation-based procedures, which introduces additional uncertainty, particularly during ice-affected periods.

In addition, several processes that influence spring flood dynamics are not explicitly represented among the predictors. Examples include spatial variability of snow water equivalent, detailed basin topography affecting melt timing, river orientation, and physical properties of river ice such as thickness, mechanical stability, and the distinction between thermal and mechanical breakup processes. The use of reanalysis-based climate data (NASA POWER) may also introduce uncertainty due to potential smoothing and implicit gap-filling in the underlying products.

The temporal aggregation of several predictors represents another constraint. Some climatic variables were introduced as monthly or seasonal aggregates rather than daily time series. Higher temporal resolution meteorological forcing may improve the representation of rapid melt events or rain-on-snow episodes that can alter the timing of hydrological response. Furthermore, the ML models used in this study rely on statistical relationships between predictors and observations and do not explicitly represent physical processes governing snow accumulation, melt, and channel hydraulics ⁷⁹. Incorporating physically based relationships, such as empirical formulations for ice breakup timing (e.g., Shulyakovski-type relationships), may provide additional insight for selected locations and is considered a direction for future work.

Future research may extend the present framework by incorporating additional cryospheric and hydrological information sources ⁸⁰. Remote sensing products describing snow cover dynamics, snow water equivalent, or river ice conditions could provide spatially distributed predictors that complement station-based observations. Basin-scale physiographic descriptors and higher-resolution meteorological datasets may also improve the representation of spatial heterogeneity in mountainous catchments. Another direction involves the integration of ML models with physically based hydrological simulations, where process-based snowmelt models provide physically constrained predictors for data-driven forecasting systems. Expansion of the observational record and inclusion of additional monitoring stations would further improve regional generalization of predictive models across different hydrological regimes.

The interpretation of model predictors indicates that the timing of the spring water-level rise in the studied basins is primarily controlled by thermal forcing and cryospheric processes during the late winter–spring transition. Variables describing accumulated positive temperatures and the first thaw date show the strongest influence on model output, which corresponds to the established role of air temperature in regulating snowmelt-driven runoff generation in cold regions. Similar relationships between temperature accumulation and the onset of spring runoff have been reported in numerous studies of snow-dominated basins^81,82. The contribution of variables describing river ice breakup and early water level rise further reflects the hydraulic effects of ice cover during the transition from winter to open-channel conditions. Changes in ice cover modify channel roughness and flow conveyance, which can affect the timing of the initial water-level response to snowmelt inputs^83,84. The combined importance of thermal, cryospheric, and hydrological predictors is consistent with the coupled nature of snowmelt and river ice processes in high-latitude hydrological regimes.

The analysis also identifies several limitations associated with data availability and predictor representation. The station-year dataset is spatially heterogeneous, with dense observational coverage in several major basins and relatively sparse records in smaller catchments. Such differences influence model generalization and partly explain the spatial variability of prediction errors. In addition, several potentially relevant processes are not explicitly represented in the predictor set, including spatial variability of snow water equivalent, detailed topographic controls on melt timing, and mechanical properties of river ice. These factors may become relevant under changing climatic conditions. Observational and modelling studies have documented systematic shifts in snowmelt timing and spring flood regimes in northern river systems associated with increasing air temperatures and changes in precipitation phase⁹.

Future work may therefore benefit from integrating additional cryospheric observations, remote sensing products describing snow cover and river ice dynamics, and higher-resolution meteorological forcing in order to improve the representation of spatial heterogeneity and climate-driven changes in spring flood processes. At the same time, these developments can be complemented by established physically based and empirical approaches from the river ice literature, including data-driven relationships developed in Russian hydrological studies, which provide interpretable representations of key processes and may support more physically grounded analysis alongside ML-based methods.

Conclusions

This study evaluated the potential of ensemble ML models to predict the onset date of the spring water-level rise in snowmelt-dominated river basins of the northeastern Asian region. Five regression algorithms were tested using grouped cross-validation by year. Among the evaluated methods, the CatBoost model provided the highest predictive performance with an out-of-fold mean absolute error of 4.54 days and . The differences between the tested ensemble models were moderate, indicating that the structure of the station-year dataset can be represented by several tree-based algorithms, while CatBoost provided the most stable results across validation folds.

Spatial analysis of prediction errors shows that model accuracy varies among river systems and is influenced by both hydrological regime and observational coverage. Major river basins with multiple stations and relatively homogeneous snowmelt-driven dynamics exhibit prediction errors of only a few days. Larger errors are observed mainly in smaller basins or in regions with complex topographic conditions, where local variability in snow accumulation, melt timing, and river ice processes may not be fully represented by the available predictors.

Model interpretation using SHAP and partial dependence analysis indicates that the timing of the spring water-level rise is primarily controlled by thermal conditions during the late winter–spring transition. Predictors associated with positive degree days, the first thaw day, and the first candidate day of water-level rise contribute the most to the model output. Variables describing river ice breakup and short-term water-level dynamics also influence the predicted timing, reflecting the role of ice processes and rapid hydrological response during the early melt period.

The results demonstrate that ML models combined with hydrometeorological and hydrological predictors can reproduce the timing of spring flood initiation with relatively low error in cold-region river systems. The proposed framework provides a data-driven approach for analysing the controls of snowmelt-driven hydrological events and may support regional-scale assessments of spring flood dynamics. Further improvements may be achieved through the inclusion of additional cryospheric predictors, higher temporal resolution meteorological forcing, and expanded observational datasets.

Author contributions

Conceptualization, I.M., V.T. and Ig.M.; Data curation, I.M., Ig.M. Project administration, V.T. and A.B.; Resources, V.N.; Software, I.M., A.B, I.M. and A.G.; Supervision, V.T., A.B., R.V., I.M., and V.N.; Validation, I.M., V.T., A.B. and A.G.; Visualization, I.M., Ig.M.; Writing—original draft, I.M., Ig.M., V.T., V.N., A.B. and A.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data availability

The code and datasets for this research are openly accessible on the repository https://zenodo.org/records/19037710

Declarations

Competing interests

The authors declare no competing interests.