Snow drought to hydrologic drought progression using machine learning and probabilistic analysis

Abstract

Snow plays a crucial role in water resource management, acting as a natural reservoir that sustains agricultural, domestic, and ecological needs. However, declining snowpack poses significant challenges to water availability, particularly in snow-dominated regions. This study explores the relationship between Snow Water Equivalent (SWE) and streamflow in snow-dominated watersheds using the Long Short-Term Memory (LSTM) model and probabilistic analysis. While LSTM model is typically used for prediction, we employed it primarily to understand how snow affects streamflow. Our analysis yielded several key findings: (1) By analyzing multiple SWE products, we found a strong relationship between SWE and streamflow, particularly with a lookback of 60–90 days. (2) The University of Arizona (UAZ) dataset consistently provided the most reliable results, showing that SWE during winter significantly influences streamflow in spring and summer. (3) Our spatial analysis revealed that basins in the western United States consistently exhibited strong model performance, underscoring the robust relationship between SWE and streamflow in these snow-dominated regions. (4) Our probabilistic analysis revealed a systematic progression from snow drought to hydrologic drought, with the likelihood of hydrologic drought increasing from 0.32 in early phases (0–14 days) to over 0.8 in later phases (60–90 days). This progression provides an early warning indicator for hydrologic drought, improving our ability to anticipate and prepare for drought conditions in snow-dominated regions.

Introduction

Snow plays an integral role in global water resources^1,2, acting as a crucial natural reservoir that supports a myriad of needs, from agricultural irrigation to domestic water supply and sustaining ecological systems^3–5. Snow, with its unique hydrological and radiative properties, significantly influences interactions between the land and the atmosphere, ensuring water is stored during the colder months and released gradually as temperature rises^6–8. This release is critical for maintaining river flows and recharging groundwater, aligning with periods of high-water demand^9–11. The reservoir functionality of snow is especially crucial, as it buffers against the variability of precipitation, ensuring water availability even in times of low rainfall^12,13. This role is particularly significant as its climatic impact transcends winter, potentially causing disruptive and costly natural hazards¹⁴ such as droughts^15–18, and wildfires¹⁹.

Given the vital role of snow in both ecosystems and societies, researchers have raised concerns about the observed widespread decrease in snowpack and its environmental consequences^14,20–22. These consequences include increased drought severity and frequency, altered streamflow patterns, and greater wildfire risk. For instance, the winter of 2020–21 saw notably below average snowpacks in many western U.S. basins, reinforcing the severe drought experienced in the summer of 2021, which reflected a significant long-term regional decline. Similar decreases in spring and winter snowpacks have been observed across much of Europe²³ and the northeastern U.S. in recent years^24–26. Due to the adverse impact of climate change and rising global temperatures^27–29, these current negative trends are expected to lead to further reductions in snowpack and increase the prevalence of low-record anomalies in snow-dominated regions^30–33. Complementing these findings, Mote et al.³⁴ found that declines in snowpack have been observed at over 90% of snow monitoring sites across the western U.S., with one-third of these being statistically significant. These trends are consistent throughout the year and across diverse climatic zones, highlighted by a study from the U.S. EPA³⁵ , which noted a 23% decrease in April snowpack levels at 93% of monitored sites from 1955 to 2022, particularly impacting regions like Washington, Oregon, northern California, and the northern Rockies.

This observed snowpack decline indicates an emerging and critical challenge known as snow drought. Snow droughts, distinct from traditional meteorological^36–43, hydrological^44–48 and agricultural droughts^44,45,49,52 by their direct impact on snowpack levels, pose a threat to water availability. They are characterized by periods where snow water equivalent is below average, affecting regions dependent on meltwater for their water supply^14,53,54. While the occurrence of snow droughts has been increasing, the progression from snow drought to hydrologic drought remains less explored.

Most research efforts have begun to determine the historical frequency and intensity of low snowpacks⁵⁵ and predict future anomalies amidst varying global and regional warming scenarios⁵⁶. However, a significant portion of this analysis has overlooked the connection between snow droughts and their effects on water availability and regional water supply downstream, particularly where snow plays a crucial role in runoff^55,57,58. To address this gap, our study investigates the conditional probability that a hydrologic drought follows a snow drought within various lag periods. By analyzing Snow Water Equivalent (SWE) and streamflow data across snow-dominated basins, we aim to quantify the likelihood and timing of hydrologic droughts following snow droughts.

Additionally, there are uncertainties associated with the measurement and modeling of snow water equivalent (SWE) across different datasets, which complicates the accurate assessment of snow impacts on water availability and streamflow. Variability in spatial and temporal resolution, data assimilation techniques, and interpolation methods among datasets introduce challenges in consistently quantifying SWE^59–63. To overcome these challenges, our approach utilizes a suite of data, including satellite remote sensing imagery, and reanalysis products, to analyze the interconnections between snow and streamflow and examine how variations in selection of historical datasets influence the accuracy of these analyses.

A notable advancement in understanding the relationship between snowpack and streamflow has been identified through significant methodological innovations. In particular, the work of Sturtevant and Harpold⁶⁴ has revealed that the overestimation of seasonal streamflow volumes derived from statistical water supply forecasts during drought periods can be effectively curtailed through the application of a nonlinear transformation to the predictor variables. Additionally, Modi et al.⁶⁵ assessed the role of historical initial hydrologic conditions in the training phase of models aimed at drought year forecasts, probing into the formation of forecasting accuracy across different forecast intervals. In alignment with these innovative strides, our study applies a Long Short-Term Memory (LSTM) model to elucidate the relationship between SWE and streamflow volume in snow-dominated basins. This methodology aims to refine the understanding of how SWE impacts streamflow by using multiple SWE products and analyzing the effect of various lookbacks on streamflow. The high accuracy achieved by our LSTM models enables us to quantify the temporal dynamics of the snow-streamflow relationship, particularly by identifying optimal lookback periods and seasonal variations across different basins. By offering a clearer picture of the interplay between snow and downstream water availability, our findings provide insights that can aid water resource managers in developing more effective water allocation strategies in snow-dependent regions. This enhanced understanding will support more informed decision-making processes, facilitating the development of sustainable water use strategies and allocation policies that are responsive to the challenges posed by snow droughts.

In summary, this study aims to address several key research objectives: (i) to identify the most reliable SWE dataset for quantifying snow-streamflow relationships in snow-dominated watersheds; (ii) to determine the optimal lookback period that captures the maximum influence of snow on streamflow; (iii) to analyze spatial patterns in these relationships across diverse geographical settings; and (iv) to quantify the probabilistic progression from snow drought to hydrologic drought across different time scales. Our findings contribute to the current understanding of snow drought by: (i) establishing a quantitative framework for assessing the snow-streamflow relationship; (ii) providing a probabilistic basis for anticipating hydrologic drought based on snow conditions; and (iii) determining the optimal temporal window during which snow drought conditions can serve as an early warning indicator for hydrologic drought.

Materials and methods

The methodology employed in this study is outlined in several steps, each contributing to our understanding of the relationships between snowpack dynamics and water availability. Initially, we collect and preprocess data, followed by the identification of snow-dominated watersheds, and then we analyze the implications of these dynamics on streamflow using LSTM models. Finally, we calculated the probability that a hydrologic drought follows a snow drought within specific lag periods.

Datasets

CAMELS

The CAMELS dataset (Catchment Attributes and Meteorology for Large-sample Studies) was developed to provide a hydrometeorological dataset for hydrological modeling and analysis across the contiguous United States. This dataset includes daily forcing data and hydrologic response data for 671 small-to-medium-sized basins, spanning a wide range of hydroclimatic conditions from 1980 to 2014. The dataset comprises area-averaged forcing data, which includes basin mean, hydrologic response units (HRUs), and elevation bands, generated by mapping daily, gridded meteorological datasets to subbasin and basin polygons using data from Daymet, Maurer, and North-American Land Data Assimilation System (NLDAS)⁶⁶. Additionally, daily streamflow data were compiled from the United States Geological Survey National Water Information System^67,68. For our study, we selected basins from the CAMELS dataset, focusing on snow-dominated catchments. The streamflow data from these selected basins were utilized to analyze the impact of snow on water availability.

Daymet

The Daymet dataset offering a comprehensive suite of daily weather parameters across Continental North America, including Mexico, the United States, Canada, as well as Hawaii and Puerto Rico. This dataset is derived from a suite of algorithms and computational tools that interpolate and extrapolate daily meteorological observations to produce gridded estimates of weather conditions on a 1 km × 1 km resolution. The parameters generated—ranging from minimum and maximum temperature to precipitation, vapor pressure, radiation, snow water equivalent (SWE), and day length—are instrumental for filling the gaps in regions devoid of meteorological instruments, thus facilitating a more detailed analysis of hydrological processes.

Spanning from 1980 to 2022 for the majority of its coverage area, Daymet’s temporal span provides a long-term perspective on weather patterns and their implications for snowpack dynamics. Daymet’s methodology includes cross-validation analyses to evaluate the sensitivity of its interpolation methods and to estimate prediction errors. This validation not only ensures the accuracy of the dataset but also provides insights into the reliability of Daymet’s weather parameter estimates, reinforcing its utility for environmental science and hydrological modeling⁶⁹.

UAZ

The Daily 4 km Gridded SWE and Snow Depth dataset is a product of the University of Arizona, supported by NASA’s MAP and SMAP Programs, covering the period from 1981 to 2022. It integrates in-situ snow measurements from the SNOTEL and COOP networks across the conterminous United States with PRISM’s modeled temperature and precipitation data. This assimilation process yields detailed daily snapshots of snow water equivalent (SWE) and snow depth at a high spatial resolution of 4 km. The spatial coverage spans from the northern border at latitude 50°N down to 24°S, and from longitude −125°W to −66.5°E, ensuring a comprehensive geographical representation of snow conditions across the U.S^70,71.

SNODAS

The SNODAS dataset, a product of the National Oceanic and Atmospheric Administration (NOAA) National Weather Service’s National Operational Hydrologic Remote Sensing Center⁷², is designed to provide detailed information on snowpack properties across the United States. It encapsulates a variety of snow-related parameters such as depth, SWE, and snowpack temperature, utilizing data assimilation techniques to ensure accuracy. This dataset is updated daily, providing temporal coverage from September 28, 2003, to the present, with a high spatial resolution of 1 km. The extensive range of parameters, including liquid and solid precipitation, snowmelt runoff, and sublimation from the snowpack, makes it a useful tool for hydrologic modeling and climate analysis⁷².

A summary of the datasets used in this study, including their temporal resolution, spatial resolution, spatial coverage, and temporal coverage, is provided in Table 1.

Table 1.

Summary of datasets used in this study.

Dataset	Temporal resolution	Spatial resolution	Spatial coverage	Temporal coverage
CAMELS	Daily	Basin-scale	671 basins across U.S	1980–2014
Daymet	Daily	1 km	North America	1980—Present
GLDAS	Daily	0.25°	Global	2003–2023
University of Arizona (UAZ)	Daily	4 km	U.S	1981—2021

Identifying snow dominated watersheds

Building on the definition by⁷³, which characterizes historically snow-dominated regions as grid cells with more than 30 mm of snow water equivalent (SWE) for more than 3 months, this study refines the criteria to better suit watershed-level analysis. Specifically, a watershed is defined as snow-dominated if, in 95% of the years in the SWE records, the SWE exceeds 30 mm for more than 3 months in a year. This criterion ensures that the selected watersheds consistently experience significant snowpack levels.

Significance of snow water equivalent in streamflow analysis through LSTM models

To elucidate the relationship between Snow Water Equivalent and streamflow in snow-dominated watersheds, we employed Long Short-Term Memory (LSTM) models. These models are particularly well-suited for capturing temporal dependencies in hydrological time series data due to their ability to learn long-term dependencies and handle sequential data effectively^74,75.

The LSTM model is a specialized type of recurrent neural network (RNN) designed to address the challenges of learning long-term dependencies that traditional RNNs struggle with^76,77. Traditional RNNs often fail to maintain information in memory for long sequences, as highlighted by research which showed their limitations in retaining sequence information beyond a brief duration^78–81. This is particularly inadequate for modeling environmental processes such as streamflow, where the influence of past events like snowmelt can span from days to years. LSTM enhances the basic RNN architecture by introducing a series of gates that regulate the flow of information.

In this study, the LSTM model is employed to explore the relationships between Snow Water Equivalent and streamflow in snow-dominated watersheds. By analyzing how well the model predicts streamflow based solely on SWE data, we can infer the strength of the relationship between these two variables. The choice of LSTM is strategic for capturing the delayed effects of snow on streamflow, which are essential for understanding water resource dynamics in these regions. The study utilizes multiple SWE products to determine which dataset has the strongest relationship with streamflow, as indicated by the model’s predictive performance. By comparing the performance of different products, we aim to identify the most reliable source for understanding how SWE impacts streamflow. Additionally, we examine various lookbacks of SWE to determine the optimal delay between SWE changes and their impact on streamflow. This involves analyzing how different lookbacks—ranging from a few days to several months—affect the accuracy and reliability of our model’s output, which are quantified using performance metrics such as Kling-Gupta Efficiency (KGE).

Model setup and configuration:

• Architecture: The LSTM model used in this analysis features a multi-layered design, with each layer capable of extracting different levels of abstraction from the input data. The first layer consists of LSTM units with varying number of units, determined dynamically through hyperparameter tuning, which processes the input data while retaining important temporal information through memory cells. This is followed by a dropout layer to mitigate overfitting by randomly ignoring neurons during training, thus providing a more generalized model. A second layer of LSTM units further refines the data processing, ensuring that the model captures deeper insights from the time series data. The final output of the model is generated through a dense layer that maps the learned features to the output variable, the streamflow.

• Hyperparameter Tuning: Hyperparameter tuning is crucial in optimizing the LSTM model to achieve the best performance. Using Keras Tuner⁸², a range of values is explored for the number of LSTM units in both layers, dropout rates, and learning rates. This tuning process involves setting up trials with different combinations of these parameters to identify the configuration that minimizes the mean squared error (MSE) on the validation set. The optimal configuration is then used to train the final model.

• Data Preparation: For this study, the input to the LSTM model is the historical SWE data, and the output is the streamflow values for the next day. The model inputs include not only the current values of SWE but also their past values, considering the memory effect inherent in hydrological processes. Different lookbacks of SWE are tested to determine the optimal time delay between SWE and its impact on streamflow. For example, for a lookback of 14 days, the input to the model will be the SWE values from the previous 14 days.

• Training Process: The dataset is divided into training, validation, and test sets, with 85% used for training and 15% for testing. Within the training set, 20% is further segregated as a validation set to monitor model performance and mitigate overfitting.

• Performance Metrics: The model’s performance is evaluated using metrics including MSE, Nash–Sutcliffe Efficiency (NSE) coefficient, and Kling-Gupta Efficiency (KGE). These metrics help quantify the model’s accuracy in predicting streamflow from SWE inputs. The formulas for these performance metrics are as follows:

  1

where is the observed streamflow value, is the predicted streamflow value, and n is the number of observations.

2

where is the mean of the observed streamflow values.

3

where r is the correlation coefficient between the observed and predicted streamflow values, is the ratio of the standard deviations of the predicted and observed streamflow, and is the ratio of the means of the predicted and observed streamflow.

By utilizing an LSTM modeling approach, combined with rigorous hyperparameter tuning and analysis of input lookbacks, this study demonstrates the significant relationship between Snow Water Equivalent (SWE) and streamflow in snow-dominated regions. The analysis clarifies the timing of snow’s impact on streamflow and identifies the most reliable dataset for understanding these dynamics. These findings are instrumental for water resources management, particularly in managing water flows in regions susceptible to snow-related variability.

Analysis of the probability of hydrologic drought following snow drought

In addition to exploring the relationship between Snow Water Equivalent (SWE) and streamflow, we analyzed the temporal progression from snow droughts to hydrologic droughts. Specifically, we calculated the conditional probability that a hydrologic drought follows a snow drought within various lag periods.

Snow and hydrologic drought

To create a baseline for comparison against current conditions, we first established a climatology for both SWE and streamflow. For streamflow, daily values from each USGS station were collected over a 35-year period. Similarly, daily SWE data was used from the UAZ dataset for each watershed. We focused on the UAZ dataset to construct the climatology because it has shown better performance in preliminary analyses, which is further elaborated in Section "Analysis of the probability of hydrologic drought following snow drought". The climatology for each calendar day was constructed by collating the observed values of that specific day across all years.

To enhance the robustness of the climatology and smooth out anomalies, a 5-day moving window was applied⁸³. This approach involves aggregating data not just from the specific day but also from two days before and two days after. Consequently, each calendar day’s climatology consists of 165 values, calculated as 5 days multiplied by 35 years, providing a reference that incorporates slight temporal variations in snow and streamflow dynamics⁸⁴.The climatology serves as the foundation for calculating daily percentiles, which are critical for identifying drought conditions. For both SWE and streamflow, each day’s observed value is compared against the respective climatology. The percentile rank for each day is calculated using the formula:

4

where is percentile for a station, representing drought, n is the ordinal rank of the day’s observed value within the climatology, W is window size (5 days), and y is the number of years used in climatology.

Drought conditions are determined based on the calculated percentiles. For both SWE and streamflow, a value falling below the 30th percentile indicates a drought condition^85,86. This threshold marks a deviation from typical conditions, highlighting periods of reduced snowpack or streamflow compared to the historical record.

Calculation of conditional probability

The conditional probability that a hydrologic drought follows a snow drought within a given lag period is calculated using the Eq. 5:

5

where T represents the lag period in days (e.g., 7, 14, 30, etc.).

This calculation was performed for each lag time and for each basin, allowing us to assess both temporal and spatial variations in the progression from snow drought to hydrologic drought.

Results and discussion

Identification of snow-dominated watersheds

Following the procedure explained in the methodology section, a total of 68 snow-dominated watersheds were identified across the contiguous United States, within the CAMELS dataset basins.

The geographical distribution and significant SWE characteristics of these watersheds were mapped to visually represent their spread and concentration across the United States. Figure 1a highlights the distribution of snow-dominated watersheds, color-coded by the mean annual SWE, illustrating a clear regional concentration in the western states. These watersheds are predominantly located in the western regions, including the Sierra Nevada, Rocky Mountains, and Cascade Range, with a few basins also present in the northeastern US, such as in Maine. This identification serves as a foundation for further analyses using the LSTM model, focusing on the relationship between snowpack and streamflow, providing a basis for exploring the impacts of snow decline on water availability.

Fig. 1.

(a) Distribution of snow-dominated watersheds across the United States, color-coded by mean annual SWE. (b) Temporal variation of SWE and streamflow for all snow-dominated basins during water years 2011–2013. Maps and visualizations were created using Python 3.11 (https://www.python.org/).

The temporal relationship between SWE and streamflow is further illustrated in Fig. 1b, showing the annual patterns of SWE and streamflow for basins. These plots highlight the synchronization between peak SWE and subsequent increases in streamflow, emphasizing the critical role of snowmelt in maintaining streamflow levels. This graph shows a strong seasonal pattern in SWE and streamflow, with SWE peaking during the winter months and streamflow peaking during the spring months, corresponding to snowmelt. The rapid increase in streamflow following the peak snowmelt period underscores the importance of snow as a critical water source during the spring and early summer months.

Significance of SWE and optimal lookback in streamflow prediction

We investigated the significance of Snow Water Equivalent (SWE) in streamflow prediction using the Long Short-Term Memory (LSTM) models. This part of the analysis focused on identifying which SWE dataset provided the best results and determining the optimal lookback between SWE measurements and streamflow predictions.

Figure 2 presents the performance metrics of the LSTM models using three different SWE datasets: UAZ, Daymet, and SNODAS. The performance was evaluated using the KGE (Fig. 2a), NSE (Fig. 2b) and MSE (Fig. 2c) metrics. Figure 2a shows the KGE values across various lookbacks for the three datasets. The UAZ dataset consistently outperformed the other datasets, exhibiting higher median KGE values across all lookbacks. Daymet also performed well but was slightly less consistent compared to UAZ. However, SNODAS showed the lowest performance, with lower KGE values and greater variability.

Fig. 2.

Performance metrics of LSTM models using three SWE products: UAZ, Daymet, and SNODAS. (a) KGE values; (b) NSE values; and (c) MSE values across various lookbacks.

Statistical analysis confirms that the UAZ dataset significantly outperforms both Daymet and SNODAS (p < 0.001, Wilcoxon signed-rank test). As shown in Table 2, the median KGE value for UAZ (0.671, 95% CI [0.663, 0.679]) is substantially higher than Daymet (0.459, 95% CI [0.437, 0.475]) and SNODAS (0.345, 95% CI [0.315, 0.370]). The narrow confidence interval for the UAZ dataset further confirms its more consistent performance across basins compared to the other datasets. The magnitude of improvement is substantial, with UAZ showing a 46.11% improvement over Daymet and a 94.43% improvement over SNODAS in terms of median KGE values. Similar to the KGE results, the UAZ dataset demonstrated superior performance, maintaining higher NSE values across different lookbacks. Daymet followed, showing reasonable performance, while SNODAS again lagged behind with lower NSE values. Figure 2c provides a detailed analysis of the Mean Squared Error (MSE) values for different lookbacks, further emphasizing the performance of the datasets.

Table 2.

Statistical summary of median KGE values for SWE datasets with 95% confidence intervals (CI).

Dataset	Median KGE	95% CI	Improvement by UAZ (%)
UAZ	0.671	[0.663–0.679]	–
Daymet	0.459	[0.437–0.475]	46.10
SNODAS	0.345	[0.315–0.370]	94.40

This analysis across different lookbacks (shown in Fig. 2) helped determine the optimal lookback for the models. The performance of the models generally increased as the lookback extended up to 60 days, after which the performance metrics slightly fluctuated without significant improvements. This finding may be attributed to the typical lag between snowfall accumulation and snowmelt-driven streamflow, where snowmelt occurs mostly within this period. Beyond 60 days, the influence of snowmelt on streamflow diminishes as other hydrological factors, such as precipitation or groundwater dynamics, become more prominent. This suggests that the optimal lookback for more accurate streamflow predictions using SWE data, for the basins analyzed in this study, is around 60 days, beyond which increases in lookback do not substantially enhance model accuracy.

The identification of an optimal lookback period helps characterize the memory of snow-dominated hydrologic systems. This timeframe represents the characteristic lag between snowpack accumulation and its manifestation in streamflow, effectively quantifying the system’s ‘memory’ of snow conditions. This memory mechanism is particularly important in snow-dominated watersheds, where water is stored in solid form for extended periods before contributing to runoff. The results suggest that SWE information from approximately two months prior provide the most accurate indication of future streamflow, highlighting this interval as a critical time window for water resource management decisions.

The relationship between Snow Water Equivalent (SWE) and streamflow is further clarified through the examination of KGE values across various lookbacks and seasons, as presented in Fig. 3. It is evident that the KGE values vary significantly across seasons. The box plots show that spring and summer seasons generally exhibit higher KGE values, particularly for lookbacks between 60 and 90 days. The high KGE values in spring and summer suggest that the LSTM model captures the relationship between SWE and streamflow more effectively during these seasons, aligning with the expected snowmelt-driven streamflow increases. The heat map in Fig. 3b further emphasizes the importance of selecting an appropriate lookback. The highest KGE values are observed around lookbacks of 60–90 days, particularly in spring and summer, confirming that the influence of SWE on streamflow is most pronounced within this time frame. This lookback range aligns with the expected delay between snowfall accumulation and subsequent snowmelt that contributes to streamflow. The KGE values during winter and fall are consistently lower, and even negative at shorter lookbacks, as depicted in both the box plots and heat map. This suggests that during these seasons, there is not a significant relationship between SWE and streamflow, possibly due to the storage of snow in the snowpack rather than immediate runoff. The findings from Fig. 3 suggest that LSTM model can effectively capture the influence of SWE on streamflow during the spring and summer periods when snowmelt drives water availability.

Fig. 3.

Seasonal performance of the LSTM model in capturing the relationship between SWE and streamflow across various lookbacks. (a) Box plots of KGE values for various lookbacks. (b) Heat map showing the median KGE values across different lookbacks and seasons.

While the overall performance metrics suggest an optimal lookback of approximately 60 days when considering the entire year (Fig. 2), our seasonal analysis reveals temporal variations in this relationship. Specifically, during summer, when snowmelt significantly influences streamflow, the optimal lookback extends to approximately 60–90 days (Fig. 3), though differences in performance within this range remain minimal. This seasonal variation highlights the dynamic nature of the SWE-streamflow relationship, suggesting that a fixed lookback may not be universally optimal across all seasons. For targeted summer modeling, a slightly longer lookback period (60–90 days) is recommended, whereas for year-round predictions, the 60-day lookback provides the best overall compromise.

Figure 4 illustrates the geographical distribution of model performance using the UAZ dataset. The circles represent the NSE values, while the color gradient indicates the KGE values. The spatial distribution shows that the model performed well across a wide range of basins, particularly in the western United States, where snow-dominated basins are more prevalent. The histograms in Fig. 4 provide a summary of the KGE and NSE values across all snow-dominated basins. Most basins achieved KGE and NSE values above 0.6, highlighting the effectiveness of the model in predicting streamflow from SWE inputs at seasonal scale.

Fig. 4.

Geographical distribution of model performance using the UAZ dataset, with circles representing NSE values and the color gradient showing KGE values. The histograms summarize the distribution of KGE and NSE across snow-dominated basins. Maps and visualizations were created using Python 3.11 (https://www.python.org/).

Notably, we observed variability in model performance among basins, even within geographically adjacent basins. For example, in Utah, Beaver River basin (Basin id: 10,234,500) achieved a high KGE value of 0.77, while nearby Coal Creek basin (Basin id: 10,242,000) yielded a much lower KGE of 0.25. This discrepancy may be attributed to differences in soil characteristics (Beaver River has shallow soils of ~ 0.60m vs. Coal Creek’s much deeper ~ 12.4m), elevation (2499 m vs. 2035 m), land cover (35% forest cover vs. 17%), and dominant vegetation (evergreen forest vs. grasslands), as well as potential reservoir regulation influencing streamflow in Coal Creek. Similarly, in Washington, Thunder Creek basin (Basin id: 12,175,500) achieved a KGE of 0.66, while nearby Newhalem Creek basin (Basin id: 12,178,100) had a lower KGE of 0.34, despite both having high forest cover (79% and 92% respectively). Differences in drainage area, land cover heterogeneity, and soil composition likely contribute to the divergence in model performance.

More broadly, spatial heterogeneity in model performance can be attributed to a combination of factors. First, topographic characteristics such as aspect, slope, and elevation can significantly influence snowmelt dynamics and the SWE-streamflow relationship^87–90. Second, land cover differences, particularly forest density and vegetation type, and coverage, affect snow interception, sublimation, and melt rates^91–93. Finally, human interventions, including reservoir operations, could modify natural flow patterns in ways not captured by our model^94–96. Together, these basin-specific factors can affect hydrological responses, resulting in varied predictive accuracy across basins despite similar climatic conditions.

The high accuracy of the LSTM model in predicting streamflow, as indicated by metrics such as KGE, NSE, and MSE, suggests that the model effectively captures the temporal dependencies between SWE and streamflow. Although the LSTM model is primarily designed for prediction, its accuracy implies that the relationship between these two variables is robust and well-represented within the model. The investigation into different lookbacks highlights the temporal dynamics between snowfall and its eventual contribution to streamflow. The findings that KGE values peak at lookbacks of 60–90 days suggest that there is a predictable delay between snowfall accumulation, snowmelt, and the resulting increase in streamflow. This relationship is crucial for understanding the seasonality of water resources in snow-dominated regions and underscores how snowmelt timing aligns with water availability. This understanding can guide water resource management by identifying critical periods when snowmelt-driven streamflow is most influential, enabling better planning and allocation of water resources.

Analysis of the probability of hydrologic drought following snow drought

To understand the temporal connection between snow droughts and subsequent hydrologic droughts, we evaluated the conditional probability that a hydrologic drought follows a snow drought given different lag times. The heatmap in Fig. 5 illustrates the probability of hydrologic drought occurring after a snow drought within a given time window across the basins. Specifically, each color-coded cell represents the likelihood of hydrologic drought following a snow drought within a specified period (lookback). For shorter lookback periods (7–14 days), most basins show relatively low probabilities of hydrologic drought following snow drought, indicated by the predominant red and orange colors. This suggests that there is typically a lag between the onset of snow drought and its manifestation as hydrologic drought. The lower probabilities observed at shorter periods (7–14 days) primarily reflect natural delays inherent to snowmelt processes, but they may also partly result from reservoir operations in regulated watersheds, which can buffer streamflow responses⁹⁶ and thus delay the onset of hydrologic drought. As the lookback period extends to 30–60 days, the probability increases substantially across most basins, as shown by the transition to yellow and green colors, reflecting the typical timing of snowmelt and its influence on streamflow and hydrologic drought development. At longer lookback periods (120–180 days), probabilities plateau or increase slightly in some basins. This stabilization indicates that the influence of snow droughts on hydrologic conditions diminishes over time as other hydrological factors, such as precipitation, become more prominent in determining drought outcomes. The box plot analysis (Fig. 5b) provides a statistical summary of these probabilities across all basins. The median probability increases substantially from approximately 0.2 at 7 days to 0.95 at 180 days, with the most significant increase occurring between 30 and 90 days.

Fig. 5.

Probability of hydrologic drought following snow drought across different temporal scales. (a) Basin-specific heatmap showing the probability of hydrologic drought occurrence following snow drought for different lookback periods across all snow-dominated basins. (b) Box plot distribution of drought response probabilities across all basins for each lookback period.

To better illustrate the spatial distribution of drought progression probabilities, we created a spatial representation of our probability analysis (Fig. 6). These maps display the conditional probability of hydrologic drought following snow drought across the contiguous United States for six distinct lookback periods (7, 14, 30, 60, 90, and 180 days). The visualization reveals both the temporal evolution and geographic variability in drought progression rates. These spatial patterns have significant implications for regional water resource management, as they identify watersheds that may require more rapid management interventions following snow drought conditions. For instance, regions demonstrating accelerated drought progression provide water managers with a narrower response window to implement effective drought mitigation strategies compared to areas where the snow-to-hydrologic drought relationship manifests more gradually.

Fig. 6.

Spatial distribution of the conditional probability that a hydrologic drought follows a snow drought across snow-dominated basins in the contiguous United States for different lookback periods (7, 14, 30, 60, 90, and 180 days). Maps and visualizations were created using Python 3.11 (https://www.python.org/).

The probability distribution analysis (Fig. 7) further characterizes this temporal evolution through four phases:

• Early Phase (0–14 days): Shows a narrow distribution with a mean probability of 0.32, indicating consistently low probabilities of drought progression across basins.

• Medium Phase (14–30 days): Exhibits a slightly higher mean probability of 0.36, representing a 14% increase from the early phase.

• Transition Phase (30–60 days): Demonstrates a significant shift with a mean probability of 0.53, marking a 45% increase from the medium phase. This period represents the critical window where the cascading effects of snow drought on hydrologic conditions become most pronounced.

• Late Phase (60–90 days): Shows a slight decrease in mean probability to 0.52. Although slightly lower than the Transition phase, the probabilities remain high, suggesting continued hydrologic impacts across basins. The wider spread in the Transition and Late phases highlights the importance of basin-specific factors in modulating drought responses.

Fig. 7.

Probability density functions of drought response across four time windows: Early (0–14 days), Medium (14–30 days), Transition (30–60 days), and Late (60–90 days).

To assess the robustness of our probability analysis to threshold selection, we conducted a sensitivity analysis using seven different percentile thresholds ranging from the 10th to 40th percentile. The results, summarized in Fig. 8, demonstrate that while absolute probability values shift with different thresholds, the temporal progression pattern remains remarkably consistent across all definitions. For stricter drought definitions (10th-20th percentiles), the overall probabilities are lower (starting at 0.26–0.32 for 14 days and reaching 0.82–0.90 for 180 days), while more lenient definitions (35th–40th percentiles) yield higher probabilities (starting at 0.35–0.36 for 14 days and reaching 0.93–0.94 for 180 days). However, the transition period of 30–60 days, where probabilities increase most rapidly, is preserved across all thresholds.

Fig. 8.

Sensitivity analysis of drought progression probabilities to threshold definition. Lines show the probability of hydrologic drought following snow drought at different lookback periods (14–180 days) for seven drought threshold definitions (10th-40th percentiles). Gray bars represent the coefficient of variation across thresholds at each lookback period, demonstrating decreasing sensitivity to threshold choice at longer lookback periods (from 9.9% at 14 days to 4.4% at 180 days).

Notably, the sensitivity to threshold choice decreases at longer time scales. The coefficient of variation across thresholds is highest at the 14-day period (~ 10%) but decreases substantially for longer periods, reaching only ~ 4% at 180 days. This convergence indicates that the longer-term drought progression relationship is particularly robust to threshold definition. The 30th percentile threshold used in our main analysis represents a middle ground among the tested thresholds and aligns with common drought monitoring practices.

The analysis reveals that the progression from snow drought to hydrologic drought is not uniform across basins but follows a generally predictable temporal pattern. This understanding can be particularly valuable for water resource managers, as it provides a quantitative basis for anticipating the likelihood and timing of hydrologic drought following observed snow drought conditions.

The relationship between snow drought and subsequent hydrologic drought demonstrated in our analysis suggests that snow drought conditions can serve as an effective early warning indicator for impending hydrologic drought. The increase in probability from early to late phases, coupled with the high probabilities observed at longer lookback periods, indicates that snow drought consistently precedes hydrologic drought in snow-dominated basins. This temporal progression provides a valuable window of opportunity for drought preparedness, typically ranging from 30 to 90 days. Water resource managers can utilize this lead time to implement preparatory measures, such as adjusting reservoir operations, modifying water allocation plans, or initiating water conservation measures before the onset of severe hydrologic drought conditions.

Limitations and future research directions

This study advances the understanding of snow drought progression to hydrologic drought through LSTM modeling and probabilistic assessments; however, we acknowledge some areas that can be considered for future research. Our analysis relied on remote sensing and reanalysis datasets, which contain uncertainties that could influence drought characterization. The spatial variability in model performance observed across basins suggests that basin-specific factors like topography, land cover, and human interventions affect the snow-streamflow relationship. Our LSTM modeling framework intentionally focused exclusively on SWE to quantify the strength of the SWE-streamflow relationship in snow-dominated basins, though incorporating additional hydrologic variables may enhance model performance in regions where non-snow factors influence runoff generation. Additionally, while our approach captures general drought progression patterns, it may not fully account for rapid snowmelt events triggered by rain-on-snow occurrences. Future research may address these aspects by incorporating additional ground-based measurements from SNOTEL sites, separating regulated and unregulated basins to better quantify how reservoir operations to modify the natural progression from snow drought to hydrologic drought, and developing more comprehensive modeling frameworks that maintain interpretability while including additional influential factors.

Conclusion

This study offers a comprehensive analysis of the influence of Snow Water Equivalent (SWE) on streamflow, utilizing Long Short-Term Memory (LSTM) models and probabilistic analysis to determine the most effective datasets and optimal lookbacks for understanding streamflow dynamics. Our key findings include:

1. The UAZ dataset consistently outperformed other SWE products (Daymet and SNODAS) across all performance metrics (KGE, NSE, and MSE) for streamflow prediction in snow-dominated watersheds.

2. The optimal lookback period for SWE influence on streamflow is 60–90 days, with seasonal variations showing stronger relationships during spring and summer when snowmelt actively contributes to streamflow.

3. Spatial analysis revealed that most basins in the western United States achieved high model performance (KGE and NSE values above 0.6), confirming the strong relationship between SWE and streamflow in snow-dominated regions.

4. Probabilistic analysis demonstrated a systematic progression from snow drought to hydrologic drought, with probabilities increasing from approximately 0.3 in early phases (0–14 days) to over 0.8 in later phases (60–90 days).

These findings enhance our understanding of snow-streamflow dynamics and provide a quantitative basis for anticipating hydrologic drought following snow drought conditions.

Future research could extend this work in several directions. The demonstrated relationship between SWE and streamflow could be incorporated into drought early warning systems, particularly in snow-dominated regions, to enhance proactive water management strategies. Additionally, this methodology could be applied to examine how climate change scenarios might affect the temporal progression from snow drought to hydrologic drought, providing valuable insights for long-term water resources planning. Future studies may also explore the integration of additional variables, such as soil moisture or temperature, to further enhance our understanding of drought progression and its drivers in snow-dominated watersheds.

Author contributions

P.M. conceptualized the study, curated the data, conducted formal analysis and investigation, and developed the methodology. P.M. also contributed to software development, data visualization, and writing the original draft. K.G. contributed to conceptualization, methodology development, and writing—review and editing. H.M. contributed to the conceptualization, secured funding for the study, supervised the research, and participated in writing—review and editing the manuscript. All authors have reviewed and approved the final version of the manuscript.

Data availability

CAMELS dataset: Available through UCAR/NCAR at https://dx.doi.org/10.5065/D6MW2F4D. Daymet dataset: Available through ORNL DAAC at https://doi.org/10.3334/ORNLDAAC/2129. University of Arizona Daily 4 km Gridded SWE dataset: Available through NSIDC at https://doi.org/10.5067/0GGPB220EX6A. SNODAS data products: Available through NSIDC at https://doi.org/10.7265/N5TB14TC. All datasets used in this study are publicly accessible and can be downloaded from their respective repositories.

Declarations

Competing interests

The authors declare no competing interests.