Spatial modeling of snow water equivalent in the high atlas mountains via a lumped process-based approach

Abstract

Snow water equivalent (SWE) is a critical variable for understanding water availability and snowmelt-driven streamflow in mountainous regions. Yet, its spatial and temporal estimation is constrained by scarce in situ measurements and the inherent challenges of deriving SWE directly from satellite observations. Thus, accurate SWE assessment is essential for predicting the spatial distribution of snowpack and its temporal contributions to downstream outflow, particularly in semi-arid snow-fed basins like Morocco’s High Atlas regions. In this study, we simulate the local and spatial distribution of SWE and outflow at 500 m using Snow17 model, ERA5-Land and satellite-derived fractional Snow Cover Area (fSCA) from Moderate Resolution Imaging Spectroradiometer (MODIS) for the period 2000–2022. The reanalysis data was downscaled and bias corrected using machine learning models (e.g. random forest). To validate results, we compared simulated snow cover area (fSCA) (transformed from SWE simulation) with fSCA issued from MODIS. The methodology was tested in the Rheraya sub-basin (Tensift basin) and applied in Ait Ouchene and Tillouguite sub-basins (Oum Er Rbia basin) in Morocco’s High Atlas Mountains. Statistical analysis shows strong model performance, with Nash–Sutcliffe Efficiency (NSE) values exceeding 0.84 for snow depth (SD) simulations. Moreover, spatio-temporal analysis revealed that SWE and snow depth are significantly higher above 2,500 m elevation, with SWE exceeding 300 mm and SD surpassing 60 cm in Tillouguite and Rheraya sub-basins. Findings also demonstrated that snowmelt contributions to outflow varied significantly with elevation, accounting for 40–46% of annual outflow above 2,500 m and playing a dominant role during spring (55–57% of seasonal outflow). Our research provides a framework for enhancing SWE/outflow estimation and understanding snowpack dynamics in semi-arid mountainous regions, highlighting the vital role of high-altitude snowpacks in water resource sustainability and management under climate change.

Introduction

Snowpack dynamics are pivotal to the global hydrological cycle, especially in semi-arid regions, where snowmelt is vital for water resources, agriculture, and hydropower generation^1,2. Morocco’s High Atlas Mountains (HAM), often known as ‘water towers,’ provide freshwater for adjacent semi-arid and arid plains^2,3. This thereby supports both local populations and ecosystems^1,2,3,4,5,6. Notably, in these regions, snowmelt significatively contributes to both runoff and groundwater recharge, by 15–50%^5,7 and 30–80% respectively⁸. Nevertheless, accurately measuring or estimating snow water equivalent (SWE) and other snow-related parameters remains a persistent challenge in the HAM^9,10.

This difficulty is especially pronounced in mountain regions, where direct field measurements of SWE are labor-intensive, less frequent than SD measurements, and unsuitable for large-scale applications^11,12,13. For example, Beaton et al.¹¹ noted that field-based measurement of SWE typically captures less than 1% of a basin’s snowpack and spatially distributed measurements are scarce. These challenges are further exacerbated by the HAM’s complex topography—characterized by varying elevation, slope, aspect, and local climatic conditions— which leads to significant spatial variability in snow accumulation and melt^1,7,14. Moreover, this complexity is compounded by data scarcity^9,13,14,15 especially at high altitudes. Notably, existing monitoring HAM stations are predominantly located at lower elevations, limiting the available data’s representativeness⁹. Notwithstanding ongoing efforts, like interpolation methods (e.g., altitudinal lapse rate^16,17 spatial model of air temperature (MSPAT)¹⁷), accurately capturing snow dynamics still faces limitations. Climate change further amplifies these challenges by reducing snow cover extent, advancements in snowmelt onset, and alterations in precipitation patterns^1,6,18. For example, projections by Tuel et al.⁶ predicted a severe decline in snowpack in the HAM, with reductions of up to 60% under moderate climate scenarios (RCP 4.5) and as high as 80% under more severe conditions (RCP 8.5). Likewise, López-Moreno et al.¹⁸ reported a decrease in the HAM’s average snow duration ranging from 27.0 to 37.4% and a decline in the mea SWE by 3.1% under RCP 4.5 and 64.9% under RCP8.5 by 2050. These changs not only result in earlier snowmelt periods but also shift runoff timing, thereby affecting water availability for downstream needs¹⁹. Consequently, these changes have profound implications for agriculture, hydropower, and regional drinking water supply^4,6,18.

Given these challenges, integrating remote sensing and reanalysis datasets into snow modeling approaches provides a promising avenue for improving SWE and runoff predictions^12,20. Remote sensing technologies, like MODIS snow-covered area (SCA)^7,12 and Sentinel-2 imagery^21,22,23,24 provide high-resolution snow cover maps, improving the snow models accuracy, especially when assimilated into hydrological models^11,22. Simultaneously, reanalysis datasets, like ERA5^9,12complement these efforts by filling gaps in meteorological data. Nonetheless, their coarse resolution often limits their effectiveness in capturing the fine-scale variability of snow processes in mountainous regions^19,25,26. Recently, advancements in downscaling reanalysis data (e.g., ERA5- Interim, ERA5-Land) using dynamic —such as those using WRF (Weather Research and Forecasting) and other models^9,12,20,27— and statistical approaches^28,29,30 have shown promise in addressing these data limitations. For instance, Alonso-González et al.¹² successfully downscaled ERA-Interim to a 10 km resolution for the Iberian Peninsula and further refined snow simulations using elevation-dependent adjustments. Conversely, Sourp et al.²⁰ achieved a 100 m resolution in the Sierra Nevada using ERA5/ERA5-Land and high-resolution DEMs, showing good agreement with observed SWE data. Likewise, in the HAM, Baba et al.^9,27 downscaled reanalysis datasets (MERRA-2 and ERA5) to high spatial resolutions (200–250 m) using DEMs and MicroMet to account for elevation, slope, and aspect. A recent review by Schilling et al.³⁰ stated the potential of machine learning (ML) models, such as random forests (RF) and neural networks, to capture non-linear relationships between variables, hence improving SWE monitoring and modeling. Additionally, studies^28,29 have shown that ML models, such as XGBoost and RF, significantly improve temperature predictions after bias correction in Italy and the High Atlas region. Moreover, bias correction methods for precipitation datasets have improved hydrological predictions by correcting remote sensing-based rainfall products in the Moroccan areas^31,32.

Conventionally, process-based models, such as Snow17, remain essential for capturing the nonlinear interactions governing snow accumulation and melt processes^33,34,35,36. These models rely on meteorological inputs, including temperature and precipitation, to estimate SWE and predict outflow (snowmelt and rainfall). Regrettably, their performance is often hindered by input data limitations in complex terrains^15,37. Nonetheless, several studies^{16,34,35,36,37,38,39,40,41,42} have demonstrated their applicability to simulate SWE across varying climatic and topographic conditions. For instance, Franz et al.³⁹ focused on the Owyhee Mountains (USA), highlighting the model’s effectiveness in predicting snowmelt. He et al.³⁷ examined the interactions between snow processes and meteorological variables in the western United States and reported that errors in meteorological forcing data can corrupt the model’s parameter estimates, ultimately affecting the reliability of SWE predictions. Further studies, such as Raleigh and Lundquist¹⁶and Franz and Karsten³⁸ explored how the Snow17 model can be calibrated using remote sensing data like MODIS SCA, improving model accuracy in regions with limited ground-based observations, including the Sierra Nevada Mountain (USA) and other mountainous areas. Besides, Eythorsson et al.⁴⁰ investigated trends in Icelandic snow conditions, demonstrating how Snow17 can effectively simulate snow dynamics under changing climate scenarios in the Northern Hemisphere. Awol et al.⁴² evaluated various snow models in the Prairie Watersheds of Canada, highlighting their applicability for operational reservoir inflow forecasting. Moreover, Follum et al.³⁶ compared snow models in Senator Beck Basin (Colorado, USA), showing the advantages of process-based models in capturing snowmelt dynamics across varied topographies. Bennett et al.³⁴ integrated fSCA data from MODIS to enhance streamflow forecasting in Alaska, USA, showcasing the potential for combining remote sensing data with traditional snow models. In addition, Agnihotri and Coulibaly⁴¹ evaluated various snowmelt estimation techniques for improved spring peak flow prediction in Canada, underscoring the importance of accurate snowmelt modeling for streamflow forecasting and highlighting the benefits of integrating snow models with hydrological forecasting systems.

In Morocco’s High Atlas, several studies have explored SWE assimilation in hydrological modeling^6,9,15,27 but only fewer^6,15 have focused on calibrating the Snow17 model or explored their application in estimating SWE under the region’s unique conditions. For instance, Tuel et al.¹⁵ integrated a sublimation model based on the radiation-derived temperature index into Snow17 to simulate snowpack dynamics in the Oum-Er-Rbia basin (2001–2011). By combining MODIS snow cover, and dynamically downscaled ERA-Interim data at 1 km, they enhance model accuracy, particularly for snowmelt and sublimation processes. Despite these advances, gaps persist in integrating snow models with high-resolution downscaled reanalysis data to improve SWE and outflow simulations in the HAM. To our best knowledge, no previous studies have integrated MODIS fractional snow cover data into the Snow17 model for the HAM to improve SWE estimation. Additionally, there is a noticeable lack of studies validating modeled outflow against observed streamflow to assess hydrological prediction accuracy in mountainous areas.

To address these challenges, this study focuses on evaluating the Snow17 model’s performance in reproducing SWE and outflow across different scales, from local (station) to spatial (basin), while addressing challenges in data-scarce regions. By assessing the model’s stability and transferability, we aim to improve the understanding and prediction of spatiotemporal snow dynamics in the HAM via a multi-faceted approach. This research is guided by the following key research questions:

• How can Earth Observation and reanalysis data be effectively combined to model SWE in ungauged or data-scarce regions, and what is the performance of such an approach in the HAM?

• Can downscaled and bias-corrected ERA5-Land reanalysis data effectively replace field measurements for local SWE/SD simulations, and how does this approach perform in the HAM?

• How well can the Snow17 model be transferred from local to spatial scales, and what is the added value of integrating MODIS fSCA data for verifying SWE/SD simulations and quantifying snowmelt-derived water resources?

To address these questions, our specific objectives are : (i) to enhance input data quality by downscaling and bias-correcting daily ERA5-Land precipitation and temperature data evaluating four machine learning models —LightGBM (LGB), Random Forest (RF), Support Vector Regression (SVR), and XGBoost (XGB)—; (ii) to optimize Snow17/SWE2HS model parameters using the Dynamically Dimensioned Search (DDS) algorithm for better SWE and snow depth simulation; (iii) to integrate MODIS fSCA into the Snow17 model, bridging remote sensing data with process-based modeling; (iv) to evaluate snow-hydrology interactions by comparing simulated outflow with observed streamflow to assess impacts on water availability.

Materials and methods

Research area

The study area is situated in Morocco’s High Atlas Mountains, including the Rheraya sub-basin (within the Tensift basin), as well as the Ait Ouchene and Tillouguite sub-basins (within the Oum Er-Rbia basin). Specifically, these sub-basins are situated between latitudes 31°0’N and 32°3’N, and longitudes 5°2’W and 8°6’W, as shown in Fig. 1. They cover 224 km² 2,421 km² and 2,488 km² respectively. Furthermore, they are characterized by steep topography, with substantial elevations ranging from about 900 to over 3,600 m, including Jbel Toubkal, which is the highest peak in North Africa. The terrain varies significantly across the sub-basins. The climate is semi-arid, exhibiting significant seasonal snow accumulation at higher altitudes during the winter months¹. Average annual precipitation varies widely with altitude, ranging from 400 mm at lower elevations to 800 mm in the upper alpine zones, with snow accounting for up to 50% of precipitation at higher altitudes^5,10. The temperature range varies considerably with elevation, contributing to distinct seasonal hydrological patterns^1,43.

The Rheraya sub-basin serves as a vital water source for downstream communities within the Tensift basin, supporting both agricultural activities and drinking water supplies. Approximately 69.94% of its area lies below 2,500 m (Table 1) with its outlet defined by the Tahanaout hydrometric station. This sub-basin has been the focus of hydrological research conducted by the International Joint Laboratory TREMA^1,2,27 and other researchers^10,14,17,21. Since 2003, numerous meteorological stations have been established in the area, including the Oukaimden-2 station (also named Oukaimden LMI) at 3,200 m and the more recent Oukaimden-1 station (also known as Oukaimden MorSnow) at 2,750 m, operated by the MorSnow team (Fig. 2). Notably, the Oukaimden-1 station represents Morocco’s first measurements of SWE, which are essential for modelling snow hydrology using the Snow17 model, as Rheraya’s hydrology is significantly influenced by snowmelt processes.

Fig. 1

(a) Our study area location within Morocco. (b) Location of Rheraya, Ait Ouchene and Tillouguite sub-basins within the Tensift and Oum Er Rbia basins, respectively. Digital elevation model extracted from Shuttle Radar Topography Mission (SRTM) (created by Qgis 3.36).

The Ait Ouchene and Tillouguite sub-basins, part of the Oum Er-Rabia (OER) basin, play a crucial role in regional water resources⁴⁴ including inflows to the Bin El Ouidane artificial reservoir. Ait Ouchene is predominantly low altitude, with 90.72% of its area situated below 2,500 m, whereas Tillouguite demonstrates a more balanced elevation distribution, with 40.41% of its area above 2,500 m (Table 1). These sub-basins have been the subject of different studies^6,15. Snowmelt is particularly important in these sub-basins, especially at higher elevations during the spring and early summer, as it sustains flows that are vital for agriculture, hydropower generation, and municipal water supplies⁶.

These sub-basins are subject to the broader impacts of climate variability and change^6,18 which may affect the timing and volume of snowmelt and the precipitation distribution. The snowpack’s sensitivity to temperature shifts, as well as the potential for changes in precipitation patterns, makes these sub-basins particularly vulnerable to climate change¹⁸.

Table 1 Percentage area by altitude range for each sub-basin studied.

Data source

Table 2 summarizes the input data sources used in this research. The observed daily meteorological data, including temperature and precipitation (Geonor T200B), along with snowpack data (SWE via Campbell Scientific CS275 and SD via ultrasonic sensor) were collected from automatic weather stations (Figs. 1 and 2). In addition, precipitation and temperature reanalysis data were sourced from the ERA5-Land dataset, published by the European Centre for Medium-Range Weather Forecasts (ECMWF), with a spatial resolution of 0.1°. Previous studies (e.g²⁰), pointed out the high performance of ERA5-Land data in snow hydro-meteorological simulations. For instance, in Morocco^29,45, Khettouch et al.^29,45. identified ERA5-Land as the top-performing dataset for precipitation estimation in the Drâa basin, while Sebbar et al.^29,45. validated its accuracy for temperature downscaling in mountainous regions, achieving RMSE values as low as 1.6 °C. For SCA, data were sourced from MODIS daily snow cover products, MOD10A1 and MYD10A1 generated from the Terra and Aqua satellites, respectively. More specifically, this dataset was derived from a customized daily snow cover product tailored to the Moroccan Atlas Mountains⁷. Following Bousbaa et al.⁷ the screening methodology included prioritized data merging (favoring MOD10A1), cloud-affected pixel replacement, elevation-based spatial filtering (< 60% missing pixels above 1000 m) for mountainous areas, and temporal gap-filling (using a moving window of 3 days before and 2 days after the missing pixel’s date) to ensure data continuity. This product provides daily snow cover information based on the processing and combination of Normalized- Difference Snow Index (NDSI) values from both MOD10A1 and MYD10A1 products. This dataset has been effectively used for various snow hydrology applications in the Moroccan Atlas Mountains^{7,9,14,27,43,46,47,48} demonstrating their suitability for Moroccan mountainous regions. Generally, the ERA5-Land and MODIS datasets were downloaded at hourly and daily steps respectively, covering the period from August 2000 to August 2022.

Table 2 Input data sources used in this research and their Spatial and Temporal resolution.

Fig. 2

(a) Overview of Oukaimden-1 (MorSnow) station at 2,751 m (longitude − 7.866°; latitude 31.206°) and the various sensors installed: (b) radiation sensor, (c) Geonor sensor (total precipitation), (d) wind sensor, (e) snow depth sensor, (f) rain sensor, (g) snow water equivalent sensor (unique in Morocco), and (h) graduated bar. i₁-i₂) Oukaimden snow variability overview.

The Digital Elevation Model (DEM) used in this study was derived from the Shuttle Radar Topography Mission (SRTM) dataset, with a spatial resolution of 30 m. Furthermore, daily streamflow data for 2000–2020 were obtained from gaging reports provided by the Tensift and Oum Er-Rabia Hydraulic Basin Agencies (ABHT and ABHOER) (as shown in Table 3).

Table 3 Hydrometric station characteristics.

Research method

Our methodology is divided into several main steps (illustrated in Fig. 3) to estimate SWE and outflow using a combination of observed, reanalysis, and remotely sensed data.

Fig. 3

Methodology used in this research to estimate SWE and outflow using Snow17 and SWE2HS models.

Initially, we collected and processed half-hourly meteorological and snowpack data, including observed time series of precipitation, temperature, snow water equivalent, and snow depth. Additionally, hourly ERA5-Land reanalysis data, daily MODIS snow cover data, and SRTM digital elevation data were collected and processed. These datasets were carefully aligned in both spatial and temporal resolutions, ensuring compatibility for further analysis. Specifically, half-hourly observed meteorological data and hourly ERA5-Land data were aggregated to daily values (24-hour accumulated values (from 00 UTC to 00 UTC of the next day) for precipitation, average for temperature) to match the temporal resolution of MODIS snow cover data. For spatial alignment, we resampled and downscaled ERA5-Land data to a 500 m resolution, using topographic variables from the DEM (elevation, slope, aspect, sun elevation). This resolution was chosen to align with MODIS-derived snow cover products, thereby improving spatial accuracy and ensuring seamless dataset integration. To correct biases in ERA5-Land data, we applied four machine learning models (e.g., LGB, RF, SVR and XGB), with the most effective model selected for subsequent simulations.

Furthermore, we employed the Snow17 model to simulate outflow and SWE, with the resulting estimates converted to SD via the SWE2HS model. It is worth noting that SWE values were transformed into fSCA via an empirical formula. An iterative process of model parameter optimization was conducted using Dynamically Dimensioned Search (DDS), along with performance evaluation to refine the simulations, resulting in reliable estimates of SWE, SD, and fSCA. It’s worth noting that the DDS optimization terminated after 10,000 simulations or if the NSE improvement plateaued (< 0.1% over 500 iterations). The ‘satisfaction’ criterion in Fig. 3 required NSE ≥ 0.8 and visual fidelity of simulated snow depth trends. If unmet, the calibration was repeated with revised parameter bounds. Once validated, we obtained the final simulated SWE and outflow outputs and prepared them for further applications, such as input for the Snowmelt Runoff Model (SRM) and hybrid AI models.

Snow cover and reanalysis data processing

The fSCA was calculated using NDSI derived from the MOD10A1 and MYD10A1 products. These products were combined to create a unified snow cover dataset. Tuel et al.¹⁵ point out that frequent cloud cover (approximately 30%) in the HAM during the wet season can lead to serious data gaps and classifications errors. To address these missing pixels caused by cloud cover or other data gaps, a spatiotemporal filtering method was employed, as outlined in previous research^7,14,47. For more details on this approach, refer to^7,47. ERA5-Land (total precipitation and temperature) datasets were processed to match the temporal resolution of the fSCA by aggregating the reanalysis data to daily time steps. For spatial consistency, all gridded datasets, including ERA5-Land variables, were resampled to a 500 m resolution, aligning with the MODIS-derived snow cover products, using bilinear interpolation. This resampling allows direct comparison of climate variables and snow cover observations are directly at the same spatial scale.

Lapse rate adjustments

Given the study area’s complex topography, lapse rate adjustments and sun-slope-aspect corrections were applied to the resampled ERA5-Land data to refine temperature and precipitation estimates. Our downscaling approach incorporated topographic variables, including elevation, slope, aspect, and sun elevation, which were resampled to align with MODIS fSCA resolution. Elevation-dependent lapse rate corrections (+ 2.92 mm/km for precipitation (calculated from Eq. 1) and − 6.27 °C/km for temperature (estimated by Eq. 2)) were applied to better represent spatial variability. Additionally, a sun-slope interaction component was introduced to account for terrain-driven radiation effects, further refining temperature corrections. The use of lapse rate adjustments is well-established in mountainous regions. For instance, Boudhar et al.¹⁷ note that the altitudinal lapse rate method (LRM) is a common technique for interpolating precipitation, based on the premise that precipitation linearly increases with elevation¹⁶. In contrast, the MSPAT model is commonly employed for air temperature predictions. This model adjusts temperature estimates by considering factors such as altitude, aspect, and slope, assuming that temperature decreases as elevation increases¹⁷.

Precipitation values $\:{P}_{i,j}\:$for each grid cell were adjusted to account for elevation differences using the following equation:

$$\:{P}_{i,j}={\:P}_{ref}+G\times\:\varDelta\:Alt$$

(1)

Here, $\:{P}_{ref}$ represents the precipitation at the reference station, $\:G$ is the lapse rate, and $\:\varDelta\:Alt$ is the elevation difference between the reference station and the grid cell. Negative precipitation values resulting from Eq. 1 were set to zero to maintain physical realism, as precipitation cannot be negative.

Temperature $\:{T}_{i,j}$ adjustments incorporated both lapse rate and the effects of slope and aspect:

$$\:{T}_{i,j}={T}_{ref}+\left(G\times\:\varDelta\:Alt\right)-A\times\:\left[cos\left(\frac{{AS}_{i,j}}{180}\pi\:\right)-cos\left(\frac{{AS}_{ref}}{180}\pi\:\right)/2\right]$$

(2)

$\:{T}_{ref}$ denotes the temperature at the reference station, G represents the air temperature lapse rate, calculated daily from two reference meteorological stations (Oukaimden-1 and Oukaimden-2). $\:{AS}_{i,j}\:$and $\:{AS}_{ref}$ denote the aspect in degrees of the pixel (i, j) and the reference station, respectively, while $\:A$ is a scaling factor for the sun-slope-aspect effect.

Bias correction via machine learning models

Correcting biases in meteorological data is a critical step to enhance the accuracy and reliability of snow/hydrology and climate simulations, especially in regions with complex terrain and variable climate conditions. In this study, we carefully selected four machine learning (ML) models (e.g., LightGBM, RF, SVR, and XGB) for their proven performance in Mediterranean and semi-arid regions^29,49. These models selected also for their capability to capture non-linear patterns, efficiently process large datasets, and address the spatial and temporal variability inherent in meteorological variables like precipitation and temperature^28,29,30. It’s worth noting that we used 70% of the dataset for training and 30% for validation. This split ensures a balance between model learning and evaluation while maintaining sufficient data for generalization. In addition, the ML model predicted biases for each grid point based on features such as elevation, slope, aspect, sun elevation and the resampled ERA5-Land data.

• LightGBM (Light Gradient Boosting Machine) is a gradient boosting framework designed for speed and efficiency⁵⁰. It is well-suited for processing large datasets, making it an excellent choice for high-resolution simulations. LightGBM uses a histogram-based approach to bin continuous features, which significantly reduces memory usage and speeds up the training process. This model can capture complex relationships within the data, and thus perform well in various machine learning tasks, including regression and classification⁵⁰.

• RF (Random Forest) is an ensemble learning method that constructs multiple decision trees during training and outputs the average prediction for regression tasks⁵¹. One of its key strengths is its robustness against overfitting, which is achieved through the diversity of the trees generated by bootstrapping the training data. Using this technique, each tree is trained a different subset, leading to a more stable and reliable model. Additionally, RF is effective in variable selection, allowing accurate predictions even when the input data is noisy or incomplete⁵¹.

• SVR (Support Vector Regression) is particularly effective in high-dimensional spaces, making it suitable for modeling complex terrain data where spatial and climatic variability are significant. SVR employs the kernel trick to map input data into a higher-dimensional space, allowing it to capture intricate relationships that may not be apparent in lower dimensions. By introducing an error margin (ε), SVR can avoid overfitting and generalize well to unseen data, making it a valuable tool in scenarios with complex data structures^48,52.

• XGBoost (Extreme Gradient Boosting) is a highly efficient and scalable gradient boosting algorithm known for its superior speed and performance, especially in regression tasks⁵³. It incorporates advanced regularization techniques to prevent overfitting and improve model generalization. XGBoost has gained popularity in various machine learning competitions and applications due to its ability to handle large datasets and its effectiveness in capturing complex patterns in the data^28,29. Studies, such as those conducted by Niazkar et al.²⁸ in northern Italy, have highlighted its strong performance in real-world scenarios, further solidifying the algorithm’s reputation as a leader in the field.

Snow17/SWE2HS models

We model daily SWE using the Snow17 model, developed by Anderson⁴² for the National Weather Service River Forecast System (NWSRFS). This conceptual model uses a temperature index approach to simulate snowpack processes like heat storage, water retention, liquid water movement, and snowmelt. Despite being initially developed and calibrated for temperate and continental climates with seasonal snowpacks in the United States, the Snow17 model has demonstrated adaptability and has been successfully applied to diverse climatic regions worldwide^{34,35,36,37,38,40,41,42,54,55,56}. This model traditionally utilizes temperature and precipitation data as inputs to simulate snow accumulation and melting dynamics. In this study, we improve the model by incorporating snow cover fraction as an additional input variable. The outputs generated by the model include SWE and outflow, which accounts for the combined contribution of snowmelt and rainfall.

The Snow17 model determines the melt of snow surfaces in a manner contingent upon the presence or absence of rain. When rain occurs on snow, the model uses the following equation to compute surface melt:

$$\:M=\sigma\:\times\:\varDelta\:t\times\:\left[{\left({T}_{a}+273.15\right)}^{4}-{273.15}^{4}\right]+0.0125\times\:P\times\:{f}_{r}\times\:{T}_{r}+UADJ\times\:\varDelta\:t\times\:\left[\left({e}_{a}-6.11\right)+0.00057\times\:{P}_{a}\times\:{T}_{a}\right]$$

(3)

where $\:M$ is the depth of melt (mm), σ is the Stefan–Boltzmann constant, ∆t is the time interval, $\:{T}_{a}$ is the air temperature (°C), $\:P$ is the water equivalent of precipitation (mm), $\:{f}_{r}\:$is the fraction of precipitation in the form of rain, $\:{T}_{r}$ is the rain temperature (°C), $\:UADJ$ is the average wind function during rain-on-snow events (mm mb^-1hr^-1), $\:{e}_{a}$ is the vapor pressure of the air (mb), and $\:{P}_{a}$ is the atmospheric pressure (mb).

In contrast, if there is no rain and the air temperature exceeds a set threshold, the Snow17 model uses a melt factor to calculate the snowmelt (Eq. 4).

$$\:M={M}_{f}\times\:\left({T}_{a}-{T}_{b}\right)$$

(4)

where $\:M$ represents the depth of melt (mm), $\:{M}_{f}\:$denotes the melt factor, which varies seasonally (mm/°C), $\:{T}_{a}$ is the air temperature and $\:{T}_{b}$ is the base temperature, above which melting begins, (typically 0 °C). The seasonal variation of the melt factor $\:{M}_{f}\:$is represented by a sinusoidal curve with maximum (MFMAX) and minimum (MFMIN) values, which are model parameters.

SWE2HS is an empirical model developed by Aschauer et al.⁵⁷ to calculate snow depth (SD) from daily SWE data (Eq. 5). It was created to address the limitations of traditional snow densification models, which often require a complex set of input variables and high temporal resolution data, making them less suitable for climatological applications⁵⁷.

$$\:\text{S}\text{D}=\:\sum_{k=1}^{n}\frac{{\text{S}\text{W}\text{E}}_{\text{k}}*{{\uprho\:}}_{water\:}}{{{\uprho\:}}_{\text{k}}}$$

(5)

$\:\text{S}\text{D}$ is snow depth (cm), $\:{\text{S}\text{W}\text{E}}_{\text{k}}$ denotes snow water equivalent at time step k (cm) $\:{{\uprho\:}}_{water\:}$ represents density of water (typically 1 g/cm³) $\:{{\uprho\:}}_{\text{k}}\:$is density of snow at time step k (g/cm³) and n is the number of time steps. k is the daily step.

Overall, the Snow17 and SWE2HS models require 12 and 6 parameters, respectively. Currently, the Snow17 model is configured with 9, while SWE2HS maintains 6 parameters. The default values and ranges for these parameters are presented in Table 4. It is worth noting that the most influential parameters in the Snow17 model are MFMIN and MFMAX (Minimum and Maximum non-rain melt factor), which govern snowmelt rates by incorporating local energy balance factors such as shading, slope, and solar irradiance^34,40,54. SCF (Snow under-catch correction factor) adjusts snowfall estimates for deficiencies in gauge measurements, sublimation, and blowing snow, ensuring accuracy, especially in short-term studies³³. UADJ (average wind during rain-on-snow events) affects heat fluxes critical for snowmelt and is derived from long-term wind datasets. Additional parameters, such as PXTEMP (temperature for rain/snow partitioning), MBASE (melt base temperature), and TIPM (surface temperature index), influence precipitation phase and snowpack temperature. A sensitivity analysis conducted by He et al.⁵⁶ indicated that SCF, MFMAX, and PXTEMP are the most influential Snow17’s parameters. Nonetheless, Franz et al.³⁹ found that solely MFMAX and PLWHC significantly impacted the model’s performance.

Table 4 Snow17/ SWE2HS parameters, description and value ranges.

In the SWE2HS model, the most influential parameters are $\:\text{R}$ (Settling resistance factor), $\:{{\uprho\:}}_{\text{n}\text{e}\text{w}}$ (New snow density), and $\:{{\uprho\:}}_{\text{m}\text{a}\text{x},\text{e}\text{n}\text{d}}$ (Final maximum snow density). Among these, $\:\text{R}$ is the most crucial, as it dictates the rate of snow densification and exhibits the highest sensitivity index, significantly affecting the model’s accuracy metrics, including R² and bias⁵⁷. The parameter $\:{{\uprho\:}}_{\text{n}\text{e}\text{w}}$ determines the initial density of newly fallen snow, which directly impacts calculations of snow depth. Meanwhile, $\:{{\uprho\:}}_{\text{m}\text{a}\text{x},\text{e}\text{n}\text{d}}$ represents the final densification state of the snowpack, influencing its long-term evolution. Other parameters, such as $\:{{\uprho\:}}_{\text{m}\text{a}\text{x},\text{i}\text{n}\text{i}\text{t}}$ (Initial maximum snow density), $\:{{\upsigma\:}}_{\text{m}\text{a}\text{x}}$ (Overburden pressure at which $\:{{\uprho\:}}_{\text{m}\text{a}\text{x},\text{e}\text{n}\text{d}}$ is achieved), and $\:{{\upvartheta\:}}_{\text{m}\text{e}\text{l}\text{t}}$ (Melt metamorphism transition rate), serve supportive roles by enhancing the model’s representation of snowpack densification and melt dynamics. Proper calibration of these parameters ensures Snow17/SWE2HS’s adaptability and reliability across diverse climatic regions^33,40,57.

Model parameters optimization

Like all empirical models, the snow model parameters require careful calibration, as they can vary with climatic conditions⁵⁷. In this study, we employed the Dynamically Dimensioned Search (DDS) algorithm, introduced by Tolson and Shoemaker⁵⁸ to optimize the Snow17/SWE2HS models parameters. DDS is a heuristic global optimization method that balances broad exploration and targeted refinement by initially searching the entire parameter space and progressively focusing on the most promising areas. Its efficiency in managing complex parameter interactions makes it particularly suitable for calibrating hydrological and environmental models, as evidenced by its successful application in various studies^42,59.

For the calibration process, we used the Nash-Sutcliffe Efficiency (NSE) as our objective function, selecting the parameter set that achieved the highest NSE during the calibration period as the optimal configuration. This involved comparing the simulated and observed daily snow depth time series. To ensure robust optimization, the DDS algorithm was executed for 10,000 simulations, balancing exploration and convergence.

Snow cover fraction Estimation and validation

The fSCA was parameterized as an asymptotic function of SWE according to Eq. 6. This formula has been utilized because it has previously demonstrated good results in the High Atlas Mountains, as reported by Boudhar et al.¹⁷ and Tuel et al.¹⁵.

$$\:\text{f}\text{S}\text{C}\text{A}={fSCA}_{max}\times\:\text{t}\text{a}\text{n}\text{h}(k\times\:SWE)$$

(6)

where $\:{fSCA}_{max}$ is the maximum permissible snow cover fraction, which is set to 0.85 ¹⁵, $\:k$=100 mm^{-1 19}, and $\:SWE$ represents the snow water equivalent (in mm). Tuel et al.¹⁵ noted that snow fraction values exceeding 85% are extremely rare in the 500 m MODIS data, even at high elevations, likely due to the pronounced small-scale snow cover variability in the High Atlas region⁶⁰.

To validate Snow17 results, we compared simulated fSCA (transformed from SWE simulated) with fSCA generated from MODIS.

Performance evaluation

We utilized several statistical metrics to evaluate the performance of models, including the normalized root mean square error (nRMSE), the coefficient of determination (R²), and the Nash-Sutcliffe Efficiency (NSE) proposed by Nash and Sutcliffe⁶¹ to measure how well the model reflects observed changes, as depicted in Eqs. (7)–(9).

$$\:\text{n}\text{R}\text{M}\text{S}\text{E}=\frac{\sqrt{\frac{1}{n}\sum\:_{i=1}^{n}{\left({O}_{i}-{S}_{i}\right)}^{2}}}{\stackrel{-}{O}}$$

(7)

$$\:{R}^{2}=\frac{{\left[\sum\:_{i=1}^{n}\left({O}_{i}-\stackrel{-}{O}\right)\left({S}_{i}-\stackrel{-}{S}\right)\right]}^{2}}{\sum\:_{i=1}^{n}{\left({O}_{i}-\stackrel{-}{O}\right)}^{2}\sum\:_{i=1}^{n}{\left({S}_{i}-\stackrel{-}{S}\right)}^{2}}$$

(8)

$$\:\text{N}\text{S}\text{E}=1-\frac{\sum\:_{i=1}^{n}{\left({O}_{i}-{S}_{i}\right)}^{2}}{\sum\:_{i=1}^{n}{\left({O}_{i}-\stackrel{-}{O}\right)}^{2}}$$

(9)

where $\:{O}_{i}$ and $\:{S}_{i}$ represent the observed and simulated data, respectively; $\:\stackrel{-}{O}\:$and $\:\stackrel{-}{S}$ denote the average values of the observed and simulated data, respectively; and n is the data quantity. Moriasi et al.⁶² define a model as producing satisfactory simulation results when the NSE is greater than 0.50, the R² exceeds 0.5, and the nRMSE is less than half of the observed data’s standard deviation.

The tuning, evaluation, and simulation processes were implemented and executed within the Python programming environment.

Results

Downscaling and bias correction

Figure 4 presents Taylor diagrams for the calibration (Fig. 4-a_1-2) and validation (Fig. 4-b₁-₂), evaluating the performance of raw ERA5-Land and four ML models (downscaled-bias corrected ERA5-Land), such as LGB, RF, SVR, and XGB, for precipitation and temperature downscaling.

Fig. 4

Taylor diagram of the (a) calibration and (b) validation results for precipitation (mm) and temperature (°C).

For precipitation, during calibration, the ML models (RF, XGB, LGB) demonstrated superior performance compared to raw ERA5-Land and SVR (Fig. 4-a₁). Among them, LGB performed best, achieving the highest correlation coefficient (~ 0.71) and the lowest RMSE (9.78 mm), indicating an excellent ability to capture the observed variability. RF and XGB also achieved high correlations (R² = 0.70 and 0.69, respectively) and lower RMSE values (14.42 mm and 12.14 mm), indicating their ability to capture nonlinear relationships and complex terrain variability. In contrast, ERA5-Land and SVR showed poor performance, with low correlations (R² ~0.19 and 0.18, respectively) and overestimated standard deviations (~ 14.90 mm for ERA5-Land). The validation results (Fig. 4-b₁) confirmed the trend observed during calibration. Specifically, raw ERA5-Land continued to struggle with capturing local precipitation variability, as displayed by its low correlation (~ 0.16) and overestimated standard deviation (~ 17.48 mm), indicating limited accuracy in capturing variability. These results align with previous studies (e.g⁶³), which reported that reanalysis datasets often struggle to resolve local precipitation variability, particularly in mountainous regions. The SVR also performed poorly, with an R² of 0.13, suggesting a weak correlation with observed data. This may be related to their sensitivity to outliers or high dimensionality⁵². In contrast, RF and XGB demonstrated much better performance with higher correlations (R² = 0.83 and 0.82, respectively) and reduced RMSE (10.21 mm and 11.68 mm) during validation. This improvement can be attributed to these models’ ability to capture nonlinear relationships^28,51.

For temperature, all models, including raw ERA5-Land, showed high correlations (~ 0.95–0.99) during both calibration and validation periods, thus demonstrating strong agreement with observations. During validation, ERA5-Land achieved an R² of 0.97, reflecting the relatively smoother spatial gradient of temperature. Thereby, making it easier to model compared to precipitation. It is obvious from Fig. 4-b₂ that the RF model stood out by better capturing variability, achieving a lower RMSE of 0.59 °C, and maintaining closer proximity to observed values (R² = 0.99). This is significant as it suggested that RF can model temperature fluctuations more accurately, a crucial factor in regions with complex topography. Additionally, RF’s ensemble approach minimizes overfitting and effectively mitigates the impact of outliers and noise⁵¹ which is particularly important in high-altitude regions where observational data can be sparse or uncertain. These findings are consistent with earlier research^28,29 suggesting that ML models can enhance temperature prediction. For instance, Niazkar et al.²⁸ reported that, in Northern Italy, XGBoost outperformed other standalone models, while K-nearest neighbors-based ensemble models excelled in bias correction for temperature data. Similarly, Sebbar et al.²⁹ found that XGBoost outperformed SVR and traditional constant lapse rate methods, reducing error metrics and improving the accuracy of ERA5-Land temperature predictions in Moroccan mountainous regions.

While all ML models improved upon raw ERA5-Land data, RF was selected for final applications because it demonstrated: (1) the most consistent performance across both precipitation and temperature variables (R²=0.70 and 0.99 respectively), (2) superior robustness in mountainous terrain, and (3) best agreement with independent snow observations. Although LGB showed marginally better precipitation statistics (R²=0.71), RF’s ensemble approach provided more reliable results for the integrated snow modeling framework (e.g⁶⁴).

Point-scale calibration results

To optimize the Snow17 and SWE2HS parameters for SD simulations, 10,000 simulations were performed using the DDS algorithms to achieve optimal results. The calibration focused on SD rather than SWE due to several critical factors: (1) Morocco’s operational snow monitoring network provides only SD measurements at most stations, with just one station collecting intermittent SWE data (Fig. 2); (2) SD measurements offer higher temporal resolution (daily records) than the limited SWE measurements ; and (3) SD serves as a more reliable indicator for validating snow cover dynamics and melt timing, which are primary drivers of snowmelt runoff. Overall, the scatter plots demonstrate a strong correlation between observed and simulated SD, with R² values of 0.88 and 0.90 for the in-situ (Fig. 5-a) and downscaled-bias corrected datasets (Fig. 5-b), respectively.

Fig. 5

Comparison of observed and simulated snow depth (cm) at the Oukaimden-2 (LMI-Terma) station using two data sets: (a) in-situ data and (b) downscaled and bias-corrected ERA5-Land data via Random Forest.

Interestingly, the RF-downscaled and bias-corrected ERA5-Land data slightly outperformed the in-situ data, showing lower error and a stronger correlation between observed and simulated SD. This improvement can be explained by the RF’s capabilities, which effectively captures complex nonlinear relationships⁵¹. Our findings align with prior studies that outlined the importance of advanced optimization algorithms^42,59 in hydrological modeling. DDS has been effectively utilized in previous studies and demonstrated good performance^42,59. For example, Awol et al.⁴² applied DDS to optimize the calibration of various lumped models, including SACSMA/SNOW17, MACHBV/SNOW17, and VIC/RVIC, using a single objective function based on a weighted average of Kling-Gupta efficiency and Peak Flow Criteria. Their results indicated that model performance can be significantly improved through parameter refinement, achieving a calibrated Kling-Gupta Efficiency (KGE) of 0.776 for the SACSMA model⁴². Similarly, Tuo et al.⁶⁵ and Tiwari et al.⁵⁹ highlighted the effectiveness of advanced calibration methods in improving the simulation of SWE and streamflow across various contexts. Specifically, Tuo et al.⁶⁵ noted that multi-objective calibration approaches yielded greater accuracy, while single-objective methods often produced less favorable results.

SCA MODIS vs. SCA Snow17 validation

The Snow17 model was validated by comparing its simulated SCA against MODIS satellite observations. The evaluation covered multiple temporal scales—daily, weekly, and monthly—and three sub-basins (Rheraya, Ait Ouchene, and Tillouguite) with varying elevations, focusing on October to May period. Statistical metrics such as R² and nRMSE provided quantitative insights into the model’s accuracy (Fig. 6).

Results revealed that the Snow17 model performed well overall. Interestingly, it showed stronger performance at higher elevations (> 2,500 m), achieving R² values of 0.76–0.84 and nRMSE values of 0.52–0.82 km² across the different temporal scales. This accuracy can be attributed to the stable snowpack dynamics in these regions, where snow persists longer and experiences fewer rapid melt or intermittent snowfall events. The consistent accumulation and melt patterns align well with Snow17’s assumptions and energy balance calculations³⁴enabling accurate SCA simulations. These results are consistent with those of Molotch et al.⁶⁶ who reported predictable snow behavior at high-elevation due to their lower sensitivity to transient weather events. Likewise, Franz et al.³⁸ demonstrated strong correlations between Snow17 simulations and MODIS SCA. In contrast, at lower elevations (≤ 2,500 m), the model’s performance deteriorated, with R² values ranging from 0.05 to 0.68 and nRMSE values increasing to 0.93–1.60 km² (Fig. 6). Therefore, factors contributing to this reduced accuracy include transient snow cover, frequent rain-on-snow events, and limitations in MODIS data retrieval due to mixed pixels and cloud interference^67,68.

Fig. 6

Comparison of SCA from MODIS and Snow17 Simulations across three sub-basins at different time levels for low and high elevation areas.

For instance, in Ait Ouchene, where only 9.28% of its area ≤ 2,500 m, model accuracy was modest with an nRMSE of 1.60 and R² of 0.62 on the daily scale. These discrepancies align with findings by Tuel et al.¹⁵ and Lundquist and Flint⁵⁵ who highlighted the challenges of simulating snowpack dynamics at lower elevations. Tuel et al.¹⁵ reported that the Snow17 model tended to overestimate snow cover at higher elevations while underestimating it at lower elevations in HAM, pointing out potential inadequacies in the SWE to SCF parameterization.

Furthermore, it was observed that temporal aggregation significantly improved model performance. As an illustration, in Tillouguite, where 40.41% of the area lies above 2,500 m, nRMSE improved from 1.12 (daily) to 1.09 (weekly) and 0.99 (monthly), while R² increased from 0.70 to 0.73 and 0.78, respectively (Fig. 6). This trend aligns with previous studies, such as Rittger et al.⁶⁷ which found that temporal smoothing reduces variability and noise in both observations and simulations. Nevertheless, Snow17 often underestimated SCA during high snow cover periods, especially mid-winter, due to limitations in simulating deep snow and extreme events.

Among the sub-basins, Rheraya exhibited the weakest performance (e.g., R² as low as 0.05 for ≤ 2,500 m daily). This is likely due to the sub-basin’s complex terrain, characterized by a steep average slope of 16.29%, compared to 7.83% and 9.9% for Ait Ouchene and Tillouguite, respectively, as reported in⁶⁹. Additionally, sparse snow cover in Rheraya complicates accurate snow modeling in dynamic, low-elevation settings. Lundquist and Flint⁵⁵ similarly noted that Snow17 struggles to account for shading effects on solar radiation, a limitation that affects snowmelt timing in topographically complex regions. This issue is particularly relevant for predicting streamflow in warmer climates, where variations between shaded and sunlit areas become more pronounced. Consequently, future research should focus on refining model parameters, as well as SWE to fSCA parametrization to reduce biases and on exploring additional data sources.

SWE and SD analysis

The spatio-temporal analysis of snow dynamics between 2000 and 2022 (covering the period from October to May) is summarized in Fig. 7.

Figure 7-a and -b illustrate the spatial distribution of mean SWE and mean snow depth, respectively. We note that areas shaded in gray indicate regions that are snow covered, with no melt or without any snow present. Overall, the findings reveal that both SWE and SD are substantially higher in areas above 2,500 m elevation. Specifically, Tillouguite and Rheraya sub-basins illustrated SWE values exceeding 300 mm and SD surpassing 60 cm. Conversely, areas below 2,500 m showed markedly reduced values. This pattern may be attributed to the precipitation-elevation relationship and temperature lapse rate effects, which are critical factors influencing snow accumulation and ablation. These values align with those of Baba et al.²⁷who reported SWE values in Tensift ranging from 80 to 120 mm during winter months, with peaks reaching 300–400 mm during snow-abundant years like 2006/2007. However, their study also noted spatially SWE values exceeding 1,000 mm in various years including 2005/2006, 2006/2007, 2008/2009, and 2014/2015.

Additionally, Fig. 7-c and -d provide statistical insights through boxplots of total snow water storage (TSWS) and total SD, respectively across elevations ranges. It can be seen that the interquartile range was significantly broader for high-elevation regions, reflecting greater variability in snow dynamics due to seasonal and interannual changes. However, low-elevation areas demonstrated smaller interquartile ranges, with TSWS values generally falling between 0.22 and 0.25 10^10 m³. A similar was noticed for snow depth. These patterns align with previous studies^{1,13,15,18,46} who suggested the pivotal role of elevation in regulating snow accumulation and melt processes, leading to significant variations in snowpack characteristics. For instance, Marchane et al.⁴⁶ identified elevation as a key determinant of snow presence in the High Atlas Mountains, noting that snow predominantly accumulates above 2,500 m due to cooler temperatures and reduced sensitivity to transient weather events.

Fig. 7

Spatial distribution of (a) mean snow water equivalent (mm) and (b) mean snow depth (cm) during October-May (2000–2022 averages). boxplot of (c) total snow water storage (TSWS) and (d) total snow depth, and (e₁-e₃) interannual trends of TSWS by low- and high-elevations and across studied.

Figure 7-e_1-3 highlights interannual variability in TSWS (units: m³d), defined as the cumulative positive daily SWE integrated over the snow season (October–May) and across each basin’s area, following Aragon and Hill⁷⁰. This metric quantifies the basin’s snow water reservoir function by capturing both the magnitude and duration of snow storage. From Fig. 7-e_1-3, it was found that sub-basins’ TSWS fluctuated significantly via years, with a notable decline in 2010/2011 followed by a gradual increase until 2013, and then another decrease in 2015/2016 and after 2018/2019 (Fig. 7-e_1-3). Furthermore, pronounced peaks are detected in snow-abundant years, like 2008/2009, demonstrating the substantial role of high-altitude snowpacks in sustaining downstream water resources.

In comparison, it can be seen that low-elevation contributions were relatively minor and highly variable, except for 2008/2009. Notably, Ait Ouchene and Tillouguite sub-basins rarely exceed TSWS volumes of 34 Mm³ and 78 Mm³, respectively, except in years with extreme snowfall, such as 2008/2009. These values coincide with Tuel et al.¹⁵ who found that SWE peaks in the HAM exhibited extreme variability, ranging from 50 Mm³ to 450 Mm³, depending on precipitation variability and temperature sensitivity. Moreover, Tuel et al.⁶ suggested that the historical SWE peak of 125 Mm³ might be an underestimation, with scenarios incorporating enhanced precipitation or reduced temperatures suggesting values as high as 200 Mm³. Taia et al.⁴⁴ indicated that SWE simulated using SWAT can reached 140 Mm³ on Oued El Abid basin, covering Ait Ouchene and Tillouguite sub-basins.

Figure 8 suggested significant interannual variability in SWE anomalies, which is likely influenced by variations in precipitation and temperature. Positive anomalies (blue) indicate higher-than-average SWE, particularly evident in years such as, 2003/2004, 2012/2013, 2017/2018, with 2008/2009 standing out for its combination of high TSWS and positive SWE anomaly. These years align with wetter conditions driven by increased winter precipitation and delayed spring melt. Conversely, negative anomalies (red), as observed in years like 2020/2021, 2010/2011, 2001/2002, correspond to drought-like conditions, often associated with reduced snowfall or premature melt due to warmer temperatures. Besides, the extreme anomaly observed in 2019/2020 and 2021/2022 reflects a combination of exceptionally low snowfall and elevated temperatures, consistent with regional trends under climate change. Statistical analysis reveals that the average SWE anomaly over the study period is near zero (-2.1 mm), with a standard deviation of 85 mm, indicating high variability. The years 2019/2020 and 2021/2022 exhibit anomalies exceeding two standard deviations, highlighting their extremity in the dataset. Notably, high-elevation areas (> 2,500 m) consistently display greater SWE anomalies compared to low elevations (≤ 2,500 m), emphasizing the role of altitude in buffering against warming impacts. These findings align with previous studies in the High Atlas region^6,14,27,46 which reported trends of reduced snow cover and increased variability in recent decades. Remarkably, the Tillouguite sub-basin exhibits more pronounced positive anomalies compared to Ait Ouchene, suggesting enhanced snow retention due to higher elevation and colder temperatures.

Fig. 8

Annual SWE anomalies (mm) across Ait Ouchene and Tillouguite sub-basins for 2000–2022. Note that annual SWE anomalies represent deviations of hydrological-year mean SWE (October–May) from the 2000–2022. Positive and negative anomalies are in blue and red respectively.

Snowmelt and rainfall contribution to outflow

Figure 9 presents the annual and seasonal rainfall and snowmelt contributions to outflow, as simulated by Snow17 at low- and high-elevations for the period (2000–2022). Moreover, the intra-annual dynamics (day-of-year, DOY) and cumulative contributions of rainfall and snowmelt are illustrated Fig. 10.

Fig. 9

(a₁-a₄) Interannual rainfall and snowmelt contributions to outflow simulated by Snow17 at low- and high-elevations for 2000–2022. (b) boxplot analysis, and (c₁-c₄) seasonal distribution of rainfall and snowmelt contributions across studied sub-basin.

From Fig. 9, it has been found that these contributions vary significantly across sub-basins and elevation ranges, with noticeable interannual fluctuations (Fig. 9-a_1-3). Standard deviations ranging from 4.3 to 12.6% reflect this variability. During snow-poor years, snowmelt contributes much less to outflow. In contrast, during high-snow years, its contribution increases significantly, demonstrating its sensitivity to interannual climatic fluctuations^{1,5,8,13,18,27,44,71}. At low elevations (≤ 2,500 m), rainfall dominates outflow, particularly in the fall season. On average, its annual contribution ranges from 80 to 87%, depending on the sub-basin. Notably, autumnal rainfall accounted for over 98% of the outflow at Rheraya and approximately 97% at Ait Ouchene and Tillouguite. These results confirm that runoff driven by rainfall is the main component in these areas, as stated in previous research^1,5,8,27. Rainfall also plays a critical role in the early and mid-winter (November–February), with a progressive increase in cumulative contributions from October to May (Fig. 10). This trend aligns with dynamics observed in Mediterranean mountain regions, where higher temperatures and limited snow accumulation favor predominant rainfall-driven runoff^{1,5,13,18,27,44}. Conversely, snowmelt plays a more significant role at higher elevations (> 2,500 m).

As shown in Fig. 9-b and -c_1-3, snowmelt at high elevations contributes between 40% and 46% to the annual outflow, compared to only 12–19% at lower altitudes. This dynamic underscore the importance of snowmelt in sustaining water resources in mountainous regions, particularly during periods of low precipitation. In spring, snowmelt plays a major role, accounting for 55–57% of outflow in Ait Ouchene/Tillouguite and Rheraya (Fig. 9-b). This phenomenon results from snow accumulation during winter and its gradual melting in spring as temperatures rise.

Fig. 10

Day-of-year (DOY) intra-annual dynamics and cumulative of rainfall and snowmelt contributions of outflow simulated by Snow17 in low- and high-elevation for 2000–2022.

In addition to snowmelt, direct snowfall into river channels can also contribute to runoff, particularly in high-elevation regions where snowfall may accumulate directly over flowing water. While this contribution is typically minor compared to snowmelt due to the limited surface area of rivers relative to the watershed, it may become more significant in narrow, steep valleys where snow accumulates over streams. However, quantifying this effect is challenging due to the difficulty in distinguishing between direct snowfall input and subsequent meltwater contributions. Future studies could incorporate high-resolution snow distribution modeling or isotopic tracers to better assess this process. These findings align closely with previous research conducted in the High Atlas Mountains. For instance, Boudhar et al.⁵ using the Snowmelt Runoff Model (SRM), estimated that the snowmelt contribution to total annual runoff in the Rheraya Basin ranged from 30.8 to 48.6% for 2002–2005. In other basins, the contributions varied between 2.5% in R’dat and 51.4% in Ourika, depending on elevation and snow accumulation dynamics. From other mountainous regions, Lana-Renault et al.⁷¹ reported that in the Central Spanish Pyrenees, snowmelt contributes up to 50% of the annual discharge, despite the snowmelt period representing only 10–13% of yearly precipitation.

Comparison between outflow and streamflow anomalies

The distinction between outflow and streamflow is crucial in hydrological research, especially in snow-dominated regions such as the Morocco’s HAM, where intricate interactions influence water availability. Outflow, as simulated by Snow17, refers to the water generated at the source from snowmelt or rainfall runoff. In contrast, streamflow (gauged at 1000 m) represents the observed discharge measured at gauging stations, which includes additional factors such as contributions from groundwater, channel routing, evaporation, and human activities. Here, we used strandardized anomalies (Eq. 10) as these highlight deviations from the norm, thus offering clearer insights into variability and extremes.

$$\:Anomaly=\frac{{X}_{i}-\mu\:}{\sigma\:}$$

(10)

where ​ is $\:{X}_{i}$ the monthly value, is $\:\mu\:$ the 2000–2022 mean, and $\:\sigma\:$ is the standard deviation.

Figure 11 presents a comparaison between simulated outflow anomalies (for elevations above 2,500 m) and observed streamflow anomalies (recorded at ~ 1,000 m gauges) in the Ait Ouchene and Tillouguite basins. The analysis reveal important seasonal and interannual patterns in snowmelt-driven hydrology, while also highlighting notable discrepancies between high-elevation snowmelt signals and downstream flow responses. The seasonal patterns show clear snowmelt influence, with positive anomalies predominantly occurring from March to May. This springtime peak underscores the critical contribution of snowmelt to surface water availability. Interannual variability is equally evident, with wet years such as 2017/2018 displaying strong positive anomalies resulting from substantial snow accumulation, while dry years like 2006/2007 show negative anomalies due to reduced melt contributions.

Fig. 11

Outflow (dashed line, left axis, > 2500 m) and streamflow (solid line, right axis, ~ 1000 m) anomalies in (a) Ait Ouchene and (b) Tillouguite sub-basins. The blue shaded region indicates the 90% confidence interval for outflow anomalies.

Although both basins exhibit broadly similar timing in their anomalies - reflecting regional climatic influences - subtle differences emerge due to variations in local topography and microclimatic conditions. Several cases demonstrate significant mismatches between simulated outflow and observed streamflow. In Ait Ouchene during 2002/2003, the expected downstream response to a high-elevation snowmelt pulse in April-May was absent, likely due to water retention through infiltration, subsurface storage, or anthropogenic water use. The 2008/2009 period in the same basin showed an earlier streamflow peak in February, preceding the simulated snowmelt signal, suggesting important contributions from mid-elevation rainfall or melt processes not accounted for in the high-elevation model. At Tillouguite in 2006/2007, persistent negative streamflow anomalies occurred despite moderate spring outflow anomalies, potentially resulting from exceptionally dry conditions, soil moisture deficits, or limited snow accumulation at lower elevations.These findings illustrate the complex relationship between high-elevation snowmelt and downstream hydrology. Accurate prediction of streamflow responses requires consideration of numerous basin-specific factors beyond simple elevation-based snowmelt models, including storage dynamics, soil characteristics, and human water management practices.

Discussion

Downscaling and bias correction performance

Accurate representation of precipitation and temperature is critical for snow modeling, particularly in mountainous regions like the HAM, where local meteorological variability is strongly influenced by complex topography. Nonetheless, reanalysis datasets such as ERA5-Land, while valuable, have inherent limitations. Their coarse resolution (~ 9 km) often fails to capture localized extremes, such as intense snowfall or rapid temperature fluctuations, which are common in mountainous areas⁶³. Additionally, ERA5-Land tends to underestimate precipitation at higher elevations and may not fully resolve microclimatic effects driven by terrain features. These limitations can propagate through snow models, leading to inaccuracies in SWE and snowmelt-driven outflow simulations. To address these challenges, our study employed a downscaling and bias correction framework that integrated machine learning (e.g., RF and XGBoost) models and topographic variables (e.g., elevation, slope, aspect, and sun elevation). Our approach demonstrated that ML models significantly improved the accuracy of ERA5-Land precipitation and temperature inputs for the Snow17 model. Unlike linear correction approaches, these models effectively corrected precipitation underestimation at higher elevations and enhanced temperature representation by incorporating terrain-induced variations. Among the tested ML models, RF and XGBoost outperformed others, particularly for precipitation, achieving high correlations (R² = 0.83 and 0.82, respectively). These models effectively addressed the underestimation of precipitation at higher elevations and improved temperature representation by capturing nonlinear relationships and terrain-driven variability. RF models, in particular, are robust to outliers and noise, making them well-suited for regions with sparse observational data^28,30,51. Their ensemble approach minimizes overfitting and allows for accurate predictions even when input data are incomplete or noisy^30,51. The incorporation of topographic variables, such as elevation, slope, and aspect, further enhanced the models’ ability to account for terrain-driven variability, which is critical in mountainous regions. In contrast, SVR performed poorly, likely due to its sensitivity to hyperparameter tuning and limited ability to model intricate spatial variability in mountainous regions⁵². These results are consistent with previous research, which has demonstrated the effectiveness of ML models for downscaling and bias correction in diverse climatic^19,28,31,32. Despite our approach significantly improved the representation of precipitation and temperature, some limtitations remain. For instance, localized snowfall events or temperature inversions may not be adequately represented⁶³ likely due to the coarse resolution of reanalysis data and the difficulty of capturing fine-scale atmospheric processes in complex terrain. These factors can introduce biases in snowpack dynamics and melt timing. To address these limitations, future research should incorporate additional independent datasets and validation approaches (e.g., cross-validation), to further refine downscaling and bias correction processes.

Snow17 model performance and elevation dependence

In this research, the Snow17 model demonstrated strong performance in simulating SWE and outflow, particularly at elevations above 2,500 m, where snowpack dynamics are more stable⁴⁶. At these elevations, the model exhibited high agreement with observed SCA (R² = 0.76–0.84), accurately capturing snow accumulation and melt processes. However, model performance declined at lower elevations (< 2,500 m), where intermittent snow cover, frequent rain-on-snow events, and challenges in MODIS data retrieval introduced greater uncertainty. For example, in the Ait Ouchene sub-basin, where only 9.28% of the area lies above 2,500 m, the model’s accuracy was modest, with an RMSE of 1.60 km² and R² of 0.62 on a daily scale. These challenges are exacerbated by the complex terrain and vegetation cover at lower elevations, which influence snow accumulation and melt but are not explicitly accounted for in the temperature-index approach of Snow17. Quantitative assessments revealed that RMSE values increased by 30–50% at lower elevations compared to higher elevations, highlighting the need for improved model parameterization in these areas. Rain-on-snow events introduce additional variability in snow accumulation and melting rates, as rain accelerates snowmelt and alters the energy balance of the snowpack. Additionally, vegetation cover influences model accuracy by affecting snow retention, shading, and sub-canopy melt dynamics, which are not explicitly captured by Snow17.

One key limitation of Snow17 is its reliance on a temperature-index approach, which does not explicitly account for energy balance components such as radiative fluxes, turbulent heat exchanges, and sublimation^33,37. The absence of these components can lead to inaccuracies in snowpack simulations, particularly under conditions where sublimation is a major mass-loss process. Radiative fluxes significantly influence snowmelt rates, and their exclusion limits the model’s ability to capture variations due to changes in solar radiation and cloud cover. Likewise, sublimation—especially in arid and high-elevation regions like the HAM —can remove substantial amounts of snow, reducing SWE without generating runoff. Despite these limitations, Snow17 was selected in this research due to its computational efficiency, relatively low data requirements, and proven applicability in similar mountainous regions^6,15. While energy balance-based models, such as SNOWPACK (e.g²¹), provide more physically realistic simulations, they demand extensive meteorological inputs that may not always be available, particularly in data-scarce environments like the HAM. Thus, Snow17 remains a viable option for operational snow modeling in this region, though future improvements could involve integrating key physical processes to mitigate its limitations. Previous studies (e.g¹⁵), have demonstrated that incorporating a sublimation module can improve snowpack representation in semi-arid mountainous regions.

In addition, analysis of snowmelt contributions to outflow revealed significant elevation-dependent variability. At high elevations (> 2,500 m), snowmelt accounted for 40–46% of annual outflow and dominated spring runoff, contributing 55–57% of seasonal outflow. In contrast, at lower elevations, rainfall was the primary driver of outflow, contributing 80–87% annually. These findings underscore the critical role of high-altitude snowpacks in sustaining water resources in semi-arid regions such as the HAM, particularly during dry periods. For instance, during the drought year of 2021–2022, snowmelt contributions to outflow decreased by 15–20% compared to wetter years like 2007–2008, highlighting the sensitivity of snowmelt-driven outflow to interannual climatic fluctuations. This variability further emphasizes the vulnerability of regional water resources to climate change, as projected reductions in snowpack and shifts in snowmelt timing could significantly impact downstream water availability for agriculture, hydropower, and municipal supplies. Changes in snowmelt timing and volume under future climate scenarios could significantly impact downstream water availability. Earlier snowmelt onset due to rising temperatures may shift peak runoff to earlier in the season, reducing water availability during the critical summer months when demand is highest. Similarly, decreases in snow accumulation could lead to reduced seasonal runoff, exacerbating water scarcity issues.

Limitations and future improvements

The accurate assessment of snow dynamics in the High Atlas Mountains is crucial for understanding water resources and predicting their future availability^{1,5,6,8,15,21,43,46}. However, multiple challenges associated with both remote sensing data and model simulations persist. MODIS satellite observations face limitations due to cloudiness, coarse spatial resolution, and snow misclassification, especially over complex terrain where it is difficult to distinguish snow from vegetation^7,14,47. Additionally, the Snow17 model, while widely used for SWE and outflow simulations, introduces uncertainties due to its simplified parameterization^33,37. It’s reliance on temperature-index approach may not fully capture the dynamics of snowmelt, sublimation, and precipitation partitioning^15,16,33especially in regions with steep slopes and varying aspects. Key processes such as spatial variability in radiation, wind redistribution, and subsurface interactions are not explicitly accounted for, potentially leading to biases in snow accumulation and melt simulations. Besides, the model’s sensitivity to input data, such as temperature, precipitation, fractional snow cover, and elevation, further complicates its accuracy, particularly in the HAM’s unique topography¹⁵. These factors can lead to under- or overestimation of snow cover, especially in areas with intermittent or shallow snow presence. While incorporating energy balance components may enhance accuracy, the increased computational cost and data requirements may reduce the model’s feasibility for operational use. Implementing refinements to adress these issues requires careful consideration of computational trade-offs, data availability, and model complexity. To mitigate these uncertainties, robust calibration methods, bias correction methods, and hybrid approaches combining satellite data with physically based models are essential for improving accuracy. However, current limitations remain, including the absence of high-resolution in-situ data, the moderate resolution of MODIS data (500 m), and the challenges of accurately capturing local meteorological extremes using ERA5-Land reanalysis data. Future improvements could include the use of ensemble models and higher-resolution datasets to enhance input data accuracy, energy-balance-based approaches to better capture snowmelt dynamics, an expanded network of ground-based monitoring stations for more accurate validation, and advanced remote sensing technologies like Sentinel-2 for improved snow cover assessment. Finally, analyzing snowmelt variability across different climate scenarios can provide insights into its impact on downstream water resources, which is essential for future water management strategies.

Conclusions

Accurate simulations of snowpack characteristics, such as snow water equivalent and snow depth, are crucial for effective water resource management in snow-dominated regions like the HAM. This study addresses a significant gap in previous research integrating MODIS fSCA data into the Snow-17/SWE2HS models and validating modeled outflow against observed streamflow. We also addressed challenges related to biases in meteorological forcing datasets (ERA5-Land) by applying machine learning techniques with topographic variables, specifically Random Forest, which improved the spatial and temporal accuracy of downscaled precipitation and temperature data.

The Snow17 model’s performance was rigorously calibrated using DDS algorithm with NSE as objective function, which indicated a strong correlation between observed and simulated SD, with NSE values exceeding 0.84. Our findings revealed significant elevation-dependent variability in snow dynamics, with areas above 2,500 m showing substantially higher SWE and SD values compared to lower elevations. Specifically, SWE values surpassed 300 mm and SD exceeded 60 cm in the Rheraya and Tillouguite sub-basins. High-elevation regions displayed broader interquartile ranges in total snow water storage, reflecting considerable seasonal and interannual variability. Besides, our analysis of snowmelt and rainfall contributions to outflow highlighted stark contrasts between low- and high-elevation areas. In low-elevation regions (≤ 2,500 m), rainfall dominated outflow, contributing 80–87% annually, particularly peaking in autumn. Conversely, in high-elevation areas (> 2,500 m), snowmelt was critical, contributing 40–46% annually and becoming the primary driver of outflow during spring months. This interannual variability in snowmelt-driven outflow underscores the sensitivity of water resources to climatic fluctuations.

Concisely, this research demonstrates the Snow-17/SWE2HS model’s effectiveness in understanding snowmelt dynamics and its critical impact on outflow, highlighting the importance of high-altitude snowpacks in sustaining freshwater resources in HAM. For future studies, we recommend the integration of additional satellite data and the refinement of machine learning models to improve predictions and assess the impacts of climate variability on SWE and water availability.