The research region of the RRM SWE product is located in the land region north of 45∘ N (Fig. 1). This region consists of Asia, Europe, and North America. The land region covers Russia, the United States, Canada, Denmark, Norway, Iceland, Sweden, and Finland. This region has a cold climate and a wide area of snow cover.

In this study, we utilized ERA-Interim SWE data (Dee et al., 2011), GLDAS SWE data (Rodell et al., 2004), GlobSnow SWE data (Luojus et al., 2021), AMSR-E/AMSR2 SWE data (Tedesco and Jeyaratnam, 2019), and ERA5-Land SWE data (Muñoz Sabater, 2019) as the original input datasets for the fusion data (Table 1).

GlobSnow is a dataset of global snow cover and SWEs for the Northern Hemisphere released by the European Space Agency (ESA) (http://www.globsnow.info/swe/,last access: 17 February 2022) (Luojus et al., 2021; Pulliainen et al., 2020). The SWE products in this dataset combine the Canadian Meteorological Center (CMC) daily snow depth analysis data (Walker et al., 2011), ground weather site observational data, and satellite microwave radiometer data. We obtained the L3A_daily_SWE product of this dataset. The temporal resolution of the L3A_daily_SWE product is daily, the spatial resolution is 0.25∘, and the data format is netCDF4.

ERA-Interim is the fourth generation reanalysis data of the European Centre for Medium-Range Weather Forecasts (ECMWF) (Dee et al., 2011). The data provide a global assimilated numerical product of various surface and top atmospheric parameters from January 1979 to the present (https://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/, last access: 17 February 2022). We obtained the SWE dataset with a daily temporal resolution, a spatial resolution of 0.25∘, and netCDF4 data format. The spatial range of the data is the land region above 45∘ N.

The Advanced Microwave Scanning Radiometer-Earth Observation System (AMSR-E) is a microwave scanning radiometer on the Aqua satellite of the National Aeronautics and Space Administration (NASA) Earth Observation System (EOS) (Tedesco and Jeyaratnam, 2019). The AMSR-E provides a global daily SWE dataset from 19 June 2002 to 3 October 2011 (https://nsidc.org/data/ae_dysno, last access: 17 February 2022). AMSR2 is a microwave scanning radiometer on the GCOM-W1 satellite launched by the Japan Aerospace Exploration Agency (JAXA) in May 2012. AMSR2 provides a global SWE dataset from 2 July 2012 to the present (https://nsidc.org/data/AU_DySno/versions/1, last access: 17 February 2022). The spatial resolution of the AMSR-E SWE and AMSR2 SWE datasets is 25km×25 km, the temporal resolution is daily, and the data formats are HDF-EOS and HDF-EOS5, respectively.

The GLDAS is a model used to describe global land information; it contains data, such as global rainfall, water evaporation, surface runoff, underground runoff, soil moisture, surface snow cover distribution, temperature, and heat flow distribution (Rodell et al., 2004). This assimilation system includes data with spatial resolutions of 1∘×1∘ and 0.25∘×0.25∘ and temporal resolutions of 3 h, 1 d, and 1 month. The GLDAS data are available for download from the Goddard Earth Sciences Data and Information Services Center (GES DISC). We obtain an SWE dataset with a daily temporal resolution, 0.25∘ spatial resolution, and netCDF4 data format.

ERA5-Land is a reanalysis dataset that provides the evolution of global land parameter data from 1981 onwards (Muñoz Sabater, 2019). The dataset provides eight types of snow parameter data, including snow albedo, snow cover, snow depth, snowfall, the temperature of the snow layer, snowmelt, snow density, and SWE. This dataset provides a global SWE dataset with an hourly spatial resolution, a temporal resolution of 0.1∘×0.1∘, a temporal coverage of January 1981 to the present, and data formats of GRIB (General Regularly-distributed Information in Binary form) and netCDF4.

To maintain consistency in the spatial and temporal resolutions of the fused data, we unified the ERA-Interim SWE data, GLDAS SWE data, GlobSnow SWE data, AMSR-E/AMSR2 SWE data, and ERA5-Land SWE data into a daily temporal resolution, with a spatial resolution of 0.25∘ and geographic projection of the North Pole Lambert azimuthal equal area.

In this study, we utilize the ridge regression model of a machine learning algorithm to fuse ERA-Interim SWE data (Dee et al., 2011), GLDAS SWE data (Rodell et al., 2004), GlobSnow SWE data (Luojus et al., 2021), AMSR-E/AMSR2 SWE data (Tedesco and Jeyaratnam, 2019), and ERA5-Land SWE data (Muñoz Sabater, 2019) to generate a set of new RRM SWE datasets. The target reference data in this study are the HSSC dataset and Russian snow survey data. The digital elevation model (DEM) was used as an important environmental feature input to the ridge regression model and was included in the model training. The DEM is an auxiliary terrain feature variable in addition to the five SWE prediction feature variables: AMSR-E/AMSR2 SWE, ERA-Interim SWE, GLDAS SWE, GlobSnow SWE, and ERA5-Land SWE.

The ridge regression model is a biased estimate regression method for collinear data analysis (Friedman et al., 2010; Hoerl and Kennard, 1970b, a). By abandoning the unbiasedness of the ordinary least squares, this algorithm can obtain the regression method in which the regression coefficient is more practical and reliable at the cost of losing part of the information and reducing the accuracy. The ridge regression model is flexible in the choice of predictor variables and does not require the predictor and target variables to be independent of each other. It can effectively solve the multicollinearity problem of predictor and target variables, as well as reduce the impact of this problem on the training model (Duzan and Shariff, 2015; Saleh et al., 2019). Generally, reanalysis data based on SWE products cannot make the products and models independent of each other; i.e., they are prone to multicollinearity, which leads to distorted model estimation or difficulty in performing accurate estimations. In contrast, the ridge regression model can successfully solve the multicollinearity problem, i.e., the independence of training products and models. In addition, when integrating multiple SWE products, the accuracy of each SWE dataset is likely to differ. A small change in one of the SWE products involved in the training will cause a significant error in the final calculation results, while the ridge regression model has high accuracy and stability for these “ill-conditioned” SWE data. In addition, the main advantage of this model is that SWE products with long time series and large spatial scales are easy to prepare. The principle equation of the ridge regression model is defined as follows: 1β^ridge=argminβ∑i=1Nyi-β0-∑j=1pxijβj2+λ∑j=1pβj2, where β^ridge is the extremum solution function of ridge regression; p is the number of gridded SWE product variables involved in training; xi are the prediction feature variables, which contain two parts: one set contains the main feature variables of the gridded SWE products, and the other part consists of the DEM auxiliary feature variables; yi is the observed SWE; λ, β, βj, and β0 are the parameters to be solved; 1,…,N is the sample of the training dataset; and λ∑j=1pβj2 is the penalty function term. The total number of samples N in the training dataset is 271 651. The sample sizes of the training dataset, validation dataset, and test dataset are divided according to the ratio of 7:2:1, where the numbers of training set, validation set and test set samples are 271 651, 77 614, and 38 807, respectively. The model is developed in Python3, and the model framework is based on the “scikit-learn” machine learning library (https://scikit-learn.org/stable/index.html, last access: 17 February 2022). The code is available upon request.

The integration process of the RRM SWE product (Fig. 2) is described as follows:

The original ERA-Interim SWE data, GLDAS SWE data, GlobSnow SWE data, AMSR-E/AMSR2 SWE data, ERA5-Land SWE data, DEM data, unified temporal resolution, spatial resolution, projection, spatial range, and unit are preprocessed.

In this study, the accuracies of the RRM SWE, AMSR-E/AMSR2 SWE, ERA-Interim SWE, GLDAS SWE, GlobSnow SWE, and ERA5-Land SWE were compared using test datasets from 2015 to 2018. MAE, RMSE, R, and R2 were used to reflect the data quality of each SWE product. In addition, we compared the RRM SWE product with the SWE dataset obtained by the multisource data average method.

According to the verification results in Fig. 3 and Table 2, the RRM SWE data have the best overall accuracy, and the MAE, RMSE, R, and R2 between the observed SWEs are 0.21, 25.37 mm, 0.89, and 0.79, respectively. The overall accuracy of the GlobSnow SWE and ERA5-Land SWE products is higher than that of other SWE products. The overall deviation of the ERA5-Land SWE products is the smallest except for the RRM SWE data, with MAE and RMSE values of 0.32 and 37.02 mm, respectively. The correlation between the ERA5-Land SWE and observed SWE is the highest except for the RRM SWE data, with R and R2 values of 0.84 and 0.71, respectively. Although the overall deviation between the GlobSnow SWE dataset and the measured SWE is small, its correlation with the measured value is low. The overall deviation between the ERA5-Land SWE dataset and the measured SWE is higher than that of the GlobSnow SWE dataset, but its estimation accuracy for the high-value region of the SWE is low. In addition, the overall accuracy of the ERA-Interim SWE dataset and GLDAS SWE dataset is relatively low, but their integrities are higher than those of the GlobSnow SWE dataset and AMSR-E/AMSR2 SWE dataset in terms of temporal and spatial series. The AMSR-E/AMSR2 SWE dataset has a higher estimation accuracy for the low-value SWE region. Moreover, in the land region above 45∘ N, most of the existing SWE data products with regard to temporal and spatial degrees are missing to various degrees. Obviously, the accuracies of the existing SWE products were uneven as no type of SWE dataset is perfect.

The verification results also indicate the following ranking orders.

The MAE ranking order is RRM SWE < GlobSnow SWE = ERA5-Land SWE < ERA-Interim SWE < multisource data average SWE < AMSR-E/AMSR2 SWE < GLDAS SWE.

The RMSE ranking order is RRM SWE < ERA5-Land SWE < GlobSnow SWE < ERA-Interim SWE < multisource data average SWE < AMSR-E/AMSR2 SWE < GLDAS SWE.

The R ranking order is RRM SWE > ERA5-Land SWE > GlobSnow SWE > ERA-Interim SWE > GLDAS SWE > multisource data average SWE > AMSR-E/AMSR2 SWE.

The R2 ranking order is RRM SWE > ERA5-Land SWE > GlobSnow SWE > ERA-Interim SWE > GLDAS SWE > multisource data average SWE > AMSR-E/AMSR2 SWE.

Compared with the ERA-Interim SWE, AMSR-E/AMSR2 SWE, GLDAS SWE, GlobSnow SWE, ERA5-Land SWE, and multisource data average SWE, the MAE of the RRM SWE and observed SWE is reduced by 0.22, 0.28, 0.37, 0.11, 0.11, and 0.23, respectively. The RMSE of the RRM SWE and observed SWE is reduced by 21.44, 27.02, 39.88, 15.62, 11.65, and 26.63 mm, respectively. The correlation coefficients of the RRM SWE and observed SWE are improved by 0.20, 0.42, 0.37, 0.19, 0.05, and 0.38, respectively. The coefficient of determination of the RRM SWE and observed SWE is improved by 0.31, 0.57, 0.52, 0.30, 0.08, and 0.53, respectively. Although the multisource data average method can improve the accuracy of SWE products to some extent (better than AMSR-E/AMSR2 SWE and GLDAS SWE), the improvement of this method is still very limited. The RRM SWE product has a significant advantage over the multisource data average method, and its accuracy is much higher than that of the simple multisource data average method (Table 2). Based on the above verification results, the accuracy of the RRM SWE is significantly improved; the RRM SWE dataset has higher accuracy than that of any single grid SWE dataset, and it also fills the gap in the original SWE data in terms of spatial and temporal resolutions.

Based on the kernel density estimation method, we analyzed the density distribution of different SWE datasets (Fig. 4). The results show that the RRM SWE dataset is closer to the 1:1 line and has the highest accuracy. The RRM SWE dataset is particularly accurate for SWE estimation in the low-value region, and the test data are concentrated near the 1:1 line in the high-density region (kernel density estimation >0.00015) (Fig. 4). In contrast, the high-density regions of the GLDAS SWE dataset, ERA-Interim SWE dataset, and AMSR-E/AMSR2 SWE dataset deviate significantly from the 1:1 line, resulting in poor accuracy. The AMSR-E/AMSR2 SWE, GLDAS SWE, and GlobSnow SWE are underestimated relative to the SWE measured at the site, among which GLDAS SWE underestimated the observed SWE the most seriously, while ERA5-Land SWE overestimated the observed SWE. Although the accuracies of GlobSnow SWE and ERA5-Land SWE are relatively high, their dispersion degrees are large (the kernel density estimation for most test data is less than 0.0001). Overall, the RRM SWE data have a higher overall estimation accuracy, especially for the low-value area of SWE. For an SWE above 400 mm, the MAE and RMSE of the RRM SWE product and the measured SWE are 0.35 and 43.57 mm, respectively. The estimation accuracy of the RRM SWE product for the high-value range of SWE (SWE>400 mm) is lower than that for the low-value range of SWE (SWE<400 mm) (Fig. 4). The main reason for this is that the training accuracy of the RRM model for the high-value range of SWE is affected by the small number of stations that observe the high-value range of SWE.

However, in this study, there are still some uncertainties in the ridge regression machine learning algorithm that integrates SWE products. First, this model is strongly dependent on on-site observational data, and the fusion precision of SWE is poor in some areas with sparse observational stations. The fusion accuracy of SWE products will be affected to a certain extent without considering the prior snow cover information. The RRM SWE product is still underestimated in cases of high SWE. Then, in addition to the DEM, meteorological elements, Normalized Difference Vegetation Index (NDVI), land type, and other factors will affect the SWE estimation. Unfortunately, our current RRM presented here does not consider these factors as predictors, which is a limitation of the current RRM SWE product. Finally, in complex terrain with an elevation interval >1000 m, the RRM SWE product performed poorly, with an RMSE of 31.14 mm (Fig. 5), and the integration of SWE products remains challenging (Mortimer et al., 2020).

The accuracy of each SWE product is not absolute at different altitude gradients based on evaluations of the AMSR-E/AMSR2 SWE, ERA-Interim SWE, GLDAS SWE, GlobSnow SWE, and ERA5-Land SWE product accuracies (Fig. 5). The accuracy of a single SWE product is different from its overall accuracy. We consider the influence of altitude in the algorithm and make full use of the accuracy advantage of each SWE data for different altitude gradients.

The above verification results show that the MAE, RMSE, R, and R2 between the RRM SWE product and measured SWE perform well at altitude gradients of <100, 100–200, 200–300, 300–400, 400–500, 500–600, 600–700, 700–800, 800–900, 900–1000, and >1000 m (Fig. 5). Overall, the RRM SWE product has the highest accuracy in the elevation intervals of <100, 100–200, 200–300, 400–500, 500–600, 600–700, 700–800, 800–900, and >1000 m. The RRM SWE product itself has the best performance in the elevation interval <100 m. The ERA5-Land product has the best performance in the elevation interval 300–400 m. The GlobSnow product has the best performance in the elevation interval 900–1000 m.

The RRM SWE product has good performance in different regions, and its RMSEs in Russia, Canada, and Finland are 26.39, 29.31, and 25.29 mm, respectively; additionally, the performance of the RRM SWE product in different regions is basically similar (Table 3). The RRM SWE product performs well not only at different altitudes but also in different regions, and it has good stability.

A comparison of the spatially distributed annual average SWE distributions is made between the RRM SWE and AMSR-E/AMSR2 SWE, ERA-Interim SWE, GLDAS SWE, GlobSnow SWE, and ERA5-Land SWE in 2014, 2015, 2016, and 2017, and their spatial distribution patterns are shown in Fig. 6.

Overall, the RRM SWE dataset, AMSR-E/AMSR2 SWE dataset, ERA-Interim SWE dataset, GLDAS SWE dataset, GlobSnow SWE dataset, and ERA5-Land SWE dataset have similar spatial distribution patterns in the land region above 45∘ N, showing a trend of lower SWE at low latitudes and higher SWE at high latitudes. The AMSR-E/AMSR2 SWE dataset covers a limited extent in the land region above 45∘ N, many data points are missing, and low SWE values exist at low latitudes. In northern Siberia, the ERA-Interim SWE product has a higher SWE, and there are many abnormal, extreme SWE values (SWE>500 mm) in this dataset. In low-latitude regions, such as Alaska, northern Siberia, and the easternmost region of Russia, the SWE of GLDAS SWE products is significantly lower. The GlobSnow SWE product lacks SWE data for Greenland, and this dataset has low SWEs in the regions of Baffin Island, Koryak Mountains, Kamchatka Peninsula, and Alaska. The ERA5-Land SWE products have low SWEs in northeastern Russia, Scandinavia, and northeastern Canada. The RRM SWE dataset is more reasonable for estimating the spatial distribution of SWE in the land region above 45∘ N, and the data integrity is higher. Moreover, based on the new machine learning algorithm, a variety of SWE data products in different time series are fused, which makes the RRM SWE dataset completely temporally and spatially continuous.

The relative difference between the RRM SWE data and GLDAS SWE data is the highest, and the relative difference is greater than 80 % in most low altitude regions (Fig. 7). The relative difference between the RRM SWE data and the GlobSnow SWE data is relatively small overall, especially in most high-latitude areas where the relative difference is less than 10 % (Fig. 7). Overall, the annual average relative differences in the RRM SWE data and AMSR2 SWE, ERA-Interim SWE, GLDAS SWE, GlobSnow SWE, and ERA5-Land SWE are 37 %, 41 %, 54 %, 25 %, and 29 %, respectively (Fig. 7). Previous studies have shown that the accuracy of the SWE in the Northern Hemisphere estimated by GlobSnow SWE data is higher (Pulliainen et al., 2020), while the spatial distribution pattern of the RRM SWE data is close to the estimation result of GlobSnow SWE. In addition, the single point verification results based on the measured SWE data of meteorological stations in Sect. 3.1 show that the RRM SWE dataset has higher accuracy than the GlobSnow SWE dataset. The RRM SWE dataset has good accuracy.

Based on the Mann–Kendall trend test, we analyzed the changing trend in the region-wide annual average SWE of the AMSR-E/AMSR2 SWE, ERA-Interim SWE, GLDAS SWE, GlobSnow SWE, ERA5-Land SWE, and RRM SWE in the land region above 45∘ N from 1979 to 2019.

Based on the Mann–Kendall trend test (see Fig. 8 and Table 4), from 1979 to 2019, the test value of the ERA-Interim region-wide annual average SWE is 1.08, and there is no significant change trend under the significance test level of 0.05. The test value of the GLDAS region-wide annual average SWE was 4.95 and showed a significant increasing trend at the significance test level of 0.05. The test values of the AMSR-E/AMSR2 annual average SWE, GlobSnow annual average SWE, ERA5-Land annual average SWE, and RRM annual average SWE are -3.26, -2.54, -3.43, and -3.00, respectively, and these four SWEs showed a significant decreasing trend at the significance test level of 0.05. Based on the analysis of the RRM SWE product, between 1979 and 2019, the region-wide annual average SWE in the land region above 45∘ N decreased by 15.1 %. In the Northern Hemisphere, spring snow cover extent has decreased significantly, according to the Fifth Assessment Report (AR5) of the IPCC. Between 1967 and 2010, the spring snow cover extent decreased by an average of 1.6 % per decade, while the June snow cover extent decreased by 11.7 % per decade (Stocker, 2014). Most studies have shown that the annual variation tendency of snow depth and snow cover extent showed a significant decreasing trend in the Northern Hemisphere (Brutel-Vuilmet et al., 2013), which is consistent with the annual variation tendency of the RRM SWE dataset. This dataset can reflect the characteristics of snow cover change in the land region above 45∘ N in light of climate change and can be used as the driving data for climate models to support climate-change-related research. In addition, this dataset is expected to provide a snow data basis for the study of “Arctic amplification”.