Snow density plays a critical role in estimating water
resources and predicting natural disasters such as floods, avalanches, and
snowstorms. However, gridded products for snow density are lacking for
understanding its spatiotemporal patterns. In this study, considering the
strong spatiotemporal heterogeneity of snow density, as well as the weak and
nonlinear relationship between snow density and the meteorological,
topographic, vegetation, and snow variables, the geographically and
temporally weighted neural network (GTWNN) model is constructed for
estimating daily snow density in China from 2013 to 2020, with the support
of satellite, ground, and reanalysis data. The leaf area index of high
vegetation, total precipitation, snow depth, and topographic variables are
found to be closely related to snow density among the 20 potentially
influencing variables. The 10-fold cross-validation results show that the
GTWNN model achieves an

Seasonal snow cover occupies an important position in the global surface energy balance, hydrological cycle, and climate system (Bormann et al., 2018; Hall and Qu, 2006; Hernández et al., 2015; Li et al., 2018), which accounts for approximately 50 % of the land area in winter in the Northern Hemisphere (Frei and Robinson, 1999). Snowmelt water not only provides fresh water for one-sixth of the world's population, but also affects agriculture and ecosystems downstream (Barnett et al., 2005). Snow density is an important variable of snowpack, which influences the thermal, mechanical, and optical properties of snow layers (Surendar et al., 2015). It plays an important role in predicting natural disasters such as floods, avalanches, and snowstorms, establishing hydrological models, as well as water resource management (Fayad et al., 2017; Judson and Doesken, 2000; Roebber et al., 2003; Schweizer et al., 2003).

Snow water equivalent (SWE) is critical for evaluating the contribution of snow cover to water resources (Niedzielski et al., 2019; Varade et al., 2020), which can be obtained by multiplying snow depth (SD) and snow density. Since the 1970s, algorithms for retrieving SD using passive microwave remote sensing have been continuously optimized (Chang et al., 1987; Gharaei-Manesh et al., 2016; Pulliainen et al., 1999). However, the SWE products obtained by passive microwave remote sensing are mostly produced with a fixed value of snow density (Che et al., 2016; Pulliainen et al., 2020), due to the limited knowledge of snow density distribution. The snow density changes with time, and there is also strong spatial heterogeneity (Yang et al., 2019; Zhong et al., 2014). Snow density serves as a key variable for the accuracy of SWE products (McCreight and Small, 2014; Zaremehrjardy et al., 2021). For example, Yang et al. (2020) evaluated the accuracy of the GlobSnow-2 SWE product and found that using a fixed snow density would result in overestimated SWE in China. Therefore, the daily gridded snow density product will benefit for the estimation of SWE.

The fresh snow density is determined by the environment of falling snow, such as air temperature, relative humidity, and air pressure. After that, the size, shape, and packing of snow crystals are affected by the accumulation, sublimation, and melting of snow crystals on the surface, which leads to changes in snow density (Nakaya, 1951; Roebber et al., 2003). Snow density will also increase with snow age and SD due to the metamorphism and compaction, and the change rate is mainly influenced by melt–refreeze events and wind erosion (Bormann et al., 2013; Meløysund et al., 2007). For example, the snow density in Northwest and Northeast China from 1999 to 2008 was found to be closely related to SD, as indicated by stepwise regression analysis of snow density and temperature, precipitation, SD, and wind speed (Dai and Che, 2011).

The terrain and surface types also play an important role in snow density
(Clark et al., 2011; Judson and Doesken, 2000). For example, snow density of
tundra snow was found to be lower at higher elevations and even decreased
by approximately 0.006 g cm

The spatial and temporal differences in the distribution of multiple complex influencing variables result in obvious spatiotemporal heterogeneity of snow density. In the former USSR, snow density will increase with latitude, while the snow density of the Altai Mountains in China is more related to longitude (Zhong et al., 2014, 2021b). The average snow density shows obvious inter-monthly variation in the three major seasonal snow cover areas of China from 1957 to 2009 (Ma and Qin, 2012), and the monthly maximum snow density moved from north to south from October to January (Dai and Che, 2011). Moreover, this spatiotemporal heterogeneity is also reflected in the relationship between snow density and its influencing factors. The SD is often used to estimate snow density by different models (Lundberg et al., 2006; Sturm et al., 2010). However, the relationship between them is not robust in different time and space, where the positive and negative relationship and the significance of correlation coefficient vary greatly at small scales (López-Moreno et al., 2013).

To understand the spatiotemporal heterogeneity of snow density, people often use the ground observation data, but it is difficult to achieve large-scale monitoring due to the complex environment and limited number of the stations. One method to explain the spatial and temporal variations in snow density is to use a physical model, such as the coupled energy and mass-balance model ISNOBAL (Hedrick et al., 2018; Marks et al., 1999), which can explicitly simulate a number of snowpack properties including snow density and SWE at the regional scale, and add a physical basis of energy exchange in the snowpack. However, snow density physical models are complex and cannot achieve large-scale spatialization of snow density (Raleigh and Small, 2017). Another common method is to use statistical models trained by the climatic and snow variables to produce a snow density map, such as multiple linear regression (MLR) and binary regression tree analysis (Meløysund et al., 2007; Mizukami and Perica, 2008; Wetlaufer et al., 2016). However, the simple statistical models may not well capture the complicated nonlinear relationship of multiple influencing variables for snow density. More importantly, the models were mostly constructed for each observation independently and neglected the spatiotemporal heterogeneity of snow density as well as the relationship to its influencing variables.

Geographically weighted regression (GWR) is a model that considers spatial heterogeneity by using local multiple linear regression technology (Fotheringham et al., 1998). To further incorporate temporal dependency, the geographically and temporally weighted regression (GTWR) model has been introduced for many disciplines, such as meteorology, hydrology, and social economics (Chen et al., 2017; He and Huang, 2018; Huang et al., 2010). The machine learning approaches such as random forests (RF) (Breiman, 2001) and general regression neural network (GRNN) (Specht, 1991) have become popular to fit nonlinear relationships, and it is in the initial stage for estimating snow density (Broxton et al., 2019). We can incorporate geographical and temporal weights into a neural network model to capture the spatiotemporally variable and nonlinear relationship between snow density and its influencing variables. In addition, considering the impact of different influencing variables, the satellite data can provide information on the snow-related and topography-related variables, and the reanalysis data can provide information on the meteorology-related variables for estimating snow density based on the true value provided by ground observations. Consequently, to achieve large-scale snow density mapping, we can develop a geographically and temporally weighted neural network (GTWNN) model by considering the multiple influencing variables with the support of satellite, ground, and reanalysis data, which not only considers the spatiotemporal heterogeneity for snow density, but also explains the nonlinear relationship between snow density and different influencing variables.

The main objectives of this study are (1) to develop a GTWNN model for improving snow density mapping by addressing the spatiotemporal heterogeneity and capturing the nonlinear relationship between snow density and its influencing variables; (2) to validate the effectiveness of the proposed model in various situations and to understand the relationship between snow density and its influencing variables; and (3) to achieve daily snow density mapping by integrating satellite, ground, and reanalysis data and to understand the spatiotemporal pattern of snow density in China.

We aim to achieve snow density mapping in China, where Xinjiang, Northeast
China–Inner Mongolia, and the Tibetan Plateau are the three major regions with
stable seasonal snow cover, covering a total area of approximately 4 200 000 km

Spatial distribution of collected ground observations of snow density.

The ECMWF ERA-5 land hourly dataset is adopted to provide data on
meteorological variables, vegetation variables, and some snow variables,
which is a climate reanalysis dataset providing a consistent view of the
evolution of land variables over several decades at a spatial resolution of

The satellite products of snow albedo (SA), snow depth (SD), and snow cover
area (SCA) from 2013 to 2020 are collected from the National Cryosphere
Desert Data Center (

The topographical variables of elevation are obtained from the Shuttle Radar Topography Mission (SRTM) digital elevation model with a spatial resolution of 30 m, and then slope and aspect are derived based on the elevation.

Three kinds of data are used, including ground observation data, satellite data, and reanalysis data, where the ground observation data are used to provide the true value of snow density, and the satellite and reanalysis data are used to provide information of different influencing variables of snow density. Before the model development, data pre-processing is conducted. Firstly, since the spatial resolution varies among the different influencing variables on snow density, they are resampled to 25 km for snow density mapping using average or accumulation resampling methods depending on the data type. The spatial resolution of 25 km is determined to match that of most SD and SWE products by passive microwave remote sensing. The elevation and slope are resampled to 25 km by average, and the standard deviation of elevation (ELEVATION_STD) and slope (SLOPE_STD) are also calculated to reflect the topographic relief within the range of 25 km. Accordingly, the ground observations of snow density measured at multiple sites are averaged for each 25 km grid cell. In addition, to eliminate the influence of different dimensions, the min–max normalization method is applied to normalize different influencing variables except for MCD12Q1 data. After that, we collect 16 935 samples for model establishment and validation, where a sample refers to a grid cell with ground observations of snow density and its influencing variables.

The GTWNN model is a spatiotemporally aware model composed of a
geographically and temporally weighted (GTW) model to capture spatiotemporal
heterogeneity and a generalized regression neural network (GRNN) to deal
with the weak and nonlinear relationships between snow density and its
influencing variables, including the meteorological variables, topographical
variables, vegetation variables, and snow variables, which could be
expressed as shown in Eq. (1), and its schematic is shown in Fig. 2.

Schematic of the GTWNN model for the estimation of snow density, where GTW refers to the geographically and temporally weighted, and GRNN refers to the generalized regression neural network.

The GTW model explores the spatiotemporal heterogeneity through local
weighting, which can assess the impact of sample points on prediction points
in terms of the spatial and temporal distances (Fig. 2). The weight of
each sample point is calculated by the commonly used bi-square function (Guo
et al., 2008), as shown in Eqs. (2) and (3).

A common GRNN architecture consists of four layers (Li et al., 2020), as
shown in Fig. 2. The first layer is the input layer receiving the
influencing parameters

There are three essential parameters in the GTWNN model, including the
spatiotemporal bandwidth

In addition, the coefficient of determination (

Snow density has strong spatiotemporal heterogeneity, and we calculated statistics of the 16 935 samples generated from ground observations in terms of the snow density and the number of observations in different years, months, and snow cover regions, as shown in Fig. 3, which show the dispersion and variation fluctuations in snow density and can be used to verify the results of snow density mapping.

Descriptive statistics of the snow density and the number of
ground observations in different years

The snow density averaged in China from 2013 to 2020 is 0.140 g cm

In addition to the spatiotemporal variation in snow density, the number of ground observations also varies. The number of observation samples from 2013 to 2018 ranged from 2250 to 3250 but decreased to less than 750 in 2019 and 2020, mainly because of the lack of observations at many meteorological stations. The number of observation samples varies in different months mainly because of the richness of snow, which is higher in the snow stable period than in other periods. The number of observation samples varies spatially mainly because of the distribution of meteorological stations, where Northeast China–Inner Mongolia has the most stations, followed by Xinjiang and the Tibetan Plateau.

The Pearson correlation coefficient between snow density and its influencing variables is calculated to indicate the importance of the variables in each month, as shown in Fig. 4a, where September and May are not included because of the small number of ground observations. The influencing variables and the corresponding correlation coefficient values are various in different months because of the heterogeneity of snow. In addition, we calculate the average value from October to April for the positive and negative correlation coefficients, respectively, to indicate the importance of each influencing variable for snow density. We also count the number of months with positive or negative correlations and mark the correlations that appear in more months as “main correlation”, to clearly show the relationship between snow density and different influencing variables, as shown in Fig. 4b. In general, the correlations between snow density and all influencing variables are very weak, with the maximum average correlation coefficient of only 0.123, which indicates the great difficulty for the estimation task of snow density.

Correlation coefficients between snow density and its influencing
variables in each month

For the eight snow variables, SD shows apparently higher importance because it has the larger average correlation coefficient of 0.087, followed by ES and SMLT with an average correlation coefficient of 0.082. It is noted that snow density is mainly negatively correlated with SF, SA, and SCD, and positively correlated with other snow variables, indicating that the less new snowfall, more snowmelt, and deeper snow depth tend to have higher snow density. Among the five meteorological variables, TP has the highest average correlation coefficient of 0.110, indicating that higher precipitation can increase snow density. All five topographical variables show high positive correlation, with an average correlation coefficient value of approximately 0.1. Surprisingly, the variable LAI_HV has the largest positive correlation coefficient among all the variables, indicating the importance of vegetation for snow density estimation. In summary, LAI_HV has the strongest correlation with snow density, followed by the TP, SD, and topographic variables among the 20 variables.

The snow density estimation accuracies of the GTWNN model are assessed over China (Fig. 5a) and different snow cover regions, including Xinjiang (Fig. 5c), the Tibetan Plateau (Fig. 5d), Northeast China–Inner Mongolia (Fig. 5e), and other areas with instantaneous snow cover (Fig. 5f). To clearly present the snow density errors between estimated values and observed values, the frequency of errors together with the Gaussian fitting curve are calculated and shown in Fig. 5b.

Accuracies of the estimated snow density in China

Figure 5a shows that the

Among the three stable seasonal snow cover regions, Xinjiang achieves the
highest

The snow density estimation accuracies of each month are assessed over the
entire study area to reveal the effectiveness of the GTWNN model in different
months, as shown in Table 1. In the snow season, the snow stable period
achieves the best estimation performance with

Accuracies of snow density estimation in different months.

The accuracies in the snow accumulation and snowmelt period are inferior to those in the snow stable period, which is mainly caused by the relatively rapid changes in snow as well as the sparser observations, especially for the months of October, April, and May. It is noted that the observation error cannot be ignored, which may be caused by less snow in the early stage of snow accumulation period, or the large water content in the snowmelt period, making the observation more difficult. The accuracies in November and March are apparently higher than those in October, April, and May, mainly because the snow in these 2 months does not change so fast. The accuracies in September are not involved in the analysis because there are only 11 observations.

According to above results, we can safely conclude that the snow density estimation achieves the best performance in the snow stable period over the entire study area, and the estimations in November and March are also acceptable considering both the accuracies and the number of observations.

Furthermore, to clearly reveal the monthly accuracies of the GTWNN model in different snow cover regions, the snow density estimation accuracies for each snow period and part of the months are assessed in different snow cover regions, as shown in Fig. 6.

Accuracies of snow density estimation in different snow periods

In different snow periods, the snow stable period also achieves the highest

We choose the three months of the snow stable period and November and March to analyze monthly accuracies in different regions because of the relatively higher overall accuracies in these months, as shown in Table 1, and the results are shown in Fig. 6b. In most cases, the accuracies in Xinjiang, Northeast China–Inner Mongolia, and other areas of China first increase and then decrease from November to March and achieve the highest accuracies in January or February, when the snow cover is plentiful and stable. However, the accuracy on the Tibetan Plateau changes oppositely and achieves the highest accuracy in November because of the specialty of the snow amount changes within a year, as discussed above.

Therefore, we conclude that the accuracies of the GTWNN model are generally
related to the stability and the amount of snow. The snow density
estimations achieve the highest

The GTWNN model is compared with five other regression models to demonstrate
its advantages for snow density estimation by capturing the spatiotemporal
heterogeneity of snow density and its nonlinear relationship to influencing
variables, as shown in Table 2. The models involved for comparison include
the multiple linear regression (R) model, geographically weighted regression
(GWR) model, geographically and temporally weighted regression (GTWR) model,
general regression neural network (GRNN) model, and geographically weighted
neural network (GWNN) model. It is noted that the original R and GRNN models
are global regression models established on all samples, regardless of the
geographical and temporal weights. The R model captures the linear
relationship between snow density and its influencing variables, and the
GRNN has nonlinear mapping ability (Specht, 1991). Meanwhile, the GWR
(Fotheringham et al., 1998) and GWNN models are spatial local models
constructed from R and GRNN by setting a bandwidth

Accuracies of various regression models for estimating daily snow density.

The accuracies achieved by GTWNN are apparently higher than those achieved by GRNN and GWNN, which demonstrates the effectiveness of both the spatial and temporal dependences on improving the estimation of heterogeneous snow density. It is noted that the GWNN performs inferiorly to the GRNN model with only spatial dependence, which may be caused by the sparse distribution of the stations and indirectly suggests that the temporal dependency makes a notable contribution to improving the GRNN model. The similar accuracy differences among R, GWR, and GTWR also demonstrate the importance of the spatial and temporal dependences for snow density estimation.

Comparing the GTWNN, GWNN, and GRNN models with the GTWR, GWR, and R models, the former three models based on GRNN achieve apparently higher accuracies than the latter three models based on R. The accuracy differences mainly come from the difference between the base regression models GRNN and R, where R is a linear model and GRNN can model nonlinear relationships. Considering that the correlation coefficients between snow density and its influencing variables are relatively weak, the results show that the nonlinear GRNN models can better overcome the weak correlations than the linear R models.

The reanalysis product ERA-5 also provides gridded daily snow density data, which are produced by comprehensively considering various influencing variables, such as snow pressure, viscosity, near surface air temperature, and wind speed (Muñoz-Sabater, 2019). We compare the snow density estimated by the GTWNN model and that in ERA-5, and the results are shown in Fig. 7.

In Fig. 7a, the

Accuracies of the ERA-5 snow density product in the study area

The spatial distribution of snow density in different snow periods and the entire snow season in China are mapped and shown in Fig. 8a–d by calculating the average of the daily snow density estimated by the GTWNN model from 2013 to 2020. It is noted that the estimated daily snow density maps are masked by the daily snow cover product to remove the non-snow pixels (Hao et al., 2021b). In addition, to understand the spatiotemporal heterogeneity of snow density, we also calculate the mean snow density and coefficient of variation (CV) in different snow periods and regions, as shown in Fig. 8e and f.

Spatial distribution of mean snow density in different snow
periods in China from 2013 to 2020, including the snow accumulation period

In the snow accumulation period, the mean snow density is generally lower
than 0.13 g cm

The mean CV of snow density generally increases across China from the snow accumulation period (0.170) to the snowmelt period (0.192), as shown in Fig. 8f. However, the CV in different snow cover regions varies apparently. It continuously decreases in Xinjiang and the Tibetan Plateau from the snow accumulation period to the snowmelt period. However, the CV in Northeast China–Inner Mongolia achieves the lowest in the snow stable period, but that of the other area reaches the highest in the snow stable period, which may be related to the different snow classes, and the surface type, elevation, and altitude will also affect the variety of snow density. Totally in the whole snow season, Xinjiang shows the lowest CV, and Northeast China–Inner Mongolia has the largest CV among the three snow cover regions.

To reflect the monthly change in snow density in different snow cover regions, we calculate the mean snow density in each month of the snow season from January 2013 to December 2020, as shown in Fig. 9a–e, as well as the monthly mean snow density of the 8 years, as shown in Fig. 9f.

Mean snow density in each month of the snow season from January
2013 to December 2020 in different snow cover regions, including Xinjiang

Figure 9a–e shows that the snow density in different regions as well as the entire study area tends to increase from the start of snow accumulation to the peak and then decrease until the late snowmelt period in each year. In the snow accumulation and stable periods, snow density increases with the snow accumulation and mechanical compaction. In the early snowmelt period, snow surface melt decreases snow depth while increasing snow density via meltwater percolation, and then, most of the snow melts into water and the snow density decreases (McCreight and Small, 2014).

However, the snow density fluctuations appear different over time and space. Specifically, the months with the maximum and minimum snow density are various in different regions, which may be related to the climatic conditions. The monthly changes in Xinjiang and the Tibetan Plateau are similar and apparently different from those in Northeast China–Inner Mongolia, which is because the temperature and gradient between snow and atmosphere is small in Northeast China (Ebner et al., 2016), with low air temperature and vapor pressure in the snow stable period (Ji et al., 2017). In addition, snow cover is relatively shallow, and the metamorphism caused by the compaction is not significant (Yang et al., 2020), which allows the snow density in Northeast China–Inner Mongolia to fluctuate less during the seasonal changes. However, the seasonal evolution of snow density is obvious at the high altitudes and elevation areas of Xinjiang and the Tibetan Plateau, possibly because of the relatively high water vapor (Ji et al., 2017) and the temperature cycling between day and night that accelerates snow metamorphism (Ebner et al., 2016).

In addition, the monthly mean snow density from the estimated daily snow density map in Fig. 9f shows a similar pattern with that from the ground observations in Fig. 3b, which further demonstrates the effectiveness of the proposed GTWNN model for snow density estimation.

The constructed GTWNN model achieves daily snow density mapping by integrating a variety of influencing variables with the support of remote sensing, ground observation, and reanalysis data. Even though the validated accuracies are acceptable, it is also necessary to address three essential issues for constructing and applying the model: (1) the weak correlation between influencing variables and snow density, (2) the model evaluation and parameter estimation, and (3) the relation to the state of snow.

For the first issue, we found that the influencing variables have relatively
limited explanatory abilities for estimating snow density, as indicated by
the weak correlations in Fig. 4, which may be an important reason for the
low accuracy of the GTWNN model for snow density estimation with an

In addition, the accuracy of influencing variables would also affect the
GTWNN model estimation accuracy. We downloaded the instantaneous near
surface (2 m) air temperature and precipitation from the China
meteorological forcing dataset (CMFD), with a spatial resolution of
0.1

Accuracy comparison of estimated snow density with different sources of influencing variables.

For the second issue, there are three essential parameters in the GTWNN
model, including the scale factor

For the third issue, it is noted that the accuracy of the snow density
estimation model is closely related to the stability and amount of snow. The

Even though the ground measurement accuracy continues to improve by advanced measurement instruments (Hao et al., 2021a), it is limited to obtaining the large-scale spatial distribution of snow density, and gridded snow density data are urgently needed. To obtain the gridded snow density, snow parameters such as snow depth (Jonas et al., 2009; McCreight and Small, 2014) and meteorological data such as temperature and wind speed (Helfricht et al., 2018; Judson and Doesken, 2000; Valt et al., 2018) were used to estimate snow density mainly by using a linear regression model. The linear regression model is globally oriented and thus cannot effectively deal with the spatiotemporal heterogeneity of snow density. Accordingly, previous studies mostly achieve snow density estimation in regions that are not very large in size. The constructed GTWNN in this study considers the spatial and temporal dependences of snow density, which allows it to effectively deal with the spatiotemporal heterogeneity of snow density and thus hold the potential of being applied to large-scale areas, as demonstrated by the apparently higher accuracies than the linear regression model in our study area. In addition, it is important to overcome the weak correlation between snow density and its influencing variables to improve the estimation accuracy. Accordingly, we make two efforts in the GTWNN model. First, 20 influencing variables are integrated for the estimation with the support of multisource data. Second, the adopted GRNN model could overcome the nonlinear relationship between snow density and its influencing variables.

It is noted that the GTWNN model is a spatiotemporal interpolation model
based on the observed snow density, and the confidence of the snow density
map produced by the GTWNN model is still constrained by the distribution of
the observation stations, even though the model is able to achieve
relatively high accuracy in regions with sparse stations, e.g., the

A GTWNN model was constructed for snow density estimation and achieved daily
snow density mapping from 2013 to 2020 in China with the support of remote
sensing, ground observation, and reanalysis data. The GTWNN model has two
advantages: (1) considering the spatiotemporal heterogeneity of snow
density and (2) addressing the weak and nonlinear relationship as well as
the involvement of a variety of snow, meteorological, topographic, and
vegetation variables. The individual correlations between snow density and
20 influencing variables are very week, with the maximum average correlation
coefficient of only 0.123, and it is found that the vegetation variable
LAI_HV, meteorological variable TP, snow variable SD, and
topographic variables have a relatively close relationship to snow density.
The GTWNN model achieves an

Our research mainly uses three types of data, including the ground
observation data, satellite remote sensing data, and reanalysis data. The
daily snow depth and snow pressure measurements are collected from the China
Meteorological Administration (CMA) and the National Cryosphere Desert Data
Center (

XZ and PX formulated the study goals; HW, ZZ, Li, and TC performed the data curation; HW and XZ analyzed the data and wrote the paper draft; and PX, TC, ZZ, LD, and WL reviewed and edited the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors would like to thank the editors and reviewers for their constructive comments to improve the paper.

This study is supported by the Special Subject of National Science and Technology Basic Resources Investigation (Grant No. 2017FY100503), the National Natural Science Foundation of China (Grant No. 42171307), the Fundamental Research Funds for the Central Universities (Grant No. 020914380095), and the High-level Innovation and Entrepreneurship Talents Introduction Program of Jiangsu Province of China.

This paper was edited by Chris Derksen and reviewed by two anonymous referees.