Estimation of Snow Depth from AMSR2 and MODIS Data based on Deep Residual Learning Network

Abstract

Advanced Microwave Scanning Radiometer 2 (AMSR2) brightness temperature (TB) observations have long been utilized for snow depth (SD) estimation. However, the traditional approaches which are based on ‘point-to-point’ predictions ignore the spatial heterogeneity within a AMSR2 pixel and are limited by the coarse spatial resolution of the AMSR2 sensor. To solve these problems, a novel deep ‘area-to-point’ SD estimation model, based on a deep residual learning network by combining convolutional neural networks (CNN) and residual blocks, was proposed. The model utilizes all channels of AMSR2 TB data along with Moderate-resolution Imaging Spectroradiometer (MODIS) normalized difference snow index (NDSI) data and auxiliary geographic information. Taking the Qinghai-Tibet Plateau (QTP) as the study area, the SD with a spatial resolution of 0.005° over the 2019–2020 snow season is estimated, and the accuracy is validated by in situ SD observations from 116 stations. The results show that: (1) the proposed SD estimation model shows desirable accuracy as the root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE), and coefficient of determination (R²) of the proposed SD estimation method are 2.000 cm, 0.656 cm, −0.013 cm, and 0.847, respectively. (2) The SD estimation error is slightly larger in medium elevation or medium slope or grassland areas, and the RMSE is 2.247 cm, 3.084 cm, and 2.213 cm, respectively. (3) The proposed SD estimation method has the most satisfactory performance in low-elevation regions, and the RMSE is only 0.523 cm. The results indicate that through considering the spatial heterogeneity of snow cover and utilizing the high spatial resolution snow information presented by the MODIS snow cover product, the proposed model has good SD estimation accuracy, which is promising for application in other study regions.

1. Introduction

As a major component of the cryosphere, snow cover is a key variable in studying climate dynamics and hydrological cycles. Due to its high albedo, snow cover affects global climate and ecosystems by adjusting the portion of radiative energy received by the Earth’s surface [1,2,3]. Additionally, as an important source of water supply in semi-arid and arid regions, snow cover redistributes water resources through accumulation and melting, thereby affecting the regional and global water cycle [4]. Since snow cover provides parts of the conditions of the lower boundary of the atmosphere, it serves as an important indicator of climate change [5]. In addition, through its positive snow-albedo feedback mechanism, snow aggravates atmospheric warming [6]. Snow depth (SD) is an important and fundamental parameter for describing snow properties [7,8], influencing a large number of hydrological and geophysical processes such as snowmelt runoff, regional energy budget, geochemical cycling, and growing season length. Accurate monitoring of SD and its spatial distribution is of great scientific significance for climate change research, hydrological simulation, and water resources management [9,10]. The snow cover on the Qinghai-Tibet Plateau (QTP) strongly affects East Asia’s summer rain fall and atmospheric circulation, which further affects global climate [11,12]. The QTP is the headstream of major rivers in China, and its snowmelt water is crucial for regional agriculture and animal husbandry. However, being affected by climate change and uneven topography, variant landcover types, and the complex atmospheric circulation, the snow cover on the QTP is changing fast, is highly unstable, and shows strong heterogeneity. Therefore, accurate estimation of SD over the QTP is of significant importance for scientific research and could shed light on SD estimation in other regions.

SD is typically acquired through routine automatic weather station observations or in situ snow course investigation, and using remote sensing techniques. Compared with SD estimations using photogrammetry or imagery techniques, the SD reported by ground stations is directly measured. Thus, the in-situ-observed SD is generally considered to have the best accuracy and seen as the truth value, but the uneven and sparse distribution of meteorological stations makes it difficult to obtain the full image of snow conditions at regional and global scales, especially for uninhabited or inaccessible regions [5]. In contrast to in situ SD observations, remote sensing satellites observe the Earth from space, and have the ability to provide snow cover information simultaneously at a large scale [13]. Owing to the ability of penetrating clouds and rain, passive microwave sensors can observe the Earth under all weather conditions, which provides a large amount of observation data for SD retrieval [14,15,16]. However, the characteristics of forest cover tend to be linked with uncertainties in passive microwave SD retrievals [17,18]. For example, the microwave at 37 GHz can be strongly absorbed by standing vegetation, causing the scattering signal from the underlying snowpack to be overwhelmed by the upward microwave radiation from tree canopies and stems [19]. Since the 1970s, passive microwave observations have been widely used in SD monitoring and remote sensing technology has quickly developed, which has continuously improved the performance of passive microwave radiometers [20]. At present, the passive microwave radiometers for SD inversion mainly include Scanning Multichannel Microwave Radiometer (SMMR) [21], Special Sensor Microwave/Imager (SSM/I) [22], Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E), Advanced Microwave Scanning Radiometer 2 (AMSR2), and Microwave Radiation Imager (MWRI). Snow cover attenuates the microwave radiation from the underlying surface for wavelengths similar to the size of the snow grain [23], and this attenuation effect is highly dependent on the mass of the snowpack [23,24]. Since the underlying surface has a large influence on the low frequency band and the scattering effect of snow cover contributes more to the high frequency band of the microwave radiometer, it is possible to utilize brightness temperature difference (BTD) over different channels to estimate SD [25]. Using Nimubs-7-SMMR observations, Chang et al. [23] proposed to estimate SD by utilizing the BTD between 18 GHz and 36 GHz. However, due to the limited penetration ability to thick snow at 36 GHz [26] and the coarse spatial resolution of passive microwave observations, the SD inversion based on Chang’s algorithm engenders significant uncertainties [16,27].

Based on Chang’s algorithms, Grody et al. [28] carried out a series of experiments to identify rainfall, cold desert, frozen soil, and snow, and established a non-snow information identification model, which improved the snow identification accuracy. Foster et al. [29] introduced the transmittance of the forest area to reduce SD inversion error in forest regions. The usage of channels other than 18 GHz and 36 GHz has been tried and evaluated by researchers. Through analyzing the correlation between the station-observed snow water equivalent (SWE) and AMSR-E TB, Derkson [19] found that the BTD between 10 GHz and 18 GHz were better than the traditional 18 GHz and 36 GHz when capturing the inter-seasonal SWE variability across forested regions. Kelly [30] indicated that a 23 GHz channel can be used to identify shallow snow. Chang et al. [31] introduced an 89 GHz channel into the SD inversion algorithm, and improved accuracy was obtained over most regions in China. Furthermore, using brightness temperature (TB), research has shown that the introduction of auxiliary factors, such as high-resolution meteorological and graphical data, can improve SD inversion accuracy to some extent. Wang et al. [32] used BTDs in several different combinations of AMSR2 channels and auxiliary data (i.e., terrain, geographic location, and cloud-free snow product) to build an SD estimation model, and achieved good accuracy in the QTP. However, this model makes SD estimations on a point-to-point scale, which ignores the spatial correlation of snow cover. In summary, most traditional SD retrieval methods utilize only several combinations of BTDs and the model is usually fitted through linear regression; therefore, accuracy is highly correlated with the study area.

Different from traditional empirical statistical approaches, machine learning (ML) is a type of data-driven method which is based on a sample dataset to train a classification or regression model through complex non-linear mapping [33]. In recent years, ML techniques have rapidly developed and have been used in the estimation of geophysical variables, such as runoff [34,35], rainfall [36,37], and vegetation fraction [38]. For SD estimation, multiple models based on support vector machines (SVMs) [39] and artificial neural networks (ANNs) [40,41] have been developed and proved to have efficient performance. Xu et al. [42] developed a machine learning SD retrieval model using SSM/I brightness temperature, snow grain size, and forest cover and evaluated their results with AMSR-E SWE product. However, the ML SD estimation methods suffer from several drawbacks, including, but not limited to, the following: (1) most algorithms estimate SD on a ‘point-to-point’ model, which ignores the spatial heterogeneity of snow cover; (2) the relatively coarse spatial resolution (~25 km) of passive microwave data cannot accurately describe the distribution characteristics of snow cover, especially in complex mountainous areas. Convolutional neural networks (CNNs), which are capable of extracting hierarchical, high-level, and spatial pattern features of remote sensing images, have been successfully used in estimations of solar radiation [43], soil moisture [44], land surface temperature [45], and the merging of satellite and gauge precipitation [46]. However, as far as we know, CNNs have not been explored in SD estimations. This might be because the spatiotemporal variation of snow cover is affected by not only a series of complex chemical and physical processes of snow cover itself, but also by multiple environmental factors. Furthermore, with the inherent multi-channel characteristic of CNN, it is natural to combine multiple layers of TBs and auxiliary information as inputs of CNN to predict SD. However, with the increasing depth of deep CNNs, the accuracy of the network tends to get saturated and decrease [47], and this problem can be dealt with through introducing residual blocks into the network. Thus, this paper proposes a novel deep SD estimation model based on deep residual networks (ResNet); i.e., a type of CNN, which has the ability to utilize the spatial pattern of snow information and improve the accuracy of SD estimates.

Satellite-borne optical sensors usually have higher spatial resolution than that of microwave sensors, giving it the ability to provide more detailed distributions of land surface variables [48]. For example, the MODIS snow cover products with a temporal resolution of 1 day and a spatial resolution of 500 m (e.g., MOD10A1 and MYD10A1) have been widely applied to the various snow application studies. Previous studies have shown that the MODIS snow cover products have high accuracy under clear sky conditions; e.g., the overall accuracy of snow cover identification of MOD10A1 and MYD10A1 exceeds 92% in central Asia [49] and the accuracy is 93% for MOD10A1 in Canada [50]. However, at present, the SD estimation methods based on passive microwave observations do not take advantage of the more detailed snow cover distribution information presented by optical snow products. Thus, the proposed model utilizes both the AMSR2 TB and the MODIS snow cover product to estimate SD over the QTP, which combines the cloud penetration ability of microwave data and the high spatial resolution and precision of optical data.

The rest of this paper is organized as follows. The study area of this paper, as well as the data used, is described in Section 2. Section 3 provides the detailed model structure, the model flow chart, and the validation methodologies. The results are given in Section 4. Section 5 outlines discussions on the importance of spatial information and the choice of using TB or BTD. Finally, the conclusions and areas for possible improvements are given in Section 6.

2. Study Area and Data

2.1. Study Area

The QTP (25$°$48′–39$°$54′ N, 68$°$00′–104$°$72′ E) is located in the southwest of China, which spans from the Pamirs in the west, the Hengduan Mountains in the east, the Himalayan Mountains in the south, and to Altun and the Qilian Mountains in the north; covering an area of approximately 2.57 million km². Regarded as the world’s third pole, the QTP is the most extensive and highest plateau in the world, with an average elevation of over 4000 m [51] (Figure 1). The climate of the QTP is cold with limited precipitation: the winter is windy, cold, and long, while the summer is rainy and it frequently hails [52]. Decreasing with the increase in altitude, annual average temperature ranges from −15 °C to 10 °C [53]. The QTP is mostly covered by alpine steppe, alpine desert steppe, and alpine meadow, which takes up more than 63.5% of the total area [54]. As the water source of major rivers in Asia (including Yangtze, Yellow, Lantsang, Ganges, Brahmaputra and Salween), the snow cover in QTP is directly linked to ecosystems in downstream areas [55,56]. Furthermore, the changes in SD over the QTP can significantly affect monsoon and summer precipitation over the Indian Ocean [57,58]. In summary, the complex conditions of the underlying surface, as well as the regional climate, causes snow cover in the QTP to change rapidly and remain highly heterogeneous; making SD difficult to accurately estimate.

2.2. Data

2.2.1. AMSR2 Brightness Temperature Data

The AMSR2 passive microwave TB data were obtained from G-Portal (https://gportal.jaxa.jp/gpr/ (accessed on 20 May 2022)) of the Japanese Aerospace Exploration Agency (JAXA). The sensor was operated by the Global Change Observation Mission-W1 (GCOM-W1) satellite, which was launched in May 2012. AMSR2 has 14 channels at 7 frequencies (6.9, 7.3, 10.65, 18.7, 23.8, 36.5, and 89 GHz), and each frequency has dual polarizations (vertical and horizontal). There are two transit times for the GCOM-W1 satellite each day: the ascending pass is at around 13:30 (local time), and the descending pass is at around 01:30 (local time). The daily AMSR2 TB data were projected into an equirectangular projection with a spatial resolution of 0.1°. Because the emission of the intervening atmosphere and the sky radiation was small and neglectable [30,59], in this study, the TB data from all 7 frequencies, 6.9, 7.3, 10.65, 18.7, 23.8, 36.5, and 89 GHz (hereafter abbreviated as 6, 7, 10, 18, 23, 36, and 89 GHz) from 1 January 2013 to 31 March 2020, were selected. A 3-day adjacent temporal filter (ATF) procedure was applied to the AMSR2 TB to fill the scanning gaps; that is, the AMSR2 TB of the previous day and the next day were used to fill the missing pixels after averaging. ATF is a widely accepted temporal filter method for snow cover based on the assumption that the snow can persist on the surface for a certain period of time [5], and has been used in the gap-filling of AMSR2 TB [32]. The original TB data were then resampled to a spatial resolution of 0.005°.

2.2.2. MODIS Data

The MODIS data used in this study include the MODIS Collection 6 snow cover products (MOD10A1 and MYD10A1) and MODIS land cover type data (MCD12Q1). MOD10A1 and MYD10A1 are daily snow cover products with a spatial resolution of 0.005°, which contain raw NDSI data, NDSI snow cover, snow albedo, and quality control flags. NDSI snow cover is coded as integers and has a range of 0–100 for valid pixels, and were used in this study. The tiling systems of MOD10A1 and MYD10A1 are integerized sinusoidal grids, and there are 18 vertical tiles and 36 horizontal tiles globally, in total. In this study, nine tiles, the horizontal 25-vertical 5-tile (abbreviated here and afterwards as h23v05), h24v05, h24v06, h25v05, h25v06, h26v05, h26v06, h27v05, and h27v06 from 1 January 2013 to 31 March 2020, were collected from NASA’s EOSDIS “Earthdata” (https://earthdata.nasa.gov/ (accessed on 24 May 2022)). These tiles were first mosaicked to cover the entire QTP, then were reprojected to the ellipsoid WGS84 geographic coordinates. After the above processes, the daily MOD10A1 and MYD10A1 were first combined (the priority was assigned to MOD10A1) and then a 5-day ATF method was carried out to eliminate part of the cloud gaps. Then, all remaining missing pixels were reconstructed through a U-Net with partial convolutions [60]. This reconstruction approach utilized both spatial and temporal information of snow cover, and it has been proved to have competent accuracy [60].

The MCD12Q1 used in this study was yearly land cover type data with a spatial resolution of 0.005°, with a tiling system of integerized sinusoidal grids. This product includes a total of 17 land cover types, among which 11 types are natural vegetation, 3 types are non-vegetation land, and 3 types are developed and mosaic lands [61]. In this study, 9 tiles of MCD12Q1 data, the h23v05, h24v05, h24v06, h25v05, h25v06, h26v05, h26v06, h27v05, and h27v06 from 2013 to 2020 were collected from NASA’s EOSDIS “Earthdata” (https://earthdata.nasa.gov/ (accessed on 24 May 2022)). Similar to the preprocessing procedures of MOD10A1 and MYD10A1, the MCD12Q1 data was first mosaicked over the QTP and reprojected to the ellipsoid WGS84 geographic coordinates.

2.2.3. Meteorological SD Data

Daily in-situ-observed SD from 116 meteorological stations over the QTP were collected from China Meteorological Data Service (http://data.cma.cn (accessed on 15 May 2022)). The national meteorological stations report SD in integerized centimeters, and the minimum value for snow cover is 1 cm. Figure 1 depicts the locations of each meteorological station.

2.2.4. Digital Elevation Model Data

The digital elevation model (DEM) data version 004 of the Shuttle Radar Topography Mission (SRTM) over the QTP was obtained from http://srtm.csi.cgiar.org (accessed on 15 May 2022). This data had a spatial resolution of 90 m and was stored in GeoTiff format. In this paper, this data was first resampled and reprojected to the same spatial resolution and projection as previous described data; then, the elevation, slope, and aspect were extracted from it for usage in this study.

3. Methods

3.1. CNN and ResNet

CNNs are biological inspired variants of multilayers of perceptron [62] which are able to extract high-level features from input images and significantly improve the accuracy of image recognition or classification [63]. A common CNN consists of convolution layers, activation layers such as reflected linear unit (ReLU) operation, pooling operations for downsampling, functions to prevent overfitting, and finally a fully connected layer to get the final output. Batch normalization layers [64] are usually applied after convolution operations to address the internal covariate shift problem.

Several previous studies reveal that the depth of CNN networks is crucial to the model accuracy, and the increased depth of CNNs can strengthen the ability of the network to simulate complex process, which have shown improvements on many non-trivial visual recognition tasks [65,66,67]. However, research has shown it is not always when the CNN network gets deeper that the performance is better [68]. The reason for this lies in two features: (1) with the increasing network depth, the problem of gradient disappearance or gradient explosion is prone to occur [69]. Luckily, this problem has been largely addressed through normalized initialization [70,71] and intermediate normalization layers [64]. (2) The degradation problem occurs frequently with the increasing depth of CNNs; that is, the network accuracy gets saturated and then rapidly degrades [47]. To deal with this problem, He et al. [47] proposed a deep residual learning framework named ResNet which embeds residual blocks into deep CNNs to mitigate the degradation. The sketch of a residual block is depicted in Figure 2, in which the input of this block is denoted as $x$, the output is denoted as $\mathcal{H}\left(x\right)$, the residual is denoted as $\mathcal{F}\left(x\right)$, and the symbol $\oplus$ means the element-wise addition between the residual $\mathcal{F}\left(x\right)$ and the input $x$. Intuitively, if a neural network becomes deeper but its learning effect becomes worse, the problem should be in the added deeper part. Thus, when the newly added layers make the overall performance worse, we can use shortcut links to adjust the learning effect of the newly added layers. Under extreme conditions where the residual is zero, the stacked layers are equal to an identity reflection. In reality, the residual will not be zero so the stacked structure could learn new features, making the model perform better.

3.2. Deep Residual Network Framework

The detailed structure of the proposed deep residual network framework is shown in Figure 3. The network input consists of 35 layers (including 28 layers AMSR2 TB, NDSI, elevation, slope, aspect, latitude, longitude, and land cover type) with a patch size of 32 × 32 (which means a region of 16 km × 16 km), so the shape of the input is 35 × 32 × 32 (channel × height × width). The model output is the estimated SD at the central point of the patch.

Inside the model, the input patch is first sent to a convolution layer with 64 filters for feature mapping, then a max pooling layer with a kernel size of 2 × 2 and a stride of 2 is applied. After this, four residual blocks (two with 64 filters and two with 128 filters) are sequentially applied to extract the temporal and spatial patterns of snow cover from input patch groups. The output of the last residual block with shape 128 × 8 × 8 are sent to an adaptive average pooling (AAP) layer, which gives the output with shape 128 × 1 × 1. After AAP, three fully connected layers with 128, 64, and 32 nodes, respectively, are applied. At last, the output of the model represents the estimated SD value of the central pixel of the input image block. It should be noted here that each convolution operation is followed by a batch normalization layer in the proposed ResSD model, the kernel size of each convolution layer is 3 × 3 and the stride is 1, if not specifically noted in Figure 3. The activation function used in the proposed model is ReLU, expect for the output layer where a linear activation is applied. In total, the proposed deep residual network has nine convolution layers and four fully connected layers.

3.3. SD Estimation Model

A novel SD estimation model, namely ResSD, is proposed in this study. The flow chart of the ResSD is depicted in Figure 4.

In the patch generation step, we traversed the 116 stations during the snow season between 2013 to 2020 (note that the snow season is determined to be from 1 November of the first year to 31 March of the following year in this study). If a ground station had SD observation on a date, 35 layers of patches, i.e., 28 layers of AMSR2 TB, 1 layer MODIS NDSI, 3 layers from DEM data (aspect, slope, elevation), 1 layer MODIS land cover type, 1 layer latitude, and 1 layer longitude, with a shape of 32 × 32 centered on the location of the station, were extracted and stacked to form a patch group. The corresponding station-observed SD was extracted and was matched with the patch group for later model training and validation.

After traversing, the matched samples during snow season from 1 January 2013 to 31 March 2019 were selected for model training, and samples from 1 November 2019 to 31 March 2020 were selected as a temporal independent test set to evaluate the generalization ability of the developed model for validation. To ensure the portion of patch groups representing snow and non-snow were balanced as much as possible, all 10,847 patch groups indicating snow cover and 14,925 patch groups (accounting for 15% of the total non-snow patch groups) indicating no snow cover during snow season from 1 January 2013 to 31 March 2019 were finally selected to form the training dataset. Thus, in total, 25,772 patch groups were selected as the training dataset.

In this study, the proposed SD estimation model was built on PyTorch. The training epoch was 50, the learning rate was 0.0001, with an exponential decay rate of 0.5 after every 20 epochs, and the batch size was set to 32 for training. The optimizer used when training was stochastic gradient descent (SGD).

3.4. Performance Evaluation Metrics

In this study, the evaluation metrics include root mean squared error (RMSE), mean absolute error (MAE), mean bias error (MBE), and coefficient of determination (R²). Their equations are listed as follows:

(1)$\mathrm{RMSE}=\sqrt{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\left({\mathrm{SD}}_{est}^i-{\mathrm{SD}}_{truth}^i\right)}^2}$

(2)$\mathrm{MAE}=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n\left|{\mathrm{SD}}_{est}^i-{\mathrm{SD}}_{truth}^i\right|$

(3)$\mathrm{MBE}=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n\left({\mathrm{SD}}_{est}^i-{\mathrm{SD}}_{truth}^i\right)$

(4)$R^2={\left(\frac{1}{n-1}{{\displaystyle \sum }}_{i=1}^n\left(\frac{{\mathrm{SD}}_{est}^i-\overline{{\mathrm{SD}}_{est}}}{{\sigma }_{est}}\right)\left(\frac{{\mathrm{SD}}_{truth}^i-\overline{{\mathrm{SD}}_{truth}}}{{\sigma }_{truth}}\right)\right)}^2$

where ${\mathrm{SD}}_{est}^i$ is the i-th model estimated SD value, ${\mathrm{SD}}_{truth}^i$ is the corresponding i-th station-observed SD value, $n$ is the total number of patch groups for evaluation, $\overline{{\mathrm{SD}}_{dsc}}$ is the mean value of model estimated SD, $\overline{{\mathrm{SD}}_{truth}}$ is the mean value of station-observed SD, and ${\sigma }_{dsc}$ and ${\sigma }_{truth}$ are the standard deviations of model estimated SD and station-observed SD, respectively.

4. Results

4.1. The Accuracy of the Proposed ResSD Model

In this section, the performance of the ResSD model on the training dataset and the test dataset is presented. The scatter density diagram of estimated SD versus station-observed SD at different circumstances (training dataset and test dataset) is depicted in Figure 5. In the training set, the developed ResSD has an RMSE of 1.712 cm, MAE of 0.508 cm, MBE of −0.013 cm, and R² of 0.906, whereas these values are 2.000 cm, 0.656 cm, −0.013 cm, and 0.847, respectively, for the temporal independent test set. From the results, we can see that the model performance on the training set and the test set are similar, which means the proposed model has good SD estimation accuracy. This suggests that the module can adequately utilize the spatial-temporal information of the input AMSR2 TB, MODIS NDSI, and auxiliary data, to successfully excavate the spatial variation and heterogeneity of snow cover, giving accurate SD estimations over mountain areas with complex terrains. Additionally, the ResSD model has good performance on the test dataset and, when compared with the training dataset, there is no obvious performance degradation. This indicates that the proposed model has good SD estimation ability and has the potential to be applied to other regions. On the whole, the ResSD model slightly underestimated SD over the QTP, especially when the snowpack was thick. A neglectable overestimate of SD can be found for very shallow or no snow cover.

To further discover the SD estimation performance, the RMSE of the estimated SD under different ranges of station-observed SD is given in Table 1. Overall, the RMSE increases with the increase in station-observed SD. For different ranges with increasing SD, the RMSEs were 0.919 cm, 3.233 cm, 4.711 cm, 8.403 cm, and 27.009 cm, respectively. The observed SD of more than 30 cm appears at only one station, which leads to insufficient information of very deep snow cover being added to the model. Previously, research conducted by Wang et al. [32] showed similar results: the RMSEs of their model increased with the increase of in-situ-observed SD, and the RMSE reached 37.91 cm when SD was larger than 30 cm. The estimated SD on 116 stations over the QTP showed best accuracy (RMSE of 0.919 cm) in shallow snow areas (SD no greater than 3 cm).

4.2. Accuracy under Different Terrain and Land Cover Conditions

To further evaluate the performance of the proposed model under different terrain and land cover conditions, Figure 6 depicts the spatial distribution of the RMSEs for the estimated SD over the QTP for different (a) elevation, (b) slope, (c) aspect, and (d) land cover, based on 116 meteorological stations.

The number of stations with RMSE at 0–0.5 cm, 0.5–1.0 cm, 1–2 cm, 2–5 cm, 5–10 cm, and larger than 10 cm are 42, 44, 16, 9, 1, and 2, respectively (two stations had no observations in 2019–2020 snow season; thus, they are not included in the statistics). When looking at the elevation of meteorological stations, the estimated SD performed best when the elevation was below 2500 m (RMSE = 0.523 cm) and performed worst when the elevation was between 2500 m and 4000 m (RMSE = 2.247 cm). The RMSE of regions with elevations larger than 4000 m was 1.815. The reason for this might be that the stations with elevation lower than 2500 m mostly reported zero SD observations, resulting in a smaller RMSE (Table 1). On the contrary, the stations with reported SD larger than 30 cm were all distributed in locations with an elevation between 2500 m and 4000 m, which led to a larger RMSE of this elevation range.

On a flat ground, when slope is less than 10°, the estimated SD shows moderate accuracy with RMSE of 1.881 cm, and this value increases to 3.804 cm when the slope is between 10° and 20°. An interesting result occurs under the condition of a steeper ground when the slope is larger than 20°, where the estimated SD shows best accuracy (RMSE = 0.669 cm) compared with the in-situ-observed SD. The reason might be that only six stations were located on positions with a slope larger than 20°, and their maximum reported SD over the 2019–2020 snow season were 2 cm, 2 cm, 2 cm, 4 cm, 4 cm, and 10 cm, respectively, which makes the RMSE smaller. Since the snow is more prone to be affected by the blowing wind and more difficult to persist when the slope is steep, this result is reasonable.

The determination of a shady slope and a sunny slope in this study is as follows. Let the aspect of 0° represent a slope facing due north, 90° represent facing due east, 180° represent facing due south, and 270° represent facing due west, then the aspect from 270° and 360° and from 0° to 90° is considered as the shady slope, and the aspect between 90° and 270° is categorized into a sunny slope. The RMSE on shady slopes and sunny slopes are similar, and the sunny slopes have a slightly larger RMSE (2.108 cm) than that of the shady slope (1.869 cm).

The RMSE of estimated SD over grassland was 2.213 cm, which was notably larger than that of the forest regions (RMSE = 0.624 cm) and bare land (RMSE = 1.030 cm), and this result was consistent with the findings of Wang et al. [32]. The reason might be because only ten stations are located in forest regions, and their reported SD during 2019–2020 snow season was no more than 5 cm, which resulted in relatively small RMSEs. The number of stations located in bare land areas is nine, among which 5 stations had maximum reported SD observations at 1 cm, and the maximum reported SD of these nine stations during 2019–2020 snow season was 9 cm. Thus, the RMSE over bare land was also small. The stations with large observed SDs were all distributed in grassland areas, resulting in a larger RMSE over grassland.

From Figure 6, it is clear that stations with RMSE larger than 2 cm mainly locate in the middle east region and southern border of the QTP, with medium elevation or on medium slope or in grassland. This is because most of the stations with large observed SDs were located in grassland and regions with elevations from 2500 m to 4000 m, which resulted in larger RMSEs on these terrain and land cover conditions. On the other hand, stations with RMSE less than 0.5 cm were relatively balanced over the entire QTP. Most stations (68.75%) in the low-elevation zone (<2500 m) have an RMSE less than 0.5 cm, which also agreed with most stations located in bare land (66.67%), forest regions (60.00%), and regions with slope larger than 20° (66.67%).

4.3. Performance of ResSD Model in Time Domain

Taking representative stations under different conditions as an example, the changing trend of the estimated SD and the station-observed SD at stations Tongren, Dachaidan, Hezuo and Jiali are depicted in Figure 7. The regions with elevations lower than 2500 m account for 3.4% of the QTP and have 16 meteorological stations, among which Tongren is selected for analysis. Areas with elevations from 2500 m to 4000 m make up 27.1% of the study area and contains most of the stations (74); thus, two of these stations, Dachaidan and Hezuo, are selected. The remaining 24 stations are located in regions with elevations higher than 4000 m, and Jiali is chosen for analysis. Tongren and Dachaidan represent stations with grassland land cover, while Hezuo is located in a forest region, and Jiali has a land cover of bare land. Stations Tongren, Dachaidan, and Hezuo represent shallow and fast-changing snow cover, while the snow cover of Dachaidan is relatively persistent.

Overall, the estimated SD at all four stations showed good consistency with the in-situ-observed SD. The estimated SD at Tongren oscillates with the wildly changing station-observed SD, and its value is very close to 0 when no snow cover is observed at this station. For more persistent shallow snow cover at Dachaidan, the trend of estimated SD fit well with the station-observed SD. At station Hezuo, the snow cover is shallow and changes fast, but our model correctly identifies the no-snow cover period and reflects snow information when a non-zero SD is observed. For Jiali station, the SD from the proposed ResSD model fits well with the station-observed SD before the middle of January 2020. After this, the proposed model tends to give non-zero SD predictions when no snow cover is observed, but the trend of predicted SD is also reasonable. The results show that, while at some stations the RMSE may not be satisfactory, the fit between the trend of predicted SD and station-observed SD can still be effective.

Once again, we want to highlight that the proposed ResSD model tends to overestimate SD in very shallow snow conditions, and underestimate SD when snow cover is deep. This trend can be clearly seen in Figure 7b, where the SD is underestimated, and in Figure 7d, where an overestimate of the SD is found. On the one hand, this result is reasonable and acceptable because, due to the issue of spatial representation, the point-based ground observation may not well represent the snow information within its corresponding pixel. For example, during the snow melt period at station Jiali, the snow cover near the meteorological station may have already melted, but there might still be a snow signal in the corresponding pixel, which leads to an overestimate of SD in the proposed ResSD model. On the other hand, the mismatch between the predicted SD and the station-observed SD implies that our model may not fully grasp the correlations between TBs and SD. Thus, incorporating SD observations from more stations into the model for training may help to improve performance.

4.4. The Distribution of Estimated SD over the QTP

The estimated SD maps with a spatial resolution of 0.005° over the entire QTP on (a) 1 November 2019, (b) 1 December 2019, (c) 1 January 2020, (d) 1 February 2020, and (e) 1 March 2020 are illustrated in Figure 8. Since the proposed ResSD model is a regression model instead of a classification model, the model output SD is a float number instead of an integer. Thus, in Figure 8, we choose to consider the estimated SD as zero when it is smaller than a certain threshold (here we set it to 0.5 cm), and plot it with white color to distinguish from other matters. As shown in Figure 8, during the 2019–2020 snow season the snow is mainly distributed in two regions: the high elevation region in southern western QTP and the mountainous areas in the middle and eastern QTP, which is fairly reasonable. The patterns of SD correspond well with the shape of mountain ridges when compared with Figure 1. In Figure 8a–e, the spatial-temporal variation of snow cover in the QTP can be viewed, with an obvious snow accumulation period from Figure 8a–d and a snow melt trend from Figure 8d,e. In Figure 8, it is clear that the areas with estimated SD larger than 50 cm are located in the high mountains near the western boarder of the QTP. Except for the above mentioned two regions, most areas in the QTP have SD less than 5 cm. Figure 8 shows that the proposed ResSD model is able to give a detailed SD variation information over the entire QTP at a fine resolution of 0.005°.

5. Discussion

Differently from existing SD retrieval or estimation algorithms based on satellite observations, ResSD utilizes both the advantage of spatial information and pixel level attribute to estimate SD. To discuss the effect of spatial pattern to the accuracy of SD estimation, two widely used models are built for comparative analysis. The first model is a deep neural network, which is another deep learning model, and is referred to as DNN_SD. The second model is a random forest model which is an ensemble learning method, and has been proven to have good performance, referred to as RF_SD. Unlike the previously described ResSD model, the inputs of DNN_SD and RF_SD are AMSR2 TB, MODIS NDSI, and auxiliary information only at the pixel where meteorological stations are located, which means these two models make “point-to-point” SD predictions without using the spatial pattern of the input data.

The DNN_SD model used here consists of an input layer with 35 nodes, 4 hidden layers consisting of 64, 32, 16, and 4 nodes, and an output layer representing the predicted SD value. After each hidden layer, an activation layer with ReLU and a batch normalization layer is applied. The RF_SD model used here has 20 estimators, the maximum leaf nodes are 150, and the max depth is 50. The above-mentioned model parameters are determined through a trial-and-error method. Similar to the training and validation procedure of ResSD, the data from 1 January 2013 to 31 March 2019 during the snow season are used to form the training dataset, and the data during the 2019–2020 snow season constitute the test dataset. Figure 9 shows the scatter density diagram of DNN_SD estimated SD and RF_SD estimated SD versus in-situ-observed SD.

From Figure 9 it is clear that, compared with the performance of ResSD (Figure 4), the SD predictions given by DNN_SD and RF_SD show worse agreements with in situ observations. The RMSE, MAE, MBE, and R² of DNN_SD on validation datasets are 2.725 cm, 0.880 cm, −0.259 cm, and 0.698, respectively, which are all not as satisfactory as that of the ResSD model. The results of RF_SD on the validation dataset are even worse than that of DNN_SD, with RMSE of 3.083 cm, MAE of 1.006 cm, and R² of 0.618, except for a smaller MBE of 0.030 cm. The underestimation of SD under thick snow conditions is more severe for both DNN_SD and RF_SD models when compared with ResSD. In addition, the relatively small R² for DNN_SD and RF_SD on both the training dataset and the validation dataset show these two models cannot properly grasp the snow information from the inputs. It is noted that the overall accuracy of DNN_SD is better than that of RF_SD, which shows that DNN has better performance than the ensemble learning method like RF. However, DNN_SD does not adequately use the spatial information of neighboring pixels. These results imply that without the spatial patterns of input TB, NDSI, and the auxiliary data (i.e., elevation, slope, aspect, latitude, longitude and landcover type), the SD estimation accuracy of ‘point-to-point’ based machine learning approaches like DNN and RF might be hampered. The convolution operation in ResSD model gives it the ability to receive snow information over an area as input and learn the spatial pattern, making it more robust when faced with complex snow conditions. In summary, ResSD gives the best SD estimation compared to DNN_SD and RF_SD, and this discussion shows that spatial information is crucial for the estimation of SD with passive microwave observations.

The traditional SD inversion models such Chang’s algorithm have the advantage of fast calculation speed and are applicable for most regions. However, these algorithms are essentially linear regression models, which assume a linear relationship between the SD and the one or more selected channels of BTD. These kinds of models fail to capture (1) the non-linear relationships between the observed SD and BTD, and (2) the hidden snow information inherited by other non-selected BTD channels. Additionally, the lack of spatial patterns in the input data makes it difficult for traditional models to grasp the spatial information of SD. As has been discussed in this section, the usage of spatial information is important for a more accurate estimation of SD, which may require improvements for traditional SD inversion methods.

6. Conclusions

The accurate estimation of SD using passive microwave observations has long been an important issue in the study of cryosphere. However, the microwave remote sensing techniques give snow information a coarse spatial resolution, and the traditional ‘point-to-point’ based estimations by SD ignores spatial information. In addition, the detailed snow information given by high-resolution optical remote sensing data has not been fully utilized in the estimation of SD. Based on deep residual networks, this paper proposed a deep ‘area-to-point’ SD estimation model which utilizes AMSR2 TB, MODIS, and NDSI product, as well as other auxiliary information, to give SD estimations with a spatial resolution of 0.005°. To evaluate the accuracy of the estimated SD, this study presented: (1) accuracy evaluation of the training dataset and the validation dataset, (2) accuracy under different terrain and land cover conditions, (3) the performance of ResSD model in time domain, and (4) the distribution of the estimated SD over the QTP. To testify the importance of spatial pattern of snow for SD estimations, the performance of the proposed ResSD model and other two point-to-point based models were compared and discussed. The validation results show that the estimated SD generated from the proposed ResSD show high accuracy and reliability and has good consistency with station-observed SD. The discussions show that the spatial information of snow is important and necessary for accurate estimations of SD.

Although the proposed ResSD estimation model performed well, there are still limitations and drawbacks that need to be improved. Possible improvement could be achieved through: (1) collecting SD observations from more stations to strengthen the model robustness; (2) introducing other types of auxiliary information into the model, such as surface temperature, snow covered days, etc.; and (3) further optimizing the model’s structure and parameters. This work could be further applied to the retrieval or estimation of other geophysical variables, such as soil moisture and vegetation fraction.

Author Contributions

D.X. and J.H. conceived and designed the experiments; D.X. performed the experiments and wrote the paper; D.X. and J.H. analyzed the data; C.H. and W.Z. contributed to discussions and revisions. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data that support the findings of this study are available from the website given in the manuscript.

Acknowledgments

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Table

Figure 1. Elevation of the QTP and position of meteorological stations.

Figure 2. The structure of a residual block.

Figure 3. The structure of the proposed deep residual network. Conv stands for convolution operation; AAP stands for adaptive average pooling operation; symbol [Forumla omitted. See PDF.] represents the element-wise addition between the inputs.

Figure 4. Flow chart of the proposed SD estimation framework (ResSD).

Figure 5. The scatter density diagram of estimated SD (cm) versus in-situ-observed SD (cm) at (a) training dataset and (b) test dataset. The red line is y = x line while the blue line is the trend of estimated SD versus in-situ-observed SD after linear regression.

Figure 6. The spatial distribution of the RMSE for the estimated SD over the QTP for different (a) elevation, (b) slope, (c) aspect, and (d) land cover based on 116 meteorological stations.

Figure 7. Comparison between the ResSD estimated SD and the in-situ-observed SD at station (a) Tongren, (b) Dachaidan, (c) Hezuo, and (d) Jiali. Red line shows the estimated SD. The observed SD are shown with blue bars.

Figure 8. Estimated SD from the proposed ResSD model over the entire QTP on: (a) 1 November 2019; (b) 1 December 2019; (c) 1 January 2020; (d) 1 February 2020; (e) and 1 March 2020; after categorization into different SD intervals.

Figure 9. The scatter density diagram of DNN_SD estimated SD (cm) versus in-situ-observed SD (cm) on (a1) training dataset and (b1) validation dataset and RF_SD estimated SD (cm) versus in-situ-observed SD (cm) on (a2) training dataset and (b2) validation dataset.

Table 1

RMSEs (cm) of estimated SD versus observed SD from 116 stations over snow season 2019–2020 under different SD ranges.

Snow Depth (cm)	RMSE (cm)
$0\le \mathrm{SD}\le 3$	0.919
$3<\mathrm{SD}\le 6$	3.233
$6<\mathrm{SD}\le 10$	4.711
$10<\mathrm{SD}\le 30$	8.403
$\mathrm{SD}>30$	27.009

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