Uncertainty Analysis of Snow Depth Retrieval Products over China via the Triple Collocation Method and Ground-Based Measurements

Abstract

Snow depth is a crucial variable when assessing the hydrological cycle and total water supply. Therefore, thorough and large-scale assessments of the widely used gridded snow depth products are highly important. In previous studies, triple collocation analysis (TCA) was applied as a complementary method to assess various snow depth products. Nevertheless, TCA-derived errors have not yet been validated against ground-based measurements. Specifically, the reliability of the TCA for quantitatively evaluating snow depth datasets remains unknown. In this study, we first generate a long-term snow depth product using our previously proposed remotely sensed retrieval algorithm. Then, we assess the results obtained with this algorithm together with other widely used assimilated (GlobSnow-v3.0) and reanalysis (ERA5-land and MERRA2) products. The reliability of the TCA method is investigated by comparing the errors derived from TCA and from ground-based measurements, as well as their relative performance rankings. Our results reveal that the unRMSE values of snow depth products are highly correlated with the TCA-derived errors, and both provide consistent performance rankings across most areas. However, in northern Xinjiang (NXJ), the TCA-derived errors for MERRA2 are underestimated against the ground-based results. Furthermore, we decomposed the covariance equations of TCA to assess their scientific robustness, and we found that the variance of MERRA2 is low due to the narrow dynamic range and severe underestimation in the snow season. Additionally, any two datasets in the triplet must exhibit correlation, at least displaying the same trend in snow depth. This paper provides a comprehensive assessment of snow depth products and demonstrates the reliability of TCA-based uncertainty analysis, which is particularly useful for applying multiproduct snow depth ensembles in the future.

1. Introduction

Snow depth is a key parameter that quantitatively reflects the snow mass globally. Long-term snow depth datasets at large scales are critical for many scientific studies and applications, such as climate model evaluation and forecasting [1,2,3], freshwater resource management [4,5], ecosystem evolution [6,7,8,9], and determination of freshwater availability [10,11].

There is a growing number of gridded snow depth datasets available to the snow community, such as stand-alone PMW products (e.g., the Japan Aerospace Exploration Agency GCOM-W/AMSR2 and the China Meteorological Administration FY-3/MWRI), data assimilation products (e.g., the European Space Agency GlobSnow-v3.0), and reanalysis datasets (e.g., the European Centre for Medium-Range Weather Forecasts ERA5-land and the Modern-Era Retrospective Analysis for Research and Applications MERRA2). To statistically quantify the errors in gridded snow depth data, these products are typically evaluated in comparison to ground-based measurements. Generally, the representativeness of station measurements in flat and open areas is reliable, but it can be poor in areas of mixed forest vegetation and complex topography [12,13,14,15]. Additionally, limitations in the spatial coverage of these networks limit the scope of ground-based validation. Therefore, to evaluate large-scale snow depth datasets in the absence of a known reference (or true) snow depth benchmark, statistical methodologies are commonly applied to analyze the error distribution of snow depth retrieval, e.g., triple collocation analysis (TCA), without the need for a ground-based reference.

In recent years, the TCA method has been extensively utilized for validating satellite products, such as sea surface salinity/sea ice [16,17], soil moisture [18,19,20,21], freeze/thaw [22,23,24,25], and precipitation [18,23,26]. Nonetheless, few studies have been conducted to validate the gridded snow depth products via the TCA technique. Qiao et al. (2022) first used the TCA method to assess the uncertainty of multisource snow depth products and reported that the performance of snow depth products is strongly related to forest coverage and topographical factors [27]. He et al. (2023) also used the TCA method to assess the accuracy of three gridded snow depth products encompassing Arctic sea ice and further merged them on the basis of weights calculated from error variance estimates [28]. In their studies, the TCA method was directly used to assess the uncertainty of gridded snow depth products and then to fuse them, in order to obtain more accurate snow depth estimates. However, the reliability of the TCA method has not yet been demonstrated. This study represents the first attempt in the snow remote sensing community to apply ground-based measurements to evaluate the reliability of the TCA method in assessing the uncertainty of different types of snow depth products.

In this study, we evaluated four gridded snow depth products, including a stand-alone PMW product (referred to as the pixel-based hereafter), a Bayesian assimilation product that combines ground-based data with satellite-borne observations (GlobSnow-v3.0), and two reanalysis products (ERA5-land and MERRA2). The pixel-based algorithm was developed in our previous studies [29,30]. Unlike traditional static empirical methods, this algorithm relies solely on PMW observations but incorporates spatially dynamic fitting coefficients, demonstrating superior performance. However, it has never been comprehensively assessed or compared with other snow depth products. We first generate a long-term (1988–2022) snow depth dataset on the basis of our previously proposed pixel-based retrieval algorithm. We then verify its performance using multiple ground-based datasets and compare it with widely used assimilated (GlobSnow-v3.0) and reanalysis (ERA5-land and MERRA2) products. Finally, we conduct a validation of the TCA-derived errors against the ground-based measurements and assess the reliability of TCA in validating and comparing the performances of the snow depth products. This study provides the first reliability assessment of the TCA method for uncertainty analyses of snow depth retrieval products and contributes to improving the spatial representativeness of point-based observations and the merging of multiple snow depth products.

2. Data and Methodology

2.1. Ground-Based Snow Depth Measurements

We collected multiple ground-based reference datasets across China to evaluate the four existing gridded snow depth products (see Section 2.2). A total of 571 weather stations (with snow records) from 2002 to 2022 managed by the National Meteorological Information Centre, China Meteorology Administration (CMA; http://data.cma.cn/en, accessed on 3 January 2023), were used in this study (black solid points in Figure 1). These stations record the daily snow depth (cm), air temperature (°C), etc. Here, only measurements in areas where daily averaged air temperatures are less than zero were selected, avoiding the influence of wet snow on the validation results. Therefore, most measured snow depth data were distributed across three stable snow cover areas in China (northern Xinjiang (NXJ), Northeast China (NE), and the Qinghai-Tibet Plateau (QTP)).

A field campaign supported by the Chinese Snow Survey project was conducted from December 2017 to March 2019. Several snow courses and dense sampling quadrats were designed (Figure 1). We collected data from four snow courses (colorful solid lines in Figure 1, a total of 413 samples) distributed in NXJ and NE China in this study. The snow depth, density, air temperature, and stratigraphy of the snowpack were recorded every 10 to 20 km. Typically, there was only one measurement within a matched satellite pixel. In this case, we removed possible wet snow samples according to air temperature records.

Three 25 km × 25 km quadrats were designed along the snow course (Figure 1, quadrat ①, quadrat ②, and quadrat ③). Dense sampling was performed from January 2018 to March 2019. In each quadrat, snow depth and density were measured. Typically, there were 4~25 measurements within a matched satellite pixel. The measurements within each grid cell were averaged to represent the true snow depth.

2.2. Snow Depth Retrieval Methods and Existing Products

Table 1 summarizes the key characteristics of the four selected gridded snow depth products from different international institutions. Our study specifically excludes stand-alone PMW products from AMSR2 and FY-3D/MWRI due to their documented limitations: the AMSR2 algorithm, designed for global snow cover monitoring, demonstrates systematic overestimation across Chinese territories [31], while the FY-3D/MWRI algorithm, despite previous regional improvements over China [32], consistently underestimates snow depth beyond 30 cm. The pixel-based algorithm is empirical and solely relies on PMW observations, but the fitting coefficients are spatially dynamic, which offers significant advantages over traditional static empirical methods [29,30]. Thus, this methodological advancement justifies its selection as the representative stand-alone PMW product. The GlobSnow-v3.0 algorithm is developed on the basis of satellite PMW remote sensing, but it assimilates ground-based synoptic snow depth observations using Bayesian data assimilation [33,34], demonstrating superior robustness to the stand-alone PMW products over China. ERA5-land and MERRA2 are model-based reanalysis products, but the land surface model results and the atmospheric data are different. Notably, ERA5-land tends to reflect snow cover well in elevated regions [35], whereas MERRA2 shows better overall performance over China [36]. Therefore, these four gridded snow depth datasets were selected in this study. Additionally, these four products are independent in principle due to methodological independence.

Here, we introduce a snow depth retrieval algorithm that couples a snow emission model and a machine learning technique; for details, see [29]. The predictor variables for the machine learning model (random forest), namely, the brightness temperature differences between 18.7 and 36.5 GHz, longitude, elevation, and effective grain size (effGS), are as follows:

$$SD=\mathrm{R}\mathrm{F}\left\{{(Tb}_{18.7V}-{Tb}_{36.5V}), longitude, elevation, effGS\right\}$$

(1)

where RF denotes the random forest machine learning trainer and effGS is the grain size determined using ordinary kriging interpolation (Figure 2). Here, 10.65 GHz is not used because it is unavailable for the SSM/I and SSMIS series of sensors. The optimization procedure for effGS involves minimizing the difference between the satellite brightness temperature and snow emission model (Helsinki University of Technology model, HUT) simulation:

$${{\mathrm{m}\mathrm{i}\mathrm{n}}_{effGS}\left\{\left[{Tb}_{18.7\mathrm{V},\mathrm{H}\mathrm{U}\mathrm{T}}\right({SD}_{\mathrm{i}\mathrm{n}\mathrm{i}},{\rho ,T}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}},effGS)-\right.\left.{Tb}_{36.5\mathrm{V},\mathrm{H}\mathrm{U}\mathrm{T}}({SD}_{\mathrm{i}\mathrm{n}\mathrm{i}},{\mathsf{\rho },T}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}},effGS)]-[{{Tb}_{18.7\mathrm{V},\mathrm{s}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{e}}-Tb}_{36.5\mathrm{V},\mathrm{s}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{e}}]\right\}}^2$$

(2)

where the snow density (ρ) is set as 0.20 g/cm³ according to field campaign measurements; T_snow denotes the snow temperature, which is the same as the air temperature used in this study; and SD_ini is the station-based snow depth.

In accordance with the methodology introduced above, a long-term spatiotemporally continuous snow depth dataset (2012–2018) was generated as a reference. The pixel-based algorithm was subsequently constructed on the basis of the reference snow depth dataset [30]. The format of this algorithm is simple and traditional, but the fitting coefficient is spatially dynamic (Figure 3). The format is as follows:

SD = slope × (Tb_18.7V − Tb_36.5V) + intercept

(3)

where slope and intercept are fitting coefficients and vary pixel by pixel. To produce a long-term snow depth dataset, only satellite observations corresponding to 18.7 and 36.5 GHz frequencies from SSM/I and SSMIS (1988–2022) were used in this study. Here, SMMR satellite observations (1979–1987) were not used because the data quality is problematic. Moreover, the revisit period is two days, differing from that of the SSM/I and SSMIS instruments.

The GlobSnow-v3.0 SWE product was downloaded from https://www.globsnow.info/ (accessed on 23 January 2019). This product is established by combining satellite-observed brightness temperatures with ground-based synoptic snow depths via Bayesian data assimilation with a snow emission model. In the GlobSnow methodology, a density value of 0.24g/cm³ is assumed in estimating SWE. Thus, we applied the constant value of snow density to convert the SWE to snow depth [33,34].

The hourly ERA5-land snow depth dataset was acquired from https://cds.climate.copernicus.eu/ (accessed on 3 January 2023) [37]. The hourly MERRA2 snow depth dataset was downloaded from https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/data_access/ (accessed on 3 January 2023) [38]. In this study, gridded snow depth datasets from ERA5-land MERRA2 obtained at 8:00 a.m., which was approximately coincident with the station sampling time, were selected. Owing to the different spatial resolutions, the ERA5-land and MERRA2 products were resampled to the same spatial size as the other products (25 km × 25 km).

Table 1. Summary of the four gridded snow depth products.

Product Name	Institution	Satellite Data Used	Algorithm	Assimilation of Snow Depth Data	Resolution	Time Series	Refs.
Pixel-based	BNU-China	SSM/I, SSMIS	Semiempirical regression method using satellite observations and machine learning-based snow depth estimates	No	25 km & daily	1988–present	[30]
GlobSnow-v3.0	FMI	SMMR, SSM/I, SSMIS	Bayesian assimilation combining ground data with satellite observations	Yes	25 km & daily	1979–present	[33,34]
ERA5-land	ECMWF	/	Land surface hydrology (HTESSEL) model with ERA5 atmospheric variables	No	9 km & hourly	1950–present	[35]
MERRA2	NASA	/	Catchment land surface model with MERRA2 atmospheric variables	No	50 km & hourly	1980–present	[38]

Table 1. Summary of the four gridded snow depth products.

Product Name	Institution	Satellite Data Used	Algorithm	Assimilation of Snow Depth Data	Resolution	Time Series	Refs.
Pixel-based	BNU-China	SSM/I, SSMIS	Semiempirical regression method using satellite observations and machine learning-based snow depth estimates	No	25 km & daily	1988–present	[30]
GlobSnow-v3.0	FMI	SMMR, SSM/I, SSMIS	Bayesian assimilation combining ground data with satellite observations	Yes	25 km & daily	1979–present	[33,34]
ERA5-land	ECMWF	/	Land surface hydrology (HTESSEL) model with ERA5 atmospheric variables	No	9 km & hourly	1950–present	[35]
MERRA2	NASA	/	Catchment land surface model with MERRA2 atmospheric variables	No	50 km & hourly	1980–present	[38]

2.3. Triple Collocation Method for Error Analysis

The triple collocation method was proposed by Stoffelen in 1998 [39]. It is designed for error estimation without ground truth data and is thus also effective for data fusion. Typically, three independent input products are used in the triple collocation method:

$${\phi }_1=\phi +{\gamma }_1$$

(4)

$${\phi }_2=\phi +{\gamma }_2$$

(5)

$${\phi }_3=\phi +{\gamma }_3$$

(6)

where φ₁, φ₂, and φ₃ are the snow depth estimates (unit: cm) from three independent products. φ denotes the truth value, and γ₁, γ₂, and γ₃ are the residual errors for the three independent products. A smaller γ value indicates better snow depth estimation performance. Then, covariance matrices were computed through transformation Equations (4)–(6):

$$({\phi }_1-{\phi }_2)({\phi }_1-{\phi }_3)={\gamma }_1{\gamma }_1-{\gamma }_1{\gamma }_2-{\gamma }_1{\gamma }_3+{\gamma }_2{\gamma }_3$$

(7)

$$({\phi }_1-{\phi }_2)({\phi }_2-{\phi }_3)={\gamma }_1{\gamma }_2-{\gamma }_2{\gamma }_2-{\gamma }_1{\gamma }_3+{\gamma }_2{\gamma }_3$$

(8)

$$({\phi }_1-{\phi }_3)({\phi }_2-{\phi }_3)={\gamma }_1{\gamma }_2-{\gamma }_3{\gamma }_2-{\gamma }_1{\gamma }_3+{\gamma }_3{\gamma }_3$$

(9)

where γ_iγ_j (i ≠ j) is equal to zero for a sufficient number of training samples (>1000). Thus, the variance of the residual error is expressed as follows:

$${\sigma }_1^2=〈({\phi }_1-{\phi }_2)({\phi }_1-{\phi }_3)〉$$

(10)

$${\sigma }_2^2=〈({\phi }_1-{\phi }_2)({\phi }_2-{\phi }_3)〉$$

(11)

$${\sigma }_3^2=〈({\phi }_1-{\phi }_3)({\phi }_2-{\phi }_3)〉$$

(12)

where ${\sigma }_1^2$, ${\sigma }_2^2$, and ${\sigma }_3^2$ denote the variances of residual errors for three snow depth estimates. The symbol <> denotes the average of all samples.

In this study, we selected three products (pixel-based, ERA5-land, and MERRA2) and calculated the corresponding TCA errors. Here, GlobSnow-v3.0 was excluded because it masks complex-terrain areas where the standard deviation of elevation within a grid cell exceeds 200 m [33,34]. Although both ERA5-land and MERRA2 are model-based reanalysis products, the land surface model and the atmospheric-data-driven model yield different results. Therefore, their random errors are independent. To obtain the TCA error of GlobSnow-v3.0, we used the GlobSnow-v3.0, ERA5-land, and MERRA2 datasets. Owing to the masking of complex-terrain areas for GlobSnow-v3.0, the spatial coverage of TCA-derived errors is small compared with that of other snow depth products.

2.4. Workflow for Elevating Gridded Snow Depth Products Across China

Figure 4 shows the workflow for elevating remotely sensed and reanalysis snow depth products across China. We first optimized effGS via the HUT snow emission model by minimizing the modeling output on the basis of the satellite-observed brightness temperature at frequencies of 18.7 and 36.5 GHz (Figure 4). Here, an RF model was trained using snow depth and predictor variables, such as satellite-observed Tb, effGS, and other static parameters, to generate a snow depth reference dataset from 2012 to 2018. A pixel-based algorithm was then built through pixel-based regression with the reference snow depth dataset produced by the RF algorithm. Eventually, long-term remotely sensed snow depth datasets from 1988 to 2022 were generated with the pixel-based algorithm using SSM/I and SSMIS data. To ensure spatial consistency across datasets, we resampled both ERA5-land and MERRA2 products to a uniform 25 km × 25 km grid resolution using nearest-neighbor interpolation, matching the spatial scale of the other datasets in our analysis. To validate the snow depth products (pixel-based, GlobSnow-v3.0, ERA5-land, and MERRA2), we collected multiple reference (station-based and field campaign) snow depth measurements from 2002 to 2022. Additionally, a triple collocation method was applied to conduct an uncertainty analysis (Figure 4). To demonstrate the reliability of the triple collocation method for assessing snow depth products, we conducted a validation of the triple collocation method against ground-based measurements.

3. Results

3.1. Validation and Comparison of Snow Depth Estimates

Figure 5 shows the validation and comparison of pixel-based, GlobSnow-v3.0, ERA5-land, and MERRA2 snow depth estimates in three stable snow-covered areas across China on the basis of station measurements. The pixel-based estimates are generally similar to the station observations, for example, with unRMSE values of 5.29 and 6.01 cm in NE China and NXJ, respectively. However, the pixel-based values tend to underestimate snow depth in deep snowpack areas relative to the GlobSnow-v3.0 and ERA5-land products. We also found that the MERRA2 product tends to underestimate snow depth in NE China, but it performs best among the four products over the QTP, with the lowest unRMSE of 4.28 cm and the highest correlation coefficient of 0.79. Conversely, ERA5-land yields a serious overestimation over the QTP, with a bias of up to 23.47 cm.

To a certain extent, the assessments based on station data are not dependent because the pixel-based algorithm was trained on the basis of ground measurements, and GlobSnow-v3.0 assimilated the ground-measured snow depth values. Thus, we collected independent snow course data to further assess the four snow depth products. Figure 6 shows the results of validation and comparison for the pixel-based, GlobSnow-v3.0, ERA5-land, and MERRA2 snow depth estimates based on snow course 1, 5, and 6 data. Overall, the pixel-based estimates are highly consistent with the snow course data, with an unRMSE of 6.38 cm and a correlation coefficient of 0.62. For snow course 5, both the GlobSnow-v3.0 and the ERA5-land snow depth estimates are similar to the ground truth observations, which is consistent with the TCA result in Section 3.2. For snow course 6, the estimates for all products are similar to the ground-based measurements. Notably, the TCA results in Section 3.2 also indicated that all products have low errors near snow course 6. The ERA5-land product tends to underestimate (bias of −4.17 cm) snow depth in NE China (near snow courses 5 and 6) but overestimates snow depth in NXJ China (near snow course 1). The MERRA2 product displays serious underestimation trends in NE China and NXJ, which is consistent with the validation result in Figure 5.

Retrieving snow depth in complex terrain areas remains a challenge [4]. Snow course 2 is located near the Tianshan Mountains, and Figure 7 shows the results of validation and comparison for the snow depth estimates of the pixel-based, GlobSnow-v3.0, ERA5-land, and MERRA2 products near snow course 2. Here, the GlobSnow-v3.0 values are smaller than those for the other three products because of the mountain masking effect. These four snow depth products all display poor performance, especially for snow depths greater than 40 cm. ERA5-land products can partially reflect deep snow characteristics in some areas, but the overall uncertainty is high at 18.10 cm. MERRA2 estimates are not sensitive to snow depth in complex mountain areas. Notably, the representativeness of snow course measurements in complex mountains may be questionable.

Figure 8 shows the results of validation and comparison of the pixel-based, GlobSnow-v3.0, ERA5-land, and MERRA2 snow depth estimates based on dense field sampling data across China. The blue and red solid points denote samples from quadrants 1 and 2 of NXJ, respectively (see Figure 1), where quadrat 2 surrounds the Tianshan Mountains. The green solid points denote samples in quadrat 3 in NE China, where the terrain is flat and snow is shallow (see Figure 1). Notably, the sample size for GlobSnow-v3.0 is smaller than that for the other products because mountains are masked. Overall, the pixel-based and GlobSnow-v3.0 data are similar, and the GlobSnow-v3.0 product is slightly superior in quadrat 1. The ERA5-land product displays large uncertainties in NXJ (see blue and red solid points), with unRMSE values up to 16 cm. MERRA2 also displays variable performance in quadrat 1 (blue solid points) and quadrat 2 (red solid points).

Figure 9 shows the daily average snow depth values in the winter season for the pixel-based, GlobSnow-v3.0, ERA5-land, and MERRA2 products. The black square solid dots denote station observations. Here, GlobSnow-v3.0 estimates are only shown through March 2018 because there have been no updates since then. Overall, the pixel-based, GlobSnow-v3.0, and ERA5-land snow depth products can capture seasonal changes in snow depth. However, MERRA2 tends to underestimate snow depth, and limited variation is simulated during the snow season, which affects the TCA results (see the discussion in Section 4). These four gridded products also display interannual variations across various winter seasons. For example, the pixel-based values are overestimated for the 2019–2020 snowy season; ERA5-land values are overestimated in most winter seasons but underestimated for the 2017–2018 snow season; and GlobSnow-v3.0 values are overestimated for the 2016–2017 snow season. MERRA2 is not good at reflecting seasonal changes in snow depth, but provides excellent estimates of shallow snow depths. Moreover, these four products all display considerable uncertainty in the late snow season, which is partially due to snow metamorphism and the presence of wet snow.

3.2. Uncertainty Analysis Based on the Triple Collocation Method

Section 3.1 provides the results of validation and comparison on the basis of ground-based measurements. The representativeness of ground-measured snow depth for a 25 km × 25 km satellite pixel is unknown. Moreover, it is difficult to show the spatial distribution of errors. In this study, an uncertainty analysis based on the triple collocation method, which is independent of ground truth data, is conducted to further assess the snow depth products. In accordance with the triple collocation methodology, we randomly used three independent datasets to calculate random errors (Figure 10). Large errors are observed for GlobSnow-v3.0 estimates in the eastern portion of NE China, where the terrain is complex, typically due to forest cover and the Changbai Mountains. Pixel-based products also present large errors in mountainous and densely forested areas, which is common among empirical algorithms developed solely on the basis of satellite observations. The ERA5-land product presents large errors in high mountains, e.g., the Altai Mountains, Tianshan Mountains, Pamir Mountains, Himalaya Mountains, Hengduan Mountains, and Changbai Mountains. According to the TCA results, MERRA2 presents the best performance among the four snow depth products, which is inconsistent with the results of ground-based validation in Section 3.1 (see the discussion in Section 4).

Figure 11 shows the TCA errors for various land cover types and altitudes for the gridded snow depth products. Here, the satellite pixels where the land cover fraction is greater than 80% are selected as ‘pure landscapes’. The results show that MERRA2 presents the lowest overall errors among the four products across different land cover types (Figure 11a). Moreover, the errors of MERRA2 are insensitive to elevation (Figure 11b). GlobSnow-v3.0 and ERA5-Land presented high errors in barren and grassland areas, respectively (Figure 11a). Figure 11b shows that the TCA errors increase with altitude from 1000 to 6000 m for the pixel-based, ERA5-land, and GlobSnow-v3.0 products. In particular, ERA5-Land is strongly influenced by terrain, as also shown in Figure 10c.

3.3. Comparison of the Errors Between the TCA-Derived and Ground-Based Data

To demonstrate the reliability of the TCA method for assessing uncertainty, we overlaid the station-based errors (unRMSEs) on the TCA-derived background map (Figure 12). The TCA-derived errors are basically consistent with the station-based validation errors for the pixel-based, GlobSnow-v3.0, and ERA5-land products. For example, GlobSnow-v3.0 presents large errors for both the TCA- and station-based results in the NXJ and Changbai Mountains of NE China (Figure 12b), and ERA5-Land displays high uncertainty across mountainous areas in China (Figure 12c). For MERRA2, the TCA- and station-based errors are consistent for shallow snow cover (yellow box in Figure 12d). To our surprise, the TCA-derived errors are lower than the station-based errors for MERRA2 in NXJ (green box in Figure 12d) and higher in some areas of NE China (red box in Figure 12d). We discuss this phenomenon in Section 4.

Figure 13 further displays the scatter plots of the TCA-derived and station-based errors for the four snow depth products. The TCA-derived errors are highly similar to the station-based errors for the pixel-based, GlobSnow-v3.0, and ERA5-land products, which is consistent with the results in Figure 12. This verifies the effectiveness of quantitatively evaluating snow depth products with the TCA method. MERRA2 displays cluster-correlation characteristics (Figure 13d). In NXJ, the TCA errors are significantly lower than the station-based values (green dashed line in Figure 13d, corresponding to the green box in Figure 12d). In some areas of NE China, the TCA-based errors are significantly greater than the station-based values (red dashed line in Figure 13d, corresponding to the red box in Figure 12d). We provide an explanation for this phenomenon in Section 4.

Table 2. Summary of the comparison between the TCA-derived and station-based errors. The bold italicized numbers in brackets denote the performance rankings of the products.

Product	TCA				Station
	NE	NXJ	QTP	China	NE	NXJ	QTP	China
Pixel-based	3.21 (3)	6.19 (3)	3.64 (2)	3.35 (2)	4.07 (3)	5.28 (1)	3.68 (2)	3.58 (2)
GlobSnow-v3.0	5.94 (4)	8.44 (4)	4.58 (3)	4.85 (4)	4.59 (4)	8.42 (4)	5.76 (3)	5.88 (4)
ERA5-Land	3.02 (2)	6.19 (2)	8.46 (4)	3.61 (3)	3.93 (2)	7.27 (2)	9.05 (4)	4.36 (3)
MERRA2	2.95 (1)	3.41 (1)	1.29 (1)	2.28 (1)	3.87 (1)	7.31 (3)	2.27 (1)	3.24 (1)

shows the mean errors and performance rankings of the four products in three stable snow cover areas. The bold italic numbers in brackets denote the performance rankings of the products. The performance rankings for both the TCA- and station-based data are the same in NE China, the QTP region, and China overall. However, in NXJ, the performance rankings for the pixel-based and MERRA2 products are different. The pixel-based product is superior to MERRA2 in NXJ based on the station validation results, whereas the opposite is true for the TCA method. However, according to our ground-based validation results (Figure 5, Figure 6 and Figure 7) presented in Section 3.1, MERRA2 values are severely underestimated in NXJ. A detailed discussion of this phenomenon is provided in Section 4.

We further compare the performance rankings of the pixel-based, ERA5-land, and MERRA2 products on the basis of dense ground sampling data from NXJ (

Table 3. Comparison between TCA-derived and ground sampling-based errors in NXJ. The bold italicized numbers in brackets denote the performance rankings of the products.

Product	TCA	Ground Sampling Data
Pixel-based	5.27 (2)	3.88 (1)
ERA5-Land	7.23 (3)	6.84 (3)
MERRA2	2.41 (1)	5.71 (2)

). Here, GlobSnow-v3.0 is not included because of its spatial masking in mountain areas. The pixel-based dataset is best among the three products based on ground sampling observations. However, MERRA2 outperforms the other two products on the basis of the TCA matrix. The results in Table 3 are consistent with those in Table 2.

4. Discussion

Figure 12 and Table 2 compare the TCA-derived and station-based errors across China, and the results reveal that the consistency of error estimates and performance rankings is very similar. However, the station-based errors of MERRA2 are significantly higher than those for the TCA-derived results in NXJ, whereas the opposite is true in NE China (Figure 13). To assess the reasons for this difference, we statistically analyzed the spatial distributions of the covariance matrix and the time series of snow depth values. We found that both the variance of MERRA2 (Figure 14a) and the cross-covariance of the datasets (Figure 14b) are small, except in the Altai Mountains; thus, the TCA-derived errors are low in most areas (background map in Figure 14c). We further analyzed the time series of snow depth data (Figure 14d). The black solid dots denote the snow depth measured at each station, and the colorful solid dots represent the three gridded snow depth products. The results show that MERRA2 presents serious underestimations in the snow season. Moreover, the dynamic range of this product is narrow throughout the entire snow season, typically less than 15 cm, but it can reach 30 cm for station measurements. Thus, the narrow variation in MERRA2 leads to a small variance in MERRA2 (Figure 14a), which possibly results in low TCA errors. Figure 14 illustrates the inconsistency between the TCA-derived and station-based errors observed in Figure 12 and Table 2 and Table 3. Specifically, TCA may underestimate errors when a product cannot reflect the seasonal variations in snow depth.

Figure 12 and Figure 13 also show that the TCA-derived errors are greater than the station-based results in some areas of NE China. We further present the spatial distributions of the covariances and the time series of snow depth values in the NE China region (Figure 15). We found that the TCA errors in farmland areas (red circles in Figure 15) are greater than those for the station-based results. According to the spatial distributions of covariances, the variance of MERRA2 (Figure 15a) is small, but the cross-covariance (Figure 15b) is large, which results in high TCA errors (background map in Figure 15c). The time series of snow depth in Figure 15d shows that MERRA2 seriously overestimates snow depth. Moreover, the three products simultaneously present significant uncertainty, even different trends, which results in high cross-covariance (Figure 15b). In the eastern portion of NE China (green circle in Figure 15), the TCA errors of MERRA2 are small relative to those for the station-measured data (Figure 15c). This can be explained by the underestimation issue and the narrow dynamic range of MERRA2 (Figure 15e).

Our results showed that the TCA method does not provide robust results in some cases, e.g., there is one product with significantly high inaccuracy (underestimation for MERRA2), and some pairs of datasets display low correlations and even different trends. Additionally, the key TCA assumption is zero-error cross-correlation. Although we selected four independent products in this study, in practice, different TCA triplets may violate the above basic assumption for various reasons. In the present study, to ensure the robustness of the TCA-based metrics, the triplets are based on more than 1000 samples, and the correlation of any two datasets is greater than 0.3 [20]. In this study, we employed station-based measurements as reference data to evaluate TCA-derived errors. However, the representativeness of point-scale snow depth measurements within a coarse 25 km × 25 km pixel remains uncertain. To strengthen the robustness of our assessment, we conducted additional validation comparing TCA-derived errors with ground-based sampling errors in NXJ (Table 3). Notably, the performance rankings of the pixel-based and MERRA2 products showed inversion patterns between TCA-derived and ground-based errors, which is consistent with those observed in Table 2. This consistency across different validation reference data supports the reliability of our findings.

According to our validation results in Section 3 (Figure 5, Figure 6, Figure 7, Figure 8 and Figure 12), each product may perform well or poorly in different areas. For example, the pixel-based product displays good performance in flat and open areas but high errors in forested and high mountain areas (Figure 12a). GlobSnow-v3.0 displays a low error, except in the eastern part of NE China, where forests and mountains are predominant (Figure 12b). ERA5-land performs well in some areas of NE China (Figure 12c). Moreover, the daily averages of ERA5-Land are highly consistent with the station observations (Figure 5, Figure 14 and Figure 15) in most areas except for the QTP. MERRA2 performs well in shallow snow-covered areas, e.g., the QTP. Thus, it is necessary to realize the complementary advantages of each product by fusing multisource snow depth products to improve estimates of snow depth. This study demonstrates the reliability of the TCA method for uncertainty analysis, supporting its application in multi-dataset fusion. However, as highlighted in our findings, TCA-based fusion still presents challenges, particularly in the selection of three complementary snow depth products. Future work will explore the spatial heterogeneity of TCA errors using additional datasets, aiming to optimize product selection for different regional conditions and improve snow depth estimation accuracy.

5. Conclusions

This study presents a comprehensive uncertainty assessment of four widely used gridded snow depth products (pixel-based, GlobSnow-v3.0, ERA5-Land, and MERRA-2) through TCA, validated against multiple ground-based measurements. Furthermore, we rigorously evaluated the reliability of our uncertainty analysis by systematically comparing TCA-derived errors with ground-based measurement errors. Our results demonstrated that the TCA-derived and ground-based errors are strongly correlated, and both provide consistent performance rankings in most areas across China. For example, the rankings for the QTP region are MERRA2 > pixel-based > GlobSnow-v3.0 > ERA5-Land; those for NE China are MERRA2 > ERA5-land > pixel-based > GlobSnow-v3.0; and those over China are MERRA2 > pixel-based > GlobSnow-v3.0 > ERA5-land. We also found that the TCA-derived errors for MERRA2 are low relative to the ground-based results in NXJ. Our analysis of the TCA data demonstrated that this difference can be explained by the narrow dynamic range and severe underestimation issue of the MERRA2 product during the snow season. Additionally, we found that the low correlations between any two datasets (even with opposing trends) can hinder the performance of the TCA method. Overall, the TCA method for assessing snow depth products is reliable in most cases; for example, the triplet approach provides sufficient samples for comparison, seasonal changes are effectively estimated (without serious underestimation), and any two datasets are correlated, with similar trends. This study not only validates the reliability of the TCA method for uncertainty quantification but also reveals its methodological limitations. These findings provide critical insights for snow depth product validation, particularly in complex mountainous terrain and when utilizing multi-product ensemble approaches.