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Snow depth retrieval by using robust estimation algorithm to perform multi-SNR and multi-system fusion in GNSS-IR

<p>The PROMICE project runs 27 Automatic Weather Stations (AWSs) in Greenland. Most of these are located in the ablation zone of the Greenland ice sheet. From March to September 2020 a multi-frequency Global Navigation Satellite System (GNSS) antenna was installed on the AWS NUK-K at a small local glacier outside Nuuk with the purpose of testing the setup for high precision positioning. Due to the remote location, power supply is limited and the GNSS setup is constructed to minimize the power consumption. Therefore, data collection is limited to three hours each day, the antenna is passive and the data is stored on a local drive and not transmitted.<br><br>This study tests if the setup is feasible for GNSS Interferometric Reflectometry (GNSS-IR) measurements of snow depth. The method estimates the average snow depth over an area on the order 10-20 • 10<sup>3</sup> m<sup>2</sup>. GNSS-IR analysis shows good reflections during most of the covered time period. A sonic ranger is mounted on the PROMICE AWSs and used for measurement of snow depth. The GNSS reflector heights are compared to measurements from the sonic ranger. Though some differences are present, the GNSS-IR estimates capture the snow melt, as measured by the sonic ranger, well. The quality of the reflections decreases towards the end of the data series when the snow is melted. We expect that this is due to a rougher ice surface. However, useful reflections are still obtained but the uncertainty on the daily estimates increase significantly. The transition from snow to ice surface is confirmed by an albedo estimate based on measurements of shortwave radiation at the AWS.</p>

As a part of global fresh water resources, the change of snow storage has an important impact on the earth’s ecological environment, climate change and human development. Recently years, with the continuous development of Global Navigation Satellite System, GNSS Multipath Reflectometry technology has become one of the emerging means of snow depth measurement because of its all-weather, low cost, high spatial-temporal resolution and other advantages. Based on the study of the basic principle of snow depth measurement by GNSS-MR technology, this paper uses the observation data of p351 station in the PBO network of the United States to retrieve the local snow depth. And then the retrieved snow depth is compared with the measured snow depth of 490 station in the SNOTEL network of the United States. The results show that the correlation coefficient between the two is about 0.98, and the Root Mean Square Error is about 0.1 m, which has a good consistency. On this basis, this article analyzes GNSS-MR snow depth measurement error from three aspects: azimuth, elevation angle and snow depth, and finds that there is a certain quantitative relationship between the negative error generated by GNSS-MR snow depth measurement and the snow depth. Aiming at different error characteristics and error sources, the weakening methods are proposed and verified in practice, which provides a reference for the error correction of GNSS-MR technology in snow depth measurement and other environmental monitoring.

Snow depth or snow water equivalent in mountainous region is crucial for hydrology, water resources management, meteorological and climate research. Remote sensing can be used for snow depth monitoring in regional scale or global scale. However, the spaceborne remote sensing of snow depth in mountain is challenging because of the sensor sensitivity and spatial resolution problems. Recently, time series Sentinel-1 is used for snow depth retrieval in mountains, which shows encouraging accuracy. In this study, an algorithm to estimate the snow depth in mountainous regions using optical and passive microwave remote sensing observations is proposed, which can be applied in periods before and after the launch of Sentinel-1. The optical and passive microwave remote sensing observations and the Sentinel-1 derived snow depth in 2016-2021 are used to train the snow depth retrieval algorithm using the Extreme gradient boosting (XGBoost) machine learning algorithm. Validations are performed using cross validation method and independent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-situ</i> snow depth data. The cross validation shows correlation coefficient of 0.81 and mean absolute error (MAE) of 0.17m. The correlation coefficient and MAE of predicted snow depth and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-situ</i> snow depth in 2002-2016 are 0.61 and 0.33 m, respectively, which shows significant higher accuracy compared with AMSR-E/AMSR2 snow depth products. The site dependence of the machine learning method is also discussed. The machine learning based snow depth retrieval presented in this study can be applied to mountains globally to the optical and passive microwave remote sensing era.

Global navigation satellite system (GNSS) multipath reflectometry (MR) has emerged as a new technique that uses signals of opportunity broadcast by GNSS satellites and tracked by ground-based receivers to retrieve environmental variables such as snow depth. The technique is based on the simultaneous reception of direct or line-of-sight (LOS) transmissions and corresponding coherent surface reflections (non-LOS). Until recently, snow depth retrieval algorithms only used legacy and modernized GPS signals. Using multiple GNSS constellations for reflectometry would improve GNSS-MR applications by providing more observations from more satellites and independent signals (carrier frequencies and code modulations). We assess GPS and GLONASS for combined multi-GNSS-MR using simulations as well as field measurements. Synthetic observations for different signals indicated a lack of detectable interfrequency and intercode biases in GNSS-MR snow depth retrievals. Received signals from a GNSS station continuously operating in France for a two-winter period are used for experimental snow depth retrieval. We perform an internal validation of various GNSS signals against the proven GPS-L2-C signal, which was validated externally against in situ snow depth in previous studies. GLONASS observations required a more complex handling to account for topography because of its particular ground track repeatability. Signal intercomparison show an average correlation of 0.922 between different GPS snow depths and GPS-L2-CL, while GLONASS snow depth retrievals have an average correlation that exceeds 0.981. In terms of precision and accuracy, legacy GPS signals are worse, while GLONASS signals and modernized GPS signals are of comparable quality. Finally, we show how an optimal multi-GNSS combined daily snow depth time series can be formed employing variance factors with a ~59%-90% precision improvement compared to individual signal snow depth retrievals, resulting in snow depth retrieval with uncertainty of 1.3 cm. The developed combination strategy can also be applied for the European Galileo and the Chines BeiDou navigation systems.

Abstract. The satellite laser altimeter ICESat-2 provides accurate surface elevation observations across the globe. With a high-resolution digital elevation model (DEM), we can use such measurements to retrieve snow depth profiles even in remote areas where snow amounts are poorly constrained. However, the adoption of these retrievals remains low since they are very sparse in space, as the satellite measures along profiles, and in time, as the revisit is 3 months. Data assimilation (DA) methods can exploit snow observations to constrain snow models and provide gap-free distributed simulations. The assimilation of observations related to snow cover is well-established, but there are currently no methods to assimilate sparse ICESat-2 snow depth profiles. We propose an approach that spatially propagates information using – instead of the classic geographical distance – an abstract distance measured in a feature space defined by a topographical index and the melt-out date climatology. We demonstrate this framework for a small experimental catchment in the Spanish Pyrenees through three experiments. We assimilate different snow observations in an intermediate-complexity snow model: fractional snow-covered area (fSCA) retrievals from Sentinel-2, snow depth profiles from ICESat-2 located in proximity of the catchment or both fSCA and depth in a joint assimilation experiment. Results show that assimilating ICESat-2 snow depth profiles successfully updates the neighbouring unobserved catchment, improving the simulated average snow depth compared to the prior run. Another encouraging finding is that adding the snow depth profiles to fSCA observations leads to an accurate reconstruction of the snow depth spatial distribution. Evaluating the simulations with a set of independent drone-based snow depth maps using a probabilistic skill score, we find that for the accumulation season the joint assimilation's score improves by 19 % the established approach of only assimilating fSCA. The direct but incomplete snow depth information from ICESat-2 is a key constraint on simulated basin-average snow depth. This study makes use of globally available datasets and shows the promise of adopting ICESat-2's snow depth retrievals in seasonal snow modelling, especially when also assimilating complementary observations. In light of our encouraging results, more research with different experimental designs in varying snow conditions combined with continued methodological development is desirable to further catalyse the use of these retrievals in cryospheric and hydrologic applications.

Abstract. Lidar is an effective tool to measure snow depth over key watersheds across the United States. Lidar-derived snow depth observations from airborne platforms have demonstrated centimeter-level accuracy at high spatial resolution. However, ground-based and airborne lidar surveys are costly and limited in space and time. In recent years, there has been an emerging interest in using spaceborne lidar to estimate snow depth. Preliminary results from spaceborne lidar altimeters such as the NASA Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) can provide routine snow depth retrievals over watersheds, though further research on accuracy, coverage, and operational potential is needed. In this review, we outline the current status of research using spaceborne lidar to derive snow depth. We focus on the currently operational ICESat-2 mission, with a summary of snow observations gathered from previous studies. An example snow depth retrieval using ICESat-2 is also given over the Alaskan tundra. We also outline best practices for spaceborne lidar snow depth retrieval, based on findings from recent studies. We conclude with a discussion of ongoing challenges for spaceborne lidar, with suggestions for future studies and requirements for future mission concepts.

Snow-depth retrieval from passive microwave observations without a priori information is a highly undetermined problem. Achieving accurate snow-depth retrievals requires a priori information on the snowpack properties, such as grain size, density, physical temperature, and stratigraphy. On a practical level, however, retrieval algorithms must consider prior information, while minimizing the dependence on it, as accurate ancillary data are not globally available. In this study, we build on the previously published Bayesian Algorithm for Snow Water Equivalent Estimation (BASE) to retrieve snow depth using an airborne passive microwave data set over the tundra snow in the Eureka region. The method computes the optimal estimates of snow depth, density, grain size, and other variables, given the brightness temperature observations and prior information, using Markov chain Monte Carlo (MCMC). The airborne data set includes passive microwave brightness temperature (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> ) at 18.7 and 36.5 GHz. The in situ measurements of the snow depth provide validation data for 464 sensor footprints. The microwave radiative transfer (RT) model used is the Dense Media RT-Multilayered (DMRT-ML) model. We use a two-layer wind slab and depth hoar assumption based on the local snow cover knowledge from the previous research on the study area. To improve our understanding of the results using the airborne T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s, the inversion was also applied using the synthetic observations, where T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s were generated from the RT model. For the case with synthetic observations, the snow-depth RMSE was 0.07 cm. When the airborne T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s are used, the snow-depth RMSE was 21.8 cm. This discrepancy is due to the large spatial variability in the MagnaProbe snow-depth measurements and the fact that not all physical processes affecting the airborne T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> s are represented in the RT model. Our work verifies the feasibility and applicability of the proposed methodology regionally for the airborne retrievals and reinforces the tractable applicability of a physics-based RT model in the SWE retrievals.

Passive microwave remote sensing provides indispensable observations for constructing long-term snow depth records, which are critical for climatology, hydrology, and operational applications. Nevertheless, despite decades of snow depth monitoring, systematic evaluations of how inter-sensor brightness temperature differences (TBDs) propagate into retrieval uncertainties are still lacking. In this study, TBDs between DMSP-F18/SSMIS, FY-3D/MWRI, and AMSR2 sensors were quantified, and the sensitivity of seven snow depth retrieval algorithms to these discrepancies was systematically assessed. The results indicate that TBDs between SSMIS and AMSR2 are larger than those between MWRI and AMSR2, likely reflecting variations in sensor specifications such as frequency, observation angle, and overpass time. In terms of algorithm sensitivity, SPD, WESTDC, FY-3B, and FY-3D demonstrate less sensitivity across sensors, with standard deviations of snow depth differences generally below 2 cm. In contrast, the Foster algorithm exhibits pronounced sensitivity to TBDs, with standard deviations exceeding 11 cm and snow depth differences reaching over 20 cm in heavily forested regions (forest fracion &gt;90%). This study provides guidance for SWE virtual constellation design and algorithm selection, supporting long-term, seamless, and consistent snow depth retrievals.

Arctic sea ice and snow affect the energy balance of the global climate system through the radiation budget. Accurate determination of the snow cover over Arctic sea ice is significant for the retrieval of the sea ice thickness (SIT). In this study, we developed a new snow depth retrieval method over Arctic sea ice with a long short-term memory (LSTM) deep learning algorithm based on Operation IceBridge (OIB) snow depth data and brightness temperature data of AMSR-2 passive microwave radiometers. We compared climatology products (modified W99 and AWI), altimeter products (Kwok) and microwave radiometer products (Bremen, Neural Network and LSTM). The climatology products and altimeter products are completely independent of the OIB data used for training, while microwave radiometer products are not completely independent of the OIB data. We also compared the SITs retrieved from the above different snow depth products based on Cryosat-2 radar altimeter data. First, the snow depth spatial patterns for all products are in broad agreement, but the temporal evolution patterns are distinct. Snow products of microwave radiometers, such as Bremen, Neural Network and LSTM snow depth products, show thicker snow in early winter with respect to the climatology snow depth products and the altimeter snow depth product, especially in the multiyear ice (MYI) region. In addition, the differences in all snow depth products are relatively large in the early winter and relatively small in spring. Compared with the OIB and IceBird observation data (April 2019), the snow depth retrieved by the LSTM algorithm is better than that retrieved by the other algorithms in terms of accuracy, with a correlation of 0.55 (0.90), a root mean square error (RMSE) of 0.06 m (0.05 m) and a mean absolute error (MAE) of 0.05 m (0.04 m). The spatial pattern and seasonal variation of the SITs retrieved from different snow depths are basically consistent. The total sea ice decreases first and then thickens as the seasons change. Compared with the OIB SIT in April 2019, the SIT retrieved by the LSTM snow depth is superior to that retrieved by the other SIT products in terms of accuracy, with the highest correlation of 0.46, the lowest RMSE of 0.59 m and the lowest MAE of 0.44 m. In general, it is promising to retrieve Arctic snow depth using the LSTM algorithm, but the retrieval of snow depth over MYI still needs to be verified with more measured data, especially in early winter.

Snow depth is a general input variable in many models of agriculture, hydrology, climate, and ecology. However, there are some uncertainties in the retrieval of snow depth by remote sensing. Errors occurred in snow depth evaluation under the D-InSAR methods will affect the accuracy of snow depth inversion to a certain extent. This study proposes a scheme to estimate spatial snow depth that combines remote sensing with site observation. On the one hand, this scheme adopts the Sentinel-1 C-band of the European Space Agency (ESA), making use of the two-pass method of differential interferometry for inversion of spatial snow depth. On the other hand, the 3DVAR (three dimensional variational) fusion algorithm is used to integrate actual snow depth data of virtual stations and real-world observation stations into the snow depth inversion results. Thus, the accuracy of snow inversion will be improved. This scheme is applied in the study area of Bayanbulak Basin, which is located in the central hinterland of Tianshan Mountains in Xinjiang, China. Observation data from stations in different altitudes are selected to test the fusion method. According to the results, most of the obtained snow depth values using interferometry are lower than the observed ones. However, after the fusion using the 3DVAR algorithm, the snow depth accuracy is slightly higher than it was in the inversion results (R2 = 0.31 vs. R2 = 0.50, RMSE = 2.51 cm vs. RMSE = 1.96 cm; R2 = 0.27 vs. R2 = 0.46, RMSE = 4.04 cm vs. RMSE = 3.65 cm). When compared with the inversion results, the relative error (RE) improved by 6.97% and 3.59%, respectively. This study shows that the scheme can effectively improve the accuracy of regional snow depth estimation. Therefore, its future application is of great potential.

The goal of this study is to understand the pattern of snow distribution over mountain ranges and the capability of L-band Synthetic Aperture Radar (SAR) data to retrieve snow depth. Ground-based snow records and Airborne Lidar and SAR data collected as part of NASA's snow expedition over Mores Creek Summit in 2021 were employed for this study. The preliminary result shows that co-polarization particularly VV has better coherence and thus most optimal for snow monitoring. The impact of large temporal baseline, vegetation and elevation on coherence were analyzed. Result shows that decorrelation increases with vegetation and temporal separation as expected but decreases with elevation. A good agreement exists between lidar snow depth and snow depth recorded by SNOTEL. Snow depth retrieved from the UAVSAR data captured snow accumulation and melt pattern between the satellite acquisition dates as confirmed by the snow depth record at SNOTEL study site. Atmospheric correction of the phase change is required to improve the accuracy of InSAR techniques for snow depth estimation. This study will contribute to existing efforts in the snow science community to understand the capability of future satellite missions such as NISAR, a U.S-Indian satellite that is planned to operate on L-band.

The accurate knowledge of spatial and temporal variations of snow depth over sea ice in the Arctic basin is important for understanding the Arctic energy budget and retrieving sea ice thickness from satellite altimetry. In this study, we develop and validate a new method for retrieving snow depth over Arctic sea ice from brightness temperatures at different frequencies measured by passive microwave radiometers. We construct an ensemble-based deep neural network and use snow depth measured by sea ice mass balance buoys to train the network. First, the accuracy of the retrieved snow depth is validated with observations. The results show the derived snow depth is in good agreement with the observations, in terms of correlation, bias, root mean square error, and probability distribution. Our ensemble-based deep neural network can be used to extend the snow depth retrieval from first-year sea ice (FYI) to multi-year sea ice (MYI), as well as during the melting period. Second, the consistency and discrepancy of snow depth in the Arctic basin between our retrieval using the ensemble-based deep neural network and two other available retrievals using the empirical regression are examined. The results suggest that our snow depth retrieval outperforms these data sets.

Enhanced algorithm for estimating snow depth from geostationary satellites

Snow on sea ice influences the Arctic energy and heat budgets and is therefore important for Arctic climate studies. Methods to derive snow depth based on satellite‐borne microwave radiometer observations have existed since the 1990s. However, in the Arctic the most widely used algorithm can only be applied over first‐year ice (FYI) and does not make use of the lower frequencies, which are available since 2002. Here we present three improvements to the current passive microwave snow depth retrieval: (a) We derive new coefficients based on a regression analysis using 5 years of Operation IceBridge airborne snow depth measurements. (b) We extend the algorithm to take advantage of the lower frequency channel at 7 GHz. (c) We consider an extension of the snow depth retrieval to multiyear ice (MYI) during spring. Our results show that the gradient ratio, GR(19/7) is most suited for deriving snow over both Arctic FYI (R =°−0.73) and MYI (R = −0.57). An evaluation of the new retrieval with Operation IceBridge snow depth measurements from March and April 2015 shows a good agreement over FYI (difference = −2.1 cm; 93% of the differences below 5 cm). Over MYI the difference is −4.0 cm and 56% of the differences are below 5 cm, that is, the root mean square distance (RMSD) is larger over MYI than over FYI. We demonstrate for the first time that spring snow depth measurements can be derived from passive microwave observations over both FYI and MYI.