Snow Water Equivalent Measurements Research Articles

Bootstrap Methods for Bias-Correcting Probability Distribution Parameters Characterizing Extreme Snow Accumulations

Accurately quantifying the threat of collapse due to the weight of settled snow on the roof of a structure is crucial for ensuring structural safety. This quantification relies upon direct measurements of the snow water equivalent (SWE) of settled snow, though most weather stations in the United States only measure snow depth. The absence of direct load measurements necessitates the use of modeled estimates of SWE, which often results in the underestimation of the scale/variance parameter of the distribution of annual maximum SWE. This paper introduces a novel bias correction method that employs a bootstrap technique with regression-based models to calibrate the variance parameter of the distribution. The efficacy of this approach is demonstrated on real and simulated datasets. The findings reveal varied levels of success, with the efficacy of the proposed approach being inherently dependent on the quality of the selected regression-based model. These findings demonstrate that integrating our approach with a suitable regression-based model can produce unbiased or nearly unbiased annual maximum SWE distribution parameters in the absence of direct SWE measurements.

Quantifying regional variability of machine-learning-based snow water equivalent estimates across the Western United States

Seasonal snow-derived water is a critical component of the water supply in the mountains and downstream regions, and the accurate characterization of available water in the form of snow-water-equivalent (SWE), peak SWE, and snowmelt onset are essential inputs for water management efforts. Arising from recent advancements in artificial intelligence (AI) and machine learning (ML), we introduce a large-scale ML SWE model leveraging publicly available data sources and open-source software. The model demonstrates the application of a limited feature space in a relatively simple ML architecture without the need for process-based formulations to effectively estimate spatially continuous SWE at a daily temporal resolution. Beginning with in situ SWE measurements (i.e., SNOTEL), lidar-derived terrain features, and temporal variables, we employ localized feature engineering and optimization via gradient-boosting decision trees to identify regionally unique drivers of snowpack dynamics and use the optimal features to train regionally independent artificial neural networks to estimate regional SWE at a 1 km spatial resolution. The model results yield respectable skill in reconstructed 1 km gridded SWE magnitudes in a hindcast simulation of the 2019 water year that is independent of the training and testing data. Comparing model estimates to over 6200 observations, the model demonstrates a weighted RMSE of 15.4 cm, Kling-Gupta Efficiency metric of 0.86, and a percent bias of 0.71% across 23 snow-influenced regions in the western U.S. The model simulation produces peak SWE estimates within 10 cm for twenty of the twenty-three regions, demonstrating capability in effectively capturing regional snow accumulation processes. The demonstration of low-error ML workflows capable of providing near-real-time, spatially continuous SWE estimates at a high spatial resolution provides proof-of-concept and a foundation to effectively update snow state variables that drive water supply forecasts in snow-dominated regions.

Snow water equivalent retrieval over Idaho – Part 1: Using Sentinel-1 repeat-pass interferometry

Abstract. Snow water equivalent (SWE) is identified as the key element of the snowpack that impacts rivers' streamflow and water cycle. Both active and passive microwave remote sensing methods have been used to retrieve SWE, but there does not currently exist a SWE product that provides useful estimates in mountainous terrain. Active sensors provide higher-resolution observations, but the suitable radar frequencies and temporal repeat intervals have not been available until recently. Interferometric synthetic aperture radar (InSAR) has been shown to have the potential to estimate SWE change. In this study, we apply this technique to a long time series of 6 d temporal repeat Sentinel-1 C-band data from the 2020–2021 winter. The retrievals show statistically significant correlations both temporally and spatially with independent in situ measurements of SWE. The SWE change measurements vary between −5.3 and 9.4 cm over the entire time series and all the in situ stations. The Pearson correlation and RMSE between retrieved SWE change observations and in situ stations measurements are 0.8 and 0.93 cm, respectively. The total retrieved SWE in the entire 2020–2021 time series shows an SWE error of less than 2 cm for the nine in situ stations in the scene. Additionally, the retrieved SWE using Sentinel-1 data is well correlated with lidar snow depth data, with correlation of more than 0.47. Low temporal coherence is identified as the main reason for degrading the performance of SWE retrieval using InSAR data. We also show that the performance of the phase unwrapping algorithm degrades in regions with low temporal coherence. A higher frequency such as L-band improves the temporal coherence and SWE ambiguity. SWE retrieval using C-band Sentinel-1 data is shown to be successful, but faster revisit is required to avoid low temporal coherence. Global SWE retrieval using radar interferometry will have a great opportunity with the upcoming L-band 12 d repeat-pass NASA-ISRO Synthetic Aperture Radar (NISAR) data and the future 6 d repeat-pass Radar Observing System for Europe in L-band (ROSE-L) data.

Estimating snow water equivalent using observed snow depth data in China

Study regionChina. Study focusThe snow water equivalent (SWE) characterizes the hydrological significance of the snow and is essential for the study of water resources in snow-covered areas. However, SWE measurements are time-consuming and labour-intensive, and the amount of observed SWE data globally is small compared to snow depth (SD), particularly in China. This has limited the study of snow hydrology in China. To this end, we parameterize the SWE and briefly analyse the spatiotemporal distribution and variations of the SWE in China. New hydrological insights for the regionThe mean absolute error, root mean square error and Nash-Sutcliffe efficiency coefficient of the estimation model are 0.49 g cm−2, 0.81 g cm−2, and 0.80, respectively, which indicate that the model performs well overall. The estimation model is able to accurately estimate SWE for different seasons and altitudes in China. However, due to the influence of SD, the estimation model is more applicable in snow-rich areas such as the Northern Xinjiang, Northeast China and middle and lower Yangtze River Plain, and less applicable in the Qinghai-Tibet Plateau. The trend of SWE in China increases at high latitudes and low altitudes and decreases at low latitudes and high altitudes. The seasonality trend of SWE varies widely in different regions. The results of the study provide a new approach to the study of snow hydrology in China.

Morphological indexes to describe snow-cover patterns in a high-alpine area

Abstract The spatiotemporal distribution of snow affects hydrological and climatological processes at different scales. Accordingly, quantifying geometric features of snow-cover patterns is important, providing a valuable complement for snow water equivalent (SWE) modelling. This study on satellite-based morphological analysis originally uses two types of geometric indexes: (1) MN, Minkowski numbers (area (MN1), perimeter (MN2), Euler number (MN3)), and (2) CL, average chord length, to describe the morphology of Sentinel-2-derived snow-covered areas (SCAs), within the high-alpine site Zugspitze for a 5 year period. Results indicate that they capture the seasonal variability of snow-cover patterns, particularly during accumulation and ablation. Being to some degree independent from each other, MN2, MN3 and CL provide additional information upon shape, connectivity and length scale of snow cover, compared to most used indexes (e.g. fractional SCA). Correlation values up to +0.7 for MN2, +0.58 for MN3 and +0.46 for CL were observed with selected topographic characteristics, suggesting a close connection between geometric features of snow cover and ground features. Comparing in situ SWE measurements with MN and CL shows a correlation between −0.5 and +0.5. These indexes can hence be applied in combination with in situ data and/or modelling approaches to improve spatially distributed SWE in high-alpine catchments.

Assessment of L-band InSAR snow estimation techniques over a shallow, heterogeneous prairie snowpack

Snow water equivalent (SWE) is a critical input for weather, climate, and water resource management models at local to global scales. Despite its importance, global SWE measurements that are accurate, consistent, and at sufficiently high spatiotemporal resolutions are not currently available. L-band interferometric synthetic aperture radar (InSAR) techniques have been used to measure SWE at local to regional scales, and two upcoming L-band SAR satellite missions have renewed interest in these techniques to provide regular SWE measurements at the global scale. However, previous research demonstrating the capabilities of L-band InSAR-SWE measurement has been limited to mountain or tundra snowpack regimes. Here we examine the feasibility of applying the same techniques over a prairie snowpack, which are typically characterized by shallow snow depths (mean snow depth of 0.22 m in this study), exposed agricultural vegetation, and high spatial variability over short distances. Our study area in central Montana, USA (47.060, -109.951) was a validation site for NASA SnowEx 2021, as part of the UAVSAR snow timeseries. Airborne L-band SAR imagery was acquired by the UAVSAR platform while concurrent snow measurements were collected using uncrewed aerial vehicle (UAV)-based LiDAR, UAV-based photogrammetry, and ground-based manual techniques. This validation dataset enables an investigation of the effects of sub-pixel snow cover heterogeneity and exposed agricultural vegetation stubble on SAR data and the resulting SWE estimations. Results based on repeated application of the Kolmogorov–Smirnov test show that UAVSAR VV phase change is sensitive to differences in snow cover but relatively unaffected by differences in agricultural stubble height. However, we did not find similarly definitive results when we used the same phase change data to estimate SWE. Although broad spatial patterns were similar in both LiDAR-derived and InSAR-derived SWE estimates, considerable differences in the two estimates were apparent in areas with large sub-pixel snow depth variability. Our results indicate that additional work is necessary to derive accurate SWE estimates in prairie environments. Regular measurements from L-band SAR satellites will provide an excellent opportunity to refine InSAR-based snow estimation techniques over shallow, heterogeneous snowpacks.

Development of the snow- and ice-accounting routine (SIAR)

This paper evaluates the degrees of freedom and complexity warranted in temperature-index models to jointly simulate local snow measurements, remotely-sensed snow cover and runoff in mountainous areas. To address this issue, the snow- and ice-accounting routine (SIAR) on top of the GR4J model was developed on a dataset covering 17 mountainous catchments (45 to 3580 km2) in the French Alps and Pyrenees. Model calibration and control were based on streamflow series, fractional snow cover (FSC) computed from MODIS snow products and at least one chronicle of local measurements of snow water equivalent (SWE) acquired in each catchment for the period 2004–2016. SIAR was applied according to an adaptable number of elevation bands and different parametrizations ranging from 11 free parameters (precipitation orographic correction, temperature lapse rate, variation in the temperature lapse rate, snowfall adjustment, rainfall lapse rate, thermal inertia of the snow pack, constant and variable part of the degree-day snow melt factor, degree-day ice melt factor, 2-parameter hysteresis between SWE and FSC), to only fixed parameters. Results showed that the one-free-parameter SIAR is as efficient as more parametrized versions in simulating both local and distributed snow dynamics as well as runoff. Interestingly, using SIAR without any free parameters by fixing the snowfall adjustment to a median value of 60% only led to slight impairment of local SWE dynamics. Certain processes represented in SIAR (glacier-component, sublimation, simple energy balance, snowpack cold-content, variable melt factor) were then alternatively turned off to justify those retained in its final version. The modeling performances were also compared by applying SIAR with different distribution options ranging from full distribution according to 0.25 km2 cells to lumped mode. A number of equal-area elevation bands according to the catchment hypsometry proved to be a good compromise as it allowed snow and runoff simulations of similar accuracy to the full distribution mode, while limiting computational time. Finally, SIAR was compared with the Cemaneige snow routine, which showed its modeling performance was better. These findings suggest that it is possible, and even advisable, to limit the number of free parameters in temperature-index models in order to reduce problems of over-parameterization and equifinality.

Estimating spatiotemporally continuous snow water equivalent from intermittent satellite observations: an evaluation using synthetic data

Abstract. Accurate estimates of snow water equivalent (SWE) based on remote sensing have been elusive, particularly in mountain areas. However, there now appears to be some potential for direct satellite-based SWE observations along ground tracks that only cover a portion of a spatial domain (e.g., watershed). Fortunately, spatiotemporally continuous meteorological and surface variables could be leveraged to infer SWE in the gaps between satellite ground tracks. Here, we evaluate statistical and machine learning (ML) approaches to performing track-to-area (TTA) transformations of SWE observations in California's upper Tuolumne River watershed using synthetic data. The synthetic SWE measurements are designed to mimic a potential future P-band Signals of Opportunity (P-SoOP) satellite mission with a (along-track) spatial resolution of about 500 m. We construct relationships between multiple meteorological and surface variables and synthetic SWE observations along observation tracks, and we then extend these relationships to unobserved areas between ground tracks to estimate SWE over the entire watershed. Domain-wide, SWE inferred on 1 April using two synthetic satellite tracks (∼4.5 % basin coverage) led to percent errors of basin-averaged SWE (PEBAS) of 24.5 %, 4.5 % and 6.3 % in an extremely dry water year (WY2015), a normal water year (WY2008) and an extraordinarily wet water year (WY2017), respectively. Assuming a 10 d overpass interval, percent errors of basin-averaged SWE during both snow accumulation and snowmelt seasons were mostly less than 10 %. We employ a feature sensitivity analysis to overcome the black-box nature of ML methods and increase the explainability of the ML results. Our feature sensitivity analysis shows that precipitation is the dominant variable controlling the TTA SWE estimation, followed by net long-wave radiation (NetLong). We find that a modest increase in the accuracy of SWE estimation occurs when more than two ground tracks are leveraged. The accuracy of 1 April SWE estimation is only modestly improved for track repeats more often than about 15 d.

A Hydrograph-Based Approach to Improve Satellite-Derived Snow Water Equivalent at the Watershed Scale

For the past few decades, remote sensing has been a valuable tool for deriving global information on snow water equivalent (SWE), where products derived from space-borne passive microwave radiometers are favoured as they respond to snow depth, an important component of SWE. GlobSnow, a novel SWE product, has increased the accuracy of global-scale SWE estimates by combining remotely sensed radiometric data with other physiographic characteristics, such as snow depth, as quantified by climatic stations. However, research has demonstrated that passive microwaves algorithms tend to underestimate SWE for deep snowpack. Approaches were proposed to correct for such underestimation; however, they are computer intensive and complex to implement at the watershed scale. In this study, SWEmax information from the near real time 5-km GlobSnow product, provided by Copernicus and the European Space Agency (ESA) and GlobSnow product at 25 km resolution were corrected using a simple bias correction approach for watershed scale applications. This method, referred to as the Watershed Scale Correction (WSC) approach, estimates the bias based on the direct runoff that occurs during the spring melt season. Direct runoff is estimated on the one hand from SWEmax information as main input. Infiltration is also considered in computing direct runoff. An independent estimation of direct runoff from gauged stations is also performed. Discrepancy between these estimates allows for estimating the bias correction factor. This approach is advantageous as it exploits data that commonly exists i.e., flow at gauged stations and remotely sensed/reanalysis data such as snow cover and precipitation. The WSC approach was applied to watersheds located in Eastern Canada. It was found that the average bias moved from 33.5% with existing GlobSnow product to 18% with the corrected product, using the recommended recursive filter coefficient β of 0.925 for baseflow separation. Results show the usefulness of integrating direct runoff for bias correction of existing GlobSnow product at the watershed scale. In addition, potential benefits are offered using the recursive filter approach for baseflow separation of watersheds with limited in situ SWE measurements, to further reduce overall uncertainties and bias. The WSC approach should be appealing for poorly monitored watersheds where SWE measurements are critical for hydropower production and where snowmelt can pose serious flood-related damages.

Estimating Ground Snow Load Based on Ground Snow Depth and Climatological Elements for Snow Hazard Assessment in Northeastern China

Extreme snow loads can collapse roofs. This load is calculated based on the ground snow load (that is, the snow water equivalent on the ground). However, snow water equivalent (SWE) measurements are unavailable for most sites, while the ground snow depth is frequently measured and recorded. A new simple practical algorithm was proposed in this study to evaluate the SWE by utilizing ground snow depth, precipitation data, wind speed, and air temperature. For the evaluation, the precipitation was classified as snowfall or rainfall according to the air temperature, the snowfall or rainfall was then corrected for measurement error that is mainly caused by wind-induced undercatch, and the effect of snow water loss was considered. The developed algorithm was applied and validated using data from 57 meteorological stations located in the northeastern region of China. The annual maximum SWE obtained based on the proposed algorithm was compared with that obtained from the actual SWE measurements. The return period values of the annual maximum ground snow load were estimated and compared to those obtained according to the procedure suggested by the Chinese structural design code. The comparison indicated that the use of the proposed algorithm leads to a good estimated SWE or ground snow load. Its use allowed the estimation of the ground snow load for sites without SWE measurement and facilitated snow hazard mapping.

Comparison of manual snow water equivalent (SWE) measurements: seeking the reference for a true SWE value in a boreal biome

Abstract. Manual measurement of snow water equivalent (SWE) is still important today for several applications such as hydrological model validation. This measurement can be performed with different types of snow tube sampler or by a snow pit. Although these methods have been performed for several decades, there is an apparent lack of information required to have a consensus regarding the best reference for “true” SWE. We define and estimate the uncertainty and measurement error of different methods of snow pits and snow samplers used in a boreal biome. Analysis was based upon measurements taken over five consecutive winters (2016–2020) from the same flat and open area. This study compares two snow pit methods and three snow samplers. In addition to including the Standard Federal sampler (SFS), this study documents the first use of two new large diameter samplers, the Hydro-Québec sampler (HQS) and Université Laval sampler (ULS). Large diameter samplers had the lowest uncertainty (2.6 % to 4.0 %). Snow pit methods had higher uncertainty due to instruments (7.1 % to 11.4 %), close to that of the SFS (mean = 10.4 %). Given its larger collected snow volume for estimating SWE and its lower uncertainty, we posit that ULS represents the most appropriate method of reference for “true” SWE. By considering ULS as the reference in calculating mean bias error (MBE), different snow pit methods overestimated SWE by 16.6 % to 26.2 %, which was much higher than SFS (8.4 %). This study suggests that large diameter samplers are the best method for estimating “true” SWE in a boreal biome.

A Time Series of Snow Density and Snow Water Equivalent Observations Derived From the Integration of GPR and UAV SfM Observations

Snow depth can be mapped from airborne platforms and measured in situ rapidly, but manual snow density and snow water equivalent (SWE) measurements are time consuming to obtain using traditional survey methods. As a result, the limited number of point observations are likely insufficient to capture the true spatial complexity of snow density and SWE in many settings, highlighting the value of distributed observations. Here, we combine measured two-way travel time from repeat ground-penetrating radar (GPR) surveys along a ∼150 m transect with snow depth estimates from UAV-based Structure from Motion Multi-View Stereo (SfM-MVS) surveys to estimate snow density and SWE. These estimates were successfully calculated on eleven dates between January and May during the NASA SnowEx21 campaign at Cameron Pass, CO. GPR measurements were made with a surface-coupled Sensors and Software PulseEkko Pro 1 GHz system, while UAV flights were completed using a DJI Mavic 2 Pro platform and consisted of two orthogonal flights at ∼60 m elevation above ground level. SfM-MVS derived dense point clouds (DPCs) were georeferenced using eight ground control points and evaluated using three checkpoints, which were distributed across the ∼3.5 ha study plot containing the GPR transect. The DPCs were classified to identify the snow surface and then rasterized to produce snow-on digital surface models (DSMs) at 1 m resolution. Snow depths on each survey date were calculated by differencing these snow-on DSMs from a nearly snow-off DSM collected near the end of the melt season. SfM-derived snow depths were evaluated with independent snow depth measurements from manual probing (mean r2 = 0.67, NMAD = 0.11 m and RMSE = 0.12 m). The GPR-SfM derived snow densities were compared to snow density measurements made in snowpits (r2 = 0.42, NMAD = 39 kg m−3 and RMSE = 68 kg m−3). The integration of SfM and GPR observations provides an accurate, efficient, and a relatively non-destructive approach for measuring snow density and SWE at intermediate spatial scales and over seasonal timescales. Ongoing developments in snow depth retrieval technologies could be leveraged in the future to extend the spatial extent of this method.

Snow water equivalent change mapping from slope-correlated synthetic aperture radar interferometry (InSAR) phase variations

Abstract. Area-based measurements of snow water equivalent (SWE) are important for understanding earth system processes such as glacier mass balance, winter hydrological storage in drainage basins, and ground thermal regimes. Remote sensing techniques are ideally suited for wide-scale area-based mapping with the most commonly used technique to measure SWE being passive microwave, which is limited to coarse spatial resolutions of 25 km or greater and to areas without significant topographic variation. Passive microwave also has a negative bias for large SWE. Another method is repeat-pass synthetic aperture radar interferometry (InSAR) that allows measurement of SWE change at much higher spatial resolution. However, it has not been widely adopted because (1) the phase unwrapping problem has not been robustly addressed, especially for interferograms with poor coherence, and (2) SWE change maps scaled directly from repeat-pass interferograms are not an absolute measurement but contain unknown offsets for each contiguous coherent area. We develop and test a novel method for repeat-pass InSAR-based dry-snow SWE estimation that exploits the sensitivity of the dry-snow refraction-induced InSAR phase to topographic variations. The method robustly estimates absolute SWE change at spatial resolutions of < 1 km without the need for phase unwrapping. We derive a quantitative signal model for this new SWE change estimator and identify the relevant sources of bias. The method is demonstrated using both simulated SWE distributions and a 9-year RADARSAT-2 (C-band, 5.405 GHz) spotlight-mode dataset near Inuvik, Northwest Territories (NWT), Canada. SWE results are compared to in situ snow survey measurements and estimates from ERA5 reanalysis. Our method performs well in high-relief areas, thus providing complementary coverage to passive-microwave-based SWE estimation. Further, our method has the advantage of requiring only a single wavelength band and thus can utilize existing spaceborne synthetic aperture radar systems.

The Challenges of Simulating SWE Beneath Forest Canopies are Reduced by Data Assimilation of Snow Depth

AbstractIntermittent snow depth observations can be leveraged with data assimilation (DA) to improve model estimates of snow water equivalent (SWE) at the point scale. A key consideration for scaling assimilation to the basin scale is its performance at forested locations—where canopy‐snow interactions affect snow accumulation and melt, yet are difficult to model and parameterize. We implement a particle filter (PF) technique to assimilate intermittent snow depth observations into the Flexible Snow Model, and validate model outputs against snow density and SWE measurements across adjacent forest and open sites, at two locations with different climates and forest structures. Assimilation reduces snow depth error by 70%–90%, density error by 5%–30%, and SWE error by 50%–70% at forest locations (relative to controls). The PF simulates the seasonal evolution of the snowpack under forest canopy, including where interception losses decrease SWE in the forest during accumulation, and shading reduces melt during the ablation season (relative to open sites). Model outputs are sensitive to canopy‐related parameters, but DA reduces the range in snow depth and SWE estimates resulting from variations or uncertainties in these parameters by over 50%. These results demonstrate that the importance of accurately measuring, estimating, or calibrating canopy‐related parameters is reduced when snow depth observations are assimilated. Finally, we assimilate remotely sensed snow depth observations at 50 m resolution across the East River Basin, Colorado (1,000 km2). Across elevations, the PF increases estimated precipitation at forested sites by ∼15% relative to open sites, likely compensating for excessive sublimation of intercepted snow.

GNSS signal-based snow water equivalent determination for different snowpack conditions along a steep elevation gradient

Abstract. Snow water equivalent (SWE) can be measured using low-cost Global Navigation Satellite System (GNSS) sensors with one antenna placed below the snowpack and another one serving as a reference above the snow. The underlying GNSS signal-based algorithm for SWE determination for dry- and wet-snow conditions processes the carrier phases and signal strengths and additionally derives liquid water content (LWC) and snow depth (HS). So far, the algorithm was tested intensively for high-alpine conditions with distinct seasonal accumulation and ablation phases. In general, snow occurrence, snow amount, snow density and LWC can vary considerably with climatic conditions and elevation. Regarding alpine regions, lower elevations mean generally earlier and faster melting, more rain-on-snow events, and shallower snowpack. Therefore, we assessed the applicability of the GNSS-based SWE measurement at four stations along a steep elevation gradient (820, 1185, 1510 and 2540 m a.s.l.) in the eastern Swiss Alps during two winter seasons (2018–2020). Reference data of SWE, LWC and HS were collected manually and with additional automated sensors at all locations. The GNSS-derived SWE estimates agreed very well with manual reference measurements along the elevation gradient, and the accuracy (RMSE = 34 mm, RMSRE = 11 %) was similar under wet- and dry-snow conditions, although significant differences in snow density and meteorological conditions existed between the locations. The GNSS-derived SWE was more accurate than measured with other automated SWE sensors. However, with the current version of the GNSS algorithm, the determination of daily changes of SWE was found to be less suitable compared to manual measurements or pluviometer recordings and needs further refinement. The values of the GNSS-derived LWC were robust and within the precision of the manual and radar measurements. The additionally derived HS correlated well with the validation data. We conclude that SWE can reliably be determined using low-cost GNSS sensors under a broad range of climatic conditions, and LWC and HS are valuable add-ons.

Estimation of Snow Mass Information via Assimilation of C-Band Synthetic Aperture Radar Backscatter Observations Into an Advanced Land Surface Model

This study assimilated Sentinel-1 C-band backscatter observations over snow-covered terrain into the Noah-Multiparameterization land surface model using support vector machine (SVM) regression and an ensemble Kalman filter to improve the modeled terrestrial snow mass estimates. The data assimilation (DA) experiment was conducted across Western Colorado from September 2016 to August 2017. As part of the DA experiments, the impact of a rule-based update was evaluated by comparing snow water equivalent (SWE) estimates via DA (with [ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm {DA}}_{\rm {v1}}$</tex-math></inline-formula> ] and without [ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm {DA}}_{\rm {v2}}$</tex-math></inline-formula> ] the rule-based update) against SNOTEL SWE measurements. Results confirmed that rule-based update helped minimize SVM controllability issues, and in turn, improved the accuracy of SWE estimates relative to both open loop (OL) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm {DA}}_{\rm {v2}}$</tex-math></inline-formula> . Comparison of SWE estimates from Sentinel-1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm {DA}}_{\rm {v1}}$</tex-math></inline-formula> against SNOTEL SWE revealed that 75% of stations showed improvements in bias and correlation coefficient relative to the OL. Assimilated SWE estimates also showed statistical improvements during both the snow accumulation and snow ablation periods. However, unbiased root mean square error showed a slight increase during the snow ablation period due to the large variability in the electromagnetic response of C-band backscatter over deep and/or wet snow. Improvement of the SWE estimates also resulted in improving river discharge estimates compared to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> measurements. River discharge using Sentinel-1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm {DA}}_{\rm {v1}}$</tex-math></inline-formula> improved the Nash–Sutcliffe efficiency at all available stations. These results suggest that physically constrained SVM can serve as an efficient observation operator for snow mass DA through explicit consideration of the first-order C-band scattering mechanisms over different terrestrial snow conditions.

The Effects of Dry Snow on the SAR Impulse Response and Feasibility for Single Channel Snow Water Equivalent Estimation

Snow water equivalent (SWE) is an important surface parameter for understanding a number of Earth system processes. Synthetic aperture radar (SAR) has considerable potential for measuring SWE of dry-snow because SAR can penetrate through the snow to the ground surface and is both amplitude- and phase-sensitive to refraction from the snow. Previous work on refraction-based SWE measurement by SAR has utilized the repeat-pass InSAR phase signal to estimate changes in SWE that occur between SAR acquisitions. These are subject to temporal decorrelation effects and consider only the refraction that occurs along the SAR beam center rather than the entire synthetic aperture. This study examines the refractive effect of dry-snow along the synthetic aperture and its impact on SAR image formation including defocusing and phase bias of the system impulse response. Snow phase compensation during time domain processing to recover the snow-free impulse response function (IRF) is described and demonstrated. The feasibility of using the mapdrift and image sharpness autofocus methods to estimate SWE is examined, and the effect of key system parameters on the estimation performance is derived. Experimental validation of the method was conducted by acquiring L-band data with the Simon Fraser University (SFU) Airborne SAR System over a pair of corner reflectors installed on the Kluane icefield in northwestern Canada. Results from both simulations and the icefield experiment are presented and compared including an analysis of errors affecting the estimation.

Snow water equivalent measurement in the Arctic based on cosmic ray neutron attenuation

Abstract. Grounded in situ, or invasive, cosmic ray neutron sensors (CRNSs) may allow for continuous, unattended measurements of snow water equivalent (SWE) over complete winter seasons and allow for measurements that are representative of spatially variable Arctic snow covers, but few studies have tested these types of sensors or considered their applicability at remote sites in the Arctic. During the winters of 2016/2017 and 2017/2018 we tested a grounded in situ CRNS system at two locations in Canada: a cold, low- to high-SWE environment in the Canadian Arctic and at a warm, low-SWE landscape in southern Ontario that allowed easier access for validation purposes. Five CRNS units were applied in a transect to obtain continuous data for a single significant snow feature; CRNS-moderated neutron counts were compared to manual snow survey SWE values obtained during both winter seasons. The data indicate that grounded in situ CRNS instruments appear able to continuously measure SWE with sufficient accuracy utilizing both a linear regression and nonlinear formulation. These sensors can provide important SWE data for testing snow and hydrological models, water resource management applications, and the validation of remote sensing applications.

Combining ground-based and remotely sensed snow data in a linear regression model for real-time estimation of snow water equivalent

Effective water resources management in California relies substantially on real-time information of snow water equivalent (SWE) at basin scale and mountain ranges given that mountain snowpacks provide the primary water supply for the State. However, SWE estimation based solely on remote sensing, modeling, or ground observations does not meet contemporary operational requirements. In this context, this study develops a data-fusion framework that combines multi-source datasets including satellite-observed daily mean fractional snow-covered area (DMFSCA), snow pillow SWE measurements, physiographic data, and historical SWE patterns into a linear regression model (LRM) to improve SWE estimates in real-time. We test two LRMs: a baseline regression model (LRM-baseline) that uses physiographic data and historical SWE patterns as independent variables, and an FSCA-informed regression model (LRM-FSCA) that includes the DMFSCA from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite imagery as an additional independent variable. By incorporating the satellite-observed DMFSCA, LRM-FSCA outperforms LRM-baseline with increased median R2 from 0.54 to 0.60, and reduced median PBIAS of basin average SWE from 2.6% to 2.2% in the snow pillow SWE cross-validation. LRM-FSCA explains 87% of the variance in the snow course SWE measurements with 0.1% PBIAS, while LRM-baseline explains a lower 81% variance with 1.4% PBIAS, both of which show higher accuracy than SWE estimates from the two operational SWE datasets: the Snow Data Assimilation System (SNODAS, 73% and -2.4%, respectively) and Nationtional Water Model (NWM, 75% and -15.9%, respectively). Additionally, LRM-FSCA explains 85% of the median variance in the Airborne Snow Observatory SWE with -9.2% PBIAS, which is comparable to the LRM-baseline (86% and -11.3%, respectively) and considerably better than SNODAS (64% and 28.2%, respectively) and NWM (33% and -30.1%, respectively). This study shows a substantial model improvement by constraining the geographical and seasonal variation on snow-cover via satellite observation and highlights the values of using multi-source observations in real-time SWE estimation. The developed SWE estimation framework has crucial implications for effective water supply forecasting and management in California, where climate extremes (e.g., droughts and floods) require particularly skillful monitoring practices.

A Call for More Snow Sampling

The snowpack is important for water resources, tourism, ecology, and the global energy budget. Over the past century, we have gone from point measurements of snow water equivalent (SWE) to estimate spring and summer runoff volumes, to remote sensing of various snowpack properties at continuously finer spatial and temporal resolutions, to various complexities of snowpack and hydrological modeling, to the current fusion of field data with remote sensing and modeling, all to improve our estimates of the snowpack and the subsequent runoff. However, we are still limited by the uncertainty induced by scaling from point field measurements to the area represented by remote sensing and modeling. This paper uses several examples of fine-resolution sampling to issue a call to snow hydrologists and other earth scientists to collect more data, or at least to thoroughly evaluate their sampling strategy for collecting ground-truth measurements. Recommendations are provided for different approaches to have more representative sampling, when at all possible, to collect at least a few more samples or data points.