Intercomparison of measurements of bulk snow density and water equivalent of snow cover with snow core samplers: Instrumental bias and variability induced by observers

Manually collected snow data are often considered as ground truth for many applications such as climatological or hydrological studies. However, there are many sources of uncertainty that are not quantified in detail. For the determination of water equivalent of snow cover (SWE), different snow core samplers and scales are used, but they are all based on the same measurement principle. We conducted two field campaigns with 9 samplers commonly used in observational measurements and research in Europe and northern America to better quantify uncertainties when measuring depth, density and SWE with core samplers. During the first campaign, as a first approach to distinguish snow variability measured at the plot and at the point scale, repeated measurements were taken along two 20 m long snow pits. The results revealed a much higher variability of SWE at the plot scale (resulting from both natural variability and instrumental bias) compared to repeated measurements at the same spot (resulting mostly from error induced by observers or very small scale variability of snow depth). The exceptionally homogeneous snowpack found in the second campaign permitted to almost neglect the natural variability of the snowpack properties and focus on the separation between instrumental bias and error induced by observers. Reported uncertainties refer to a shallow, homogeneous tundra-taiga snowpack less than 1 m deep (loose, mostly recrystallised snow and no wind impact). Under such measurement conditions, the uncertainty in bulk snow density estimation is about 5% for an individual instrument and is close to 10% among different instruments. Results confirmed that instrumental bias exceeded both the natural variability and the error induced by observers, even in the case when observers were not familiar with a given snow core sampler.     

Spatiotemporal estimation of snow depth using point data from snow stakes,digital terrain models,and satellite data

Snow availability in Alpine catchments plays an important role in water resources management. In this paper, we propose a method for an optimal estimation of snow depth (areal extension and thickness) in Alpine systems from point data and satellite observations by using significant explanatory variables deduced from a digital terrain model. It is intended to be a parsimonious approach that may complement physical‐based methodologies. Different techniques (multiple regression, multicriteria analysis, and kriging) are integrated to address the following issues: We identify the explanatory variables that could be helpful on the basis of a critical review of the scientific literature. We study the relationship between ground observations and explanatory variables using a systematic procedure for a complete multiple regression analysis. Multiple regression models are calibrated combining all suggested model structures and explanatory variables. We also propose an evaluation of the models (using indices to analyze the goodness of fit) and select the best approaches (models and variables) on the basis of multicriteria analysis. Estimation of the snow depth is performed with the selected regression models. The residual estimation is improved by applying kriging in cases with spatial correlation. The final estimate is obtained by combining regression and kriging results, and constraining the snow domain in accordance with satellite data. The method is illustrated using the case study of the Sierra Nevada mountain range (Southern Spain). A cross‐validation experiment has confirmed the efficiency of the proposed procedure. Finally, although it is not the scope of this work, the snow depth is used to asses a first estimation of snow water equivalent resources.     

Quantifying snow water equivalent using terrestrial ground penetrating radar and unmanned aerial vehicle photogrammetry

This study demonstrates the potential value of a combined unmanned aerial vehicle (UAV) Photogrammetry and ground penetrating radar (GPR) approach to map snow water equivalent (SWE) over large scales. SWE estimation requires two different physical parameters (snow depth and density), which are currently difficult to measure with the spatial and temporal resolution desired for basin-wide studies. UAV photogrammetry can provide very high-resolution spatially continuous snow depths (SD) at the basin scale, but does not measure snow densities. GPR allows nondestructive quantitative snow investigation if the radar velocity is known. Using photogrammetric snow depths and GPR two-way travel times (TWT) of reflections at the snow-ground interface, radar velocities in snowpack can be determined. Snow density (RSN) is then estimated from the radar propagation velocity (which is related to electrical permittivity of snow) via empirical formulas. A Phantom-4 Pro UAV and a MALA GX450 HDR model GPR mounted on a ski mobile were used to determine snow parameters. A snow-free digital surface model (DSM) was obtained from the photogrammetric survey conducted in September 2017. Then, another survey in synchronization with a GPR survey was conducted in February 2019 whilst the snowpack was approximately at its maximum thickness. Spatially continuous snow depths were calculated by subtracting the snow-free DSM from the snow-covered DSM. Radar velocities in the snowpack along GPR survey lines were computed by using UAV-based snow depths and GPR reflections to obtain snow densities and SWEs. The root mean square error of the obtained SWEs (384 mm average) is 63 mm, indicating good agreement with independent SWE observations and the error lies within acceptable uncertainty limits.     

Long‐term change of seasonal snow cover and its effects on river runoff in the Tarim River basin,northwestern China

Spatio‐temporal variation of snow depth in the Tarim River basin has been studied by the empirical orthogonal function (EOF) based on the data collected by special sensor microwave/imager (SSM/I) and scanning multichannel microwave radiometer (SMMR) during the period from 1979 to 2005. The long‐term trend of snow depth and runoff was presented using the Mann‐Kendall non‐parametric test, and the effects of the variations of snow depth and climatic factors on runoff were analysed and discussed by means of the regression analysis. The results suggested that the snow depth variation on the entire basin was characterised by four patterns: all consistency, north–south contrast, north‐middle‐south contrast and complex. The first pattern accounting 39·13% of the total variance was dominant. The entire basin was mainly affected by one large‐scale weather system. However, the spatial and temporal differences also existed among the different regions in the basin. The significant snow depth changes occurred mainly in the Aksu River basin with the below‐normal snow depth anomalies in the 1980s and the above‐normal snow depth anomalies in the 1990s. The long‐term trend of snow depth was significant in the northwestern, western and southern parts of the basin, whereas the long‐term trend of runoff was significant in the northwestern and northeastern parts. The regression analysis revealed that the runoff of the rivers replenished by snow melt water and rainfall was related primarily to the summer precipitation, followed by the summer temperature or the maximum snow depth in the cold season. Our results suggest that snow is not the principal factor that contributes to the runoff increase in headstreams, although there was a slow increase in snow depth. It is the climatic factors that are responsible for the steady and continuous water increase in the headstreams. Copyright © 2009 John Wiley & Sons, Ltd.     

Inference and uncertainty of snow depth spatial distribution at the kilometre scale in the Colorado Rocky Mountains: the effects of sample size,random sampling,predictor quality,and validation procedures

Historically, observing snow depth over large areas has been difficult. When snow depth observations are sparse, regression models can be used to infer the snow depth over a given area. Data sparsity has also left many important questions about such inference unexamined. Improved inference, or estimation, of snow depth and its spatial distribution from a given set of observations can benefit a wide range of applications from water resource management, to ecological studies, to validation of satellite estimates of snow pack. The development of Light Detection and Ranging (LiDAR) technology has provided non‐sparse snow depth measurements, which we use in this study, to address fundamental questions about snow depth inference using both sparse and non‐sparse observations. For example, when are more data needed and when are data redundant? Results apply to both traditional and manual snow depth measurements and to LiDAR observations. Through sampling experiments on high‐resolution LiDAR snow depth observations at six separate 1.17‐km² sites in the Colorado Rocky Mountains, we provide novel perspectives on a variety of issues affecting the regression estimation of snow depth from sparse observations. We measure the effects of observation count, random selection of observations, quality of predictor variables, and cross‐validation procedures using three skill metrics: percent error in total snow volume, root mean squared error (RMSE), and R². Extremes of predictor quality are used to understand the range of its effect; how do predictors downloaded from internet perform against more accurate predictors measured by LiDAR? Whereas cross validation remains the only option for validating inference from sparse observations, in our experiments, the full set of LiDAR‐measured snow depths can be considered the ‘true’ spatial distribution and used to understand cross‐validation bias at the spatial scale of inference. We model at the 30‐m resolution of readily available predictors, which is a popular spatial resolution in the literature. Three regression models are also compared, and we briefly examine how sampling design affects model skill. Results quantify the primary dependence of each skill metric on observation count that ranges over three orders of magnitude, doubling at each step from 25 up to 3200. Whereas uncertainty (resulting from random selection of observations) in percent error of true total snow volume is typically well constrained by 100–200 observations, there is considerable uncertainty in the inferred spatial distribution (R²) even at medium observation counts (200–800). We show that percent error in total snow volume is not sensitive to predictor quality, although RMSE and R² (measures of spatial distribution) often depend critically on it. Inaccuracies of downloaded predictors (most often the vegetation predictors) can easily require a quadrupling of observation count to match RMSE and R² scores obtained by LiDAR‐measured predictors. Under cross validation, the RMSE and R² skill measures are consistently biased towards poorer results than their true validations. This is primarily a result of greater variance at the spatial scales of point observations used for cross validation than at the 30‐m resolution of the model. The magnitude of this bias depends on individual site characteristics, observation count (for our experimental design), and sampling design. Sampling designs that maximize independent information maximize cross‐validation bias but also maximize true R². The bagging tree model is found to generally outperform the other regression models in the study on several criteria. Finally, we discuss and recommend use of LiDAR in conjunction with regression modelling to advance understanding of snow depth spatial distribution at spatial scales of thousands of square kilometres. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling river water temperature using deterministic,empirical, and hybrid formulations in a Mediterranean stream

River water temperature is a common target of water quality models at the watershed scale, owing to its principal role in shaping biogeochemical processes and in stream ecology. Usually, models include physically‐based, deterministic formulations to calculate water temperatures from detailed meteorological information, which usually comes from meteorological stations located far from the river reaches. However, alternative empirical approaches have been proposed, that usually depend on air temperature as master variable. This study explored the performance of a semidistributed water quality application modelling river water temperature in a Mediterranean watershed, using three different approaches. First, a deterministic approach was used accounting for the different heat exchange components usually considered in water temperature models. Second, an empirical approximation was applied using the equilibrium temperature concept, assuming a linear relationship with air temperature. And third, a hybrid approach was constructed, in which the temperature equilibrium concept and the deterministic approach were combined. Results showed that the hybrid approach gave the best results, followed by the empirical approximation. The deterministic formulation gave the worst results. The hybrid approach not only fitted daily river water temperatures, but also adequately modelled the daily temperature range (maximum–minimum daily temperature). Other river water features directly dependent on water temperature, such as river intrusion depth in lentic systems (i.e. the depth at which the river inflow plunges to equilibrate density differences with lake water), were also correctly modelled even at hourly time steps. However, results for the different heat fluxes between river and atmosphere were very unrealistic. Although direct evidence of discrepancies between meteorological drivers measured at the meteorological stations and the actual river microclimate was not found, the use of models including empirical or hybrid formulations depending mainly on air temperature is recommended if only meteorological data from locations far from the river reaches are available. Copyright © 2008 John Wiley & Sons, Ltd.