Addressing snow model uncertainty for hydrologic prediction

Streamflow forecasting methods are moving towards probabilistic approaches that quantify the uncertainty associated with the various sources of error in the forecasting process. Multi-model averaging methods which try to address modeling deficiencies by considering multiple models are gaining much popularity. We have applied the Bayesian Model Averaging method to an ensemble of twelve snow models that vary in their heat and melt algorithms, parameterization, and/or albedo estimation method. Three of the models use the temperature-based heat and melt routines of the SNOW17 snow accumulation and ablation model. Nine models use heat and melt routines that are based on a simplified energy balance approach, and are varied by using three different albedo estimation schemes. Finally, different parameter sets were identified through automatic calibration with three objective functions. All models use the snow accumulation, liquid water transport, and ground surface heat exchange processes of the SNOW17. The resulting twelve snow models were combined using Bayesian Model Averaging (BMA). The individual models, BMA predictive mean, and BMA predictive variance were evaluated for six SNOTEL sites in the western U.S. The models performed best and the BMA variance was lowest at the colder sites with high winter precipitation and little mid-winter melting. An individual snow model would often outperform the BMA predictive mean. However, observed snow water equivalent (SWE) was captured within the 95% confidence intervals of the BMA variance on average 80% of the time at all sites. Results are promising that consideration of multiple snow structures would provide useful uncertainty information for probabilistic hydrologic prediction.     

Radiance data assimilation for operational snow and streamflow forecasting

Estimation of seasonal snowpack, in mountainous regions, is crucial for accurate streamflow prediction. This paper examines the ability of data assimilation (DA) of remotely sensed microwave radiance data to improve snow water equivalent prediction, and ultimately operational streamflow forecasts. Operational streamflow forecasts in the National Weather Service River Forecast Center (NWSRFC) are produced with a coupled SNOW17 (snow model) and SACramento Soil Moisture Accounting (SAC-SMA) model. A comparison of two assimilation techniques, the ensemble Kalman filter (EnKF) and the particle filter (PF), is made using a coupled SNOW17 and the microwave emission model for layered snow pack (MEMLS) model to assimilate microwave radiance data. Microwave radiance data, in the form of brightness temperature (TB), is gathered from the advanced microwave scanning radiometer-earth observing system (AMSR-E) at the 36.5 GHz channel. SWE prediction is validated in a synthetic experiment. The distribution of snowmelt from an experiment with real data is then used to run the SAC-SMA model. Several scenarios on state or joint state-parameter updating with TB data assimilation to SNOW-17 and SAC-SMA models were analyzed, and the results show potential benefit for operational streamflow forecasting.     

Operational snow modeling: Addressing the challenges of an energy balance model for National Weather Service forecasts

Prediction of snowmelt has become a critical issue in much of the western United States given the increasing demand for water supply, changing snow cover patterns, and the subsequent requirement of optimal reservoir operation. The increasing importance of hydrologic predictions necessitates that traditional forecasting systems be re-evaluated periodically to assure continued evolution of the operational systems given scientific advancements in hydrology. The National Weather Service (NWS) SNOW17, a conceptually based model used for operational prediction of snowmelt, has been relatively unchanged for decades. In this study, the Snow–Atmosphere–Soil Transfer (SAST) model, which employs the energy balance method, is evaluated against the SNOW17 for the simulation of seasonal snowpack (both accumulation and melt) and basin discharge. We investigate model performance over a 13-year period using data from two basins within the Reynolds Creek Experimental Watershed located in southwestern Idaho. Both models are coupled to the NWS runoff model [SACramento Soil Moisture Accounting model (SACSMA)] to simulate basin streamflow. Results indicate that while in many years simulated snowpack and streamflow are similar between the two modeling systems, the SAST more often overestimates SWE during the spring due to a lack of mid-winter melt in the model. The SAST also had more rapid spring melt rates than the SNOW17, leading to larger errors in the timing and amount of discharge on average. In general, the simpler SNOW17 performed consistently well, and in several years, better than, the SAST model. Input requirements and related uncertainties, and to a lesser extent calibration, are likely to be primary factors affecting the implementation of an energy balance model in operational streamflow prediction.     

Updating of snow depletion curve with remote sensing data

A method for using remotely sensed snow cover information in updating a hydrological model is developed, based on Bayes' theorem. A snow cover mass balance model structure adapted to such use of satellite data is specified, using a parametric snow depletion curve in each spatial unit to describe the subunit variability in snow storage. The snow depletion curve relates the accumulated melt depth to snow‐covered area, accumulated snowmelt runoff volume, and remaining snow water equivalent. The parametric formulation enables updating of the complete snow depletion curve, including mass balance, by satellite data on snow coverage. Each spatial unit (i.e. grid cell) in the model maintains a specific depletion curve state that is updated independently. The uncertainty associated with the variables involved is formulated in terms of a joint distribution, from which the joint expectancy (mean value) represents the model state. The Bayesian updating modifies the prior (pre‐update) joint distribution into a posterior, and the posterior joint expectancy replaces the prior as the current model state. Three updating experiments are run in a 2400 km² mountainous region in Jotunheimen, central Norway (61°N, 9°E) using two Landsat 7 ETM+ images separately and together. At 1 km grid scale in this alpine terrain, three parameters are needed in the snow depletion curve. Despite the small amount of measured information compared with the dimensionality of the updated parameter vector, updating reduces uncertainty substantially for some state variables and parameters. Parameter adjustments resulting from using each image separately differ, but are positively correlated. For all variables, uncertainty reduction is larger with two images used in conjunction than with any single image. Where the observation is in strong conflict with the prior estimate, increased uncertainty may occur, indicating that prior uncertainty may have been underestimated. Copyright © 2006 John Wiley & Sons, Ltd.     

Subgrid variability of snow water equivalent at operational snow stations in the western USA

The spatial distribution of snow water equivalent (SWE) is a key variable in many regional‐scale land surface models. Currently, the assimilation of point‐scale snow sensor data into these models is commonly performed without consideration of the spatial representativeness of the point data with respect to the model grid‐scale SWE. To improve the understanding of the relationship between point‐scale snow measurements and surrounding areas, we characterized the spatial distribution of snow depth and SWE within 1‐, 4‐ and 16‐km² grids surrounding 15 snow stations (snowpack telemetry and California snow sensors) in California, Colorado, Wyoming, Idaho and Oregon during the 2008 and 2009 snow seasons. More than 30 000 field observations of snowpack properties were used with binary regression tree models to relate SWE at the sensor site to the surrounding area SWE to evaluate the sensor representativeness of larger‐scale conditions. Unlike previous research, we did not find consistent high biases in snow sensor depth values as biases over all sites ranged from 74% overestimates to 77% underestimates. Of the 53 assessments, 27 surveys indicated snow station biases of less than 10% of the surrounding mean observed snow depth. Depth biases were largely dictated by the physiographic relationship between the snow sensor locations and the mean characteristics of the surrounding grid, in particular, elevation, solar radiation index and vegetation density. These scaling relationships may improve snow sensor data assimilation; an example application is illustrated for the National Operational Hydrologic Remote Sensing Center National Snow Analysis SWE product. The snow sensor bias information indicated that the assimilation of point data into the National Operational Hydrologic Remote Sensing Center model was often unnecessary and reduced model accuracy. Copyright © 2012 John Wiley & Sons, Ltd.     

Uncertainty and multiple objective calibration in regional water balance modelling: case study in 320 Austrian catchments

We examine the value of additional information in multiple objective calibration in terms of model performance and parameter uncertainty. We calibrate and validate a semi‐distributed conceptual catchment model for two 11‐year periods in 320 Austrian catchments and test three approaches of parameter calibration: (a) traditional single objective calibration (SINGLE) on daily runoff; (b) multiple objective calibration (MULTI) using daily runoff and snow cover data; (c) multiple objective calibration (APRIORI) that incorporates an a priori expert guess about the parameter distribution as additional information to runoff and snow cover data. Results indicate that the MULTI approach performs slightly poorer than the SINGLE approach in terms of runoff simulations, but significantly better in terms of snow cover simulations. The APRIORI approach is essentially as good as the SINGLE approach in terms of runoff simulations but is slightly poorer than the MULTI approach in terms of snow cover simulations. An analysis of the parameter uncertainty indicates that the MULTI approach significantly decreases the uncertainty of the model parameters related to snow processes but does not decrease the uncertainty of other model parameters as compared to the SINGLE case. The APRIORI approach tends to decrease the uncertainty of all model parameters as compared to the SINGLE case. Copyright © 2006 John Wiley & Sons, Ltd.     

Sensitivity of model parameterizations for simulated latent heat flux at the snow surface for complex mountain sites

The snowcover energy balance is typically dominated by net radiation and sensible and latent heat fluxes. Validation of the two latter components is rare and often difficult to undertake at complex mountain sites. Latent heat flux, the focus of this paper, is the primary coupling mechanism between the snow surface and the atmosphere. It accounts for the critical exchange of mass (sublimation or condensation), along with the associated snowcover energy loss or gain. Measured and modelled latent heat fluxes at a wind‐exposed and wind‐sheltered site were compared to evaluate variability in model parameters. A well‐tested and well‐validated snowcover energy balance model, Snobal, was selected for this comparison because of previously successful applications of the model at these sites and because of the adjustability of the parameters specific to latent heat transfer within the model. Simulated latent heat flux and snow water equivalent (SWE) were not sensitive to different formulations of the stability profile functions associated with heat transfer calculations. The model parameters of snow surface roughness length and active snow layer thickness were used to improve latent heat flux simulations while retaining accuracy in the simulation of the SWE at an exposed and sheltered study site. Optimal parameters for simulated latent heat flux and SWE were found at the exposed site with a shorter roughness length and thicker active layer, and at the sheltered site with a longer roughness length and thinner active layer. These findings were linked to physical characteristics of the study sites and will allow for adoption into other snow models that use similar parameters. Physical characteristics of wind exposure and cover could also be used to distribute critical parameters in a spatially distributed modelling domain and aid in parameter selection for application to other watersheds where detailed information is not available. Copyright © 2012 John Wiley & Sons, Ltd.     

Calibration of snow parameters in SWAT: comparison of three approaches in the Upper Adige River basin (Italy)

The Soil and Water Assessment Tool (SWAT) model is generally applied in alpine catchments using a unique set of snow parameters for the entire basin, and calibration is based on discharge records only. This technical note presents three calibration procedures for snow parameters of SWAT considering snow water equivalent (SWE) values computed using a dense network of snow depth measurement stations available in the Upper Adige River basin, Italy. The first two procedures calibrate snow parameters according to the average sub-basin SWE: the first one defines a unique set of parameters for the entire basin, while the second allows for sub-basin variability. The last approach includes the elevation band SWE output in the calibration for each sub-basin and qualitatively compares it to the SWE computed from the available snow depth monitoring stations. This last method provides the best agreement between SWAT model results and SWE data.     

Snow water equivalent prediction using Bayesian data assimilation methods

Using the U.S. National Weather Service’s SNOW-17 model, this study compares common sequential data assimilation methods, the ensemble Kalman filter (EnKF), the ensemble square root filter (EnSRF), and four variants of the particle filter (PF), to predict seasonal snow water equivalent (SWE) within a small watershed near Lake Tahoe, California. In addition to SWE estimation, the various data assimilation methods are used to estimate five of the most sensitive parameters of SNOW-17 by allowing them to evolve with the dynamical system. Unlike Kalman filters, particle filters do not require Gaussian assumptions for the posterior distribution of the state variables. However, the likelihood function used to scale particle weights is often assumed to be Gaussian. This study evaluates the use of an empirical cumulative distribution function (ECDF) based on the Kaplan–Meier survival probability method to compute particle weights. These weights are then used in different particle filter resampling schemes. Detailed analyses are conducted for synthetic and real data assimilation and an assessment of the procedures is made. The results suggest that the particle filter, especially the empirical likelihood variant, is superior to the ensemble Kalman filter based methods for predicting model states, as well as model parameters.     

Evaluation and bias correction of SNODAS snow water equivalent (SWE) for streamflow simulation in eastern Canadian basins

ABSTRACT

In snow-dominated basins, collection of snow data while capturing its spatio-temporal variability is difficult; therefore, integrating assimilation products could be a viable alternative for improving streamflow simulation. This study evaluates the accuracy of daily snow water equivalent (SWE) provided by the SNOw Data Assimilation System (SNODAS) of the National Weather Service at a 1-km² resolution for two basins in eastern Canada, where SWE is a critical variable intensifying spring runoff. A geostatistical interpolation method was used to distribute snow observations. SNODAS SWE products were bias-corrected by matching their cumulative distribution function to that of the interpolated snow. The corrected SWE was then used in hydrological modelling for streamflow simulation. The results indicate that the bias-correction method significantly improved the accuracy of the SNODAS products. Moreover, the corrected SWE improved the simulation performance of the peak values. Although the uncertainty of SNODAS estimates is high for eastern Canadian basins, they are still of great value for regions with few snow stations.     

EFFECTS OF FOREST ON THE SNOW PARAMETERS DERIVED FROM MICROWAVE MEASUREMENTS DURING THE BOREAS WINTER FIELD CAMPAIGN

Passive microwave data have been used to infer the areal snow water equivalent (SWE) with some success. However, the accuracy of these retrieved SWE values have not been well determined for heterogeneous vegetated regions. The Boreal Ecosystem–Atmosphere Study (BOREAS) Winter Field Campaign (WFC), which took place in February 1994, provided the opportunity to study in detail the effects of boreal forests on snow parameter retrievals. Preliminary results reconfirmed the relationship between microwave brightness temperature and snow water equivalent. The pronounced effect of forest cover on SWE retrieval was studied. A modified vegetation mixing algorithm is proposed to account for the forest cover. The relationship between the microwave signature and observed snowpack parameters matches results from this model.     

Snow water equivalent estimation in the Mallero basin using snow gauge data and MODIS images and fieldwork validation

Snow accumulation and ablation rule the temporal dynamics of water availability in mountain areas and cold regions. In these environments, the evaluation of the snow water amount is a key issue. The spatial distribution of snow water equivalent (SWE) over a mountain basin at the end of the snow accumulation season is estimated using a minimal statistical model (SWE‐SEM). This uses systematic observations such as ground measurements collected at snow gauges and snow‐covered area (SCA) data retrieved by remote sensors, here MODIS. Firstly, SWE‐SEM calculates local SWE estimates at snow gauges, then the spatial distribution of SWE over a certain area using an interpolation method; linear regressions of the first two order moments of SWE with altitude. The interpolation has been made by both confining and unconfining the spatial domain by SCA. SWE‐SEM is applied to the Mallero basin (northern Italy) for calculating the snow water equivalent at the end of the winter season for 6 years (2001–2007). For 2007, SWE‐SEM estimates are validated through fieldwork measurements collected during an ‘ad hoc’ campaign on March 31, 2007. Snow‐surveyed measurements are used to check SCA, snow density and SWE estimates. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling snow water equivalent and spring runoff in a boreal watershed,James Bay,Canada

The hydrology of boreal regions is strongly influenced by seasonal snow accumulation and melt. In this study, we compare simulations of snow water equivalent (SWE) and streamflow by using the hydrological model HYDROTEL with two contrasting approaches for snow modelling: a mixed degree‐day/energy balance model (small number of inputs, but several calibration parameters needed) and the thermodynamic model CROCUS (large number of inputs, but no calibration parameter needed). The study site, in Northern Quebec, Canada was equipped with a ground‐based gamma ray sensor measuring the SWE continuously for 5 years in a small forest clearing. The first simulation of CROCUS showed a tendency to underestimate SWE, attributable to bias in the meteorological inputs. We found that it was appropriate to use a threshold of 2 °C to separate rain and snow. We also applied a correction to account for snowfall undercatch by the precipitation gauge. After these modifications to the input dataset, we noticed that CROCUS clearly overestimated the SWE, likely as a result of not including loss in SWE because of blowing snow sublimation and relocation. To correct this, we included into CROCUS a simple parameterisation effective after a certain wind speed threshold, after which the thermodynamic model performed much better than the traditional mixed degree‐day/energy balance model. HYDROTEL was then used to simulate streamflow with both snow models. With CROCUS, the main peak flow could be captured, but the second peak because of delayed snowmelt from forested areas could not be reproduced due to a lack of sub‐canopy radiation data to feed CROCUS. Despite the relative homogeneity of the boreal landscape, data inputs from each land cover type are needed to generate satisfying simulation of the spring runoff. Copyright © 2013 John Wiley & Sons, Ltd.     

Exploring the spatiotemporal variability of the snow water equivalent in a small boreal forest catchment through observation and modelling

In snow-fed catchments, it is crucial to monitor and model the snow water equivalent (SWE), particularly when simulating the melt water runoff. SWE distribution can, however, be highly heterogeneous, particularly in forested environments. Within these locations, scant studies have explored the spatiotemporal variability in SWE in relation with vegetation characteristics, with only few successful attempts. The aim of this paper is to fill this knowledge gap, through a detailed monitoring at nine locations within a 3.49 km² forested catchment in southern Québec, Canada (47°N, 71°W). The catchment receives an annual average of 633 mm of solid precipitation and is predominantly covered with balsam fir stands. Extracted from intensive field campaign and high-resolution LiDAR data, this study explores the effect of fine scale forest features (tree height, tree diameter, canopy density, leaf area index [LAI], tree density and gap fraction) on the spatiotemporal variability in the SWE distribution. A nested stratified random sampling design was adopted to quantify small-scale variability across the catchment and 1810 manual snow samples were collected throughout the consecutive winters of 2016–17 and 2017–18. This study explored the variability of SWE using coefficients of variation (CV) and relating to the LAI. We also present existing spatiotemporal differences in maximum snow depth across different stands and its relationship with average tree diameter. Furthermore, exploiting key vegetation characteristics, this paper explores different approaches to model SWE, such as multiple linear regression, binary regression tree and neural networks (NN). We were unable to establish any relationship between the CV of SWE and the LAI. However, we observed an increase in maximum snow depth with decreasing tree diameter, suggesting an association between these variables. NN modelling (Nash-Sutcliffe efficiency [NSE] = 0.71) revealed that, snow depth, snowpack age and forest characteristics (tree diameter and tree density) are key controlling variables on SWE. Using only variables that are deemed to be more readily available (snow depth, tree height, snowpack age and elevation), NN performance falls by only 7% (NSE = 0.66).     

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.     

Impact of land-use changes on snow in a forested region with heavy snowfall in Hokkaido,Japan

Abstract

We simulated snow processes in a forested region with heavy snowfall in Japan, and evaluated both the regional-scale snow distribution and the potential impact of land-use changes on the snow cover and water balances over the entire domain. SnowModel reproduced the snow processes at open and forested sites, which were confirmed by snow water equivalent (SWE) measurements at two intensive observation sites and snow depth measurements at the Automated Meteorological Data Acquisition System sites. SnowModel also reproduced the observed snow distribution (from the MODIS snow cover data) over the simulation domain during thaw. The observed SWE was less at the forested site than at the open site. The SnowModel simulations showed that this difference was caused mainly by differences in sublimation. The type of land use changed the maximum SWE, onset and duration of snowmelt, and the daily snowmelt rate due to canopy snow interception.

Citation Suzuki, K., Kodama, Y., Nakai, T., Liston, G. E., Yamamoto, K., Ohata, T., Ishii, Y., Sumida, A., Hara, T. & Ohta, T. (2011) Impact of land-use changes in a forested region with heavy snowfall in Hokkaido, Japan. Hydrol. Sci. J. 56(3), 443–467.     

Parameter estimation in ensemble based snow data assimilation: A synthetic study

Estimating erroneous parameters in ensemble based snow data assimilation system has been given little attention in the literature. Little is known about the related methods’ effectiveness, performance, and sensitivity to other error sources such as model structural error. This research tackles these questions by running synthetic one-dimensional snow data assimilation with the ensemble Kalman filter (EnKF), in which both state and parameter are simultaneously updated. The first part of the paper investigates the effectiveness of this parameter estimation approach in a perfect-model-structure scenario, and the second part focuses on its dependence on model structure error. The results from first part research demonstrate the advantages of this parameter estimation approach in reducing the systematic error of snow water equivalent (SWE) estimates, and retrieving the correct parameter value. The second part results indicate that, at least in our experiment, there is an evident dependence of parameter search convergence on model structural error. In the imperfect-model-structure run, the parameter search diverges, although it can simulate the state variable well. This result suggest that, good data assimilation performance in estimating state variables is not a sufficient indicator of reliable parameter retrieval in the presence of model structural error. The generality of this conclusion needs to be tested by data assimilation experiments with more complex structural error configurations.     

Global sensitivity analyses for a complex hydrological model applied in an Alpine watershed

The increasing complexity of hydrological models results in a large number of parameters to be estimated. In order to better understand how these complex models work, efficient screening methods are required in order to identify the most important parameters. This is of particular importance for models that are used within an operational real‐time forecasting chain such as HQsim. The objectives of this investigation are to (i) identify the most sensitive parameters of the complex HQsim model applied in the Alpine Lech catchment and (ii) compare model parameter sensitivity rankings attained from three global sensitivity analysis techniques. The techniques presented are the (i) regional sensitivity analysis, (ii) Morris analysis and (iii) state‐dependent parameter modelling. The results indicate that parameters affecting snow melt as well as processes in the unsaturated soil zone reveal high significance in the analysed catchment. The snow melt parameters show clear temporal patterns in the sensitivity whereas most of the parameters affecting processes in the unsaturated soil zone do not vary in importance across the year. Overall, the maximum degree day factor (meltfunc_max) has been identified to play a key role within the HQsim model. Although the parameter sensitivity rankings are equivalent between methods for a number of parameters, for several key parameters differing results were obtained. An uncertainty analysis demonstrates that a parameter ranking attained from only one method is subjected to large uncertainty. Copyright © 2012 John Wiley & Sons, Ltd.     

Assessing the impact of distributed snow water equivalent calibration and assimilation of Copernicus snow water equivalent on modelled snow and streamflow performance

Accuracy of the Copernicus snow water equivalent (SWE) product and the impact of SWE calibration and assimilation on modelled SWE and streamflow was evaluated. Daily snowpack measurements were made at 12 locations from 2016 to 2019 across a 4104 km² mixed-forest basin in the Great Lakes region of central Ontario, Canada. Sub-basin daily SWE calculated from these sites, observed discharge, and lake levels were used to calibrate a hydrologic model developed using the Raven modelling framework. Copernicus SWE was bias corrected during the melt period using mean bias subtraction and was compared to daily basin average SWE calculated from the measured data. Bias corrected Copernicus SWE was assimilated into the models using a range of parameters and the parameterizations from the model calibration. The bias corrected Copernicus product agreed well with measured data and provided a good estimate of mean basin SWE demonstrating that the product shows promise for hydrology applications within the study region. Calibration to spatially distributed SWE substantially improved the basin scale SWE estimate while only slightly degrading the flow simulation demonstrating the value of including SWE in a multi-objective calibration formulation. The particle filter experiments yielded the best SWE estimation but moderately degraded the flow simulation. The particle filter experiments constrained by the calibrated snow parameters produced similar results to the experiments using the upper and lower bounds indicating that, in this study, model calibration prior to assimilation was not valuable. The calibrated models exhibited varying levels of skill in estimating SWE but demonstrated similar streamflow performance. This indicates that basin outlet streamflow can be accurately estimated using a model with a poor representation of distributed SWE. This may be sufficient for applications where estimating flow is the primary water management objective. However, in applications where understanding the physical processes of snow accumulation, melt and streamflow generation are important, such as assessing the impact of climate change on water resources, accurate representations of SWE are required and can be improved via multi-objective calibration or data assimilation, as demonstrated in this study.     

Snow distribution in a steep mid-latitude alpine catchment

Snow distribution patterns are still poorly understood in steep alpine catchments because of mass redistribution from wind and avalanching. Snow models rarely operate with sufficient resolution, physics or input data to resolve this issue explicitly, and existing sub-grid parameterisations are rarely tested in this type of terrain. To address this issue daily snow cover observations, obtained from a ground-based camera, are combined with a snow melt model to estimate the spatial distribution of snow water equivalent (SWE) in a mountainous alpine catchment. Results show the importance of slope in controlling the spatial distribution of SWE and snow duration. This distribution is linked to the physical process of gravitational transport, where there is removal of snow from steep slopes and preferential deposition on moderate-angle slopes. From a modelling perspective, if sub-grid snow variability is parameterised using a log-normal probability distribution (as is common in hydrological and land-use models) then ignoring steep/shallow slope differences leads to an overestimation of melt at the beginning of the melt season, and a premature end to the snow melt season. When modelling SWE in complex terrain, care should be taken to consider reduced SWE on steep slopes.