Articles | Volume 9, issue 4
https://doi.org/10.5194/tc-9-1523-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/tc-9-1523-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Meteorological, elevation, and slope effects on surface hoar formation
Department of Civil Engineering, University of Calgary, Alberta, Canada
M. Schirmer
Department of Civil Engineering, University of Calgary, Alberta, Canada
currently at: Centre for Hydrology, University of Saskatchewan, Saskatchewan, Canada
B. Jamieson
Department of Civil Engineering, University of Calgary, Alberta, Canada
Related authors
Florian Herla, Pascal Haegeli, Simon Horton, and Patrick Mair
Nat. Hazards Earth Syst. Sci., 24, 2727–2756, https://doi.org/10.5194/nhess-24-2727-2024, https://doi.org/10.5194/nhess-24-2727-2024, 2024
Short summary
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Snowpack simulations are increasingly employed by avalanche warning services to inform about critical avalanche layers buried in the snowpack. However, validity concerns limit their operational value. We present methods that enable meaningful comparisons between snowpack simulations and regional assessments of avalanche forecasters to quantify the performance of the Canadian weather and snowpack model chain to represent thin critical avalanche layers on a large scale and in real time.
Simon Horton, Florian Herla, and Pascal Haegeli
EGUsphere, https://doi.org/10.5194/egusphere-2024-1609, https://doi.org/10.5194/egusphere-2024-1609, 2024
Short summary
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We present a method for avalanche forecasters to analyze patterns in snowpack model simulations. It uses fuzzy clustering to group small regions into larger forecast areas based on snow characteristics, location, and time. Tested in the Columbia Mountains during winter 2022–23, it accurately matched real forecast regions and identified major avalanche hazard patterns. This approach simplifies complex model outputs, helping forecasters make informed decisions.
Florian Herla, Pascal Haegeli, Simon Horton, and Patrick Mair
EGUsphere, https://doi.org/10.5194/egusphere-2024-871, https://doi.org/10.5194/egusphere-2024-871, 2024
Short summary
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We present a spatial framework for extracting information about avalanche problems from detailed snowpack simulations and compare the numerical results against operational assessments from avalanche forecasters. Despite good aggreement in seasonal summary statistics, a comparison of daily assessments revealed considerable differences while it remained unclear which data source represented reality best. We discuss how snowpack simulations can add value to the forecasting process.
Simon Horton and Pascal Haegeli
The Cryosphere, 16, 3393–3411, https://doi.org/10.5194/tc-16-3393-2022, https://doi.org/10.5194/tc-16-3393-2022, 2022
Short summary
Short summary
Snowpack models can help avalanche forecasters but are difficult to verify. We present a method for evaluating the accuracy of simulated snow profiles using readily available observations of snow depth. This method could be easily applied to understand the representativeness of available observations, the agreement between modelled and observed snow depths, and the implications for interpreting avalanche conditions.
Florian Herla, Simon Horton, Patrick Mair, and Pascal Haegeli
Geosci. Model Dev., 14, 239–258, https://doi.org/10.5194/gmd-14-239-2021, https://doi.org/10.5194/gmd-14-239-2021, 2021
Short summary
Short summary
The adoption of snowpack models in support of avalanche forecasting has been limited. To promote their operational application, we present a numerical method for processing multivariate snow stratigraphy profiles of mixed data types. Our algorithm enables applications like dynamical grouping and summarizing of model simulations, model evaluation, and data assimilation. By emulating the human analysis process, our approach will allow forecasters to familiarly interact with snowpack simulations.
Simon Horton, Moses Towell, and Pascal Haegeli
Nat. Hazards Earth Syst. Sci., 20, 3551–3576, https://doi.org/10.5194/nhess-20-3551-2020, https://doi.org/10.5194/nhess-20-3551-2020, 2020
Short summary
Short summary
We investigate patterns in how avalanche forecasters characterize snow avalanche hazard with avalanche problem types. Decision tree analysis was used to investigate both physical influences based on weather and on snowpack variables and operational practices. The results highlight challenges with developing decision aids based on previous hazard assessments.
Simon Horton, Stan Nowak, and Pascal Haegeli
Nat. Hazards Earth Syst. Sci., 20, 1557–1572, https://doi.org/10.5194/nhess-20-1557-2020, https://doi.org/10.5194/nhess-20-1557-2020, 2020
Short summary
Short summary
Numeric snowpack models currently offer limited value to operational avalanche forecasters. To improve the relevance and interpretability of model data, we introduce and discuss visualization principles that map model data into visual representations that can inform avalanche hazard assessments.
Florian Herla, Pascal Haegeli, Simon Horton, and Patrick Mair
Nat. Hazards Earth Syst. Sci., 24, 2727–2756, https://doi.org/10.5194/nhess-24-2727-2024, https://doi.org/10.5194/nhess-24-2727-2024, 2024
Short summary
Short summary
Snowpack simulations are increasingly employed by avalanche warning services to inform about critical avalanche layers buried in the snowpack. However, validity concerns limit their operational value. We present methods that enable meaningful comparisons between snowpack simulations and regional assessments of avalanche forecasters to quantify the performance of the Canadian weather and snowpack model chain to represent thin critical avalanche layers on a large scale and in real time.
Simon Horton, Florian Herla, and Pascal Haegeli
EGUsphere, https://doi.org/10.5194/egusphere-2024-1609, https://doi.org/10.5194/egusphere-2024-1609, 2024
Short summary
Short summary
We present a method for avalanche forecasters to analyze patterns in snowpack model simulations. It uses fuzzy clustering to group small regions into larger forecast areas based on snow characteristics, location, and time. Tested in the Columbia Mountains during winter 2022–23, it accurately matched real forecast regions and identified major avalanche hazard patterns. This approach simplifies complex model outputs, helping forecasters make informed decisions.
Florian Herla, Pascal Haegeli, Simon Horton, and Patrick Mair
EGUsphere, https://doi.org/10.5194/egusphere-2024-871, https://doi.org/10.5194/egusphere-2024-871, 2024
Short summary
Short summary
We present a spatial framework for extracting information about avalanche problems from detailed snowpack simulations and compare the numerical results against operational assessments from avalanche forecasters. Despite good aggreement in seasonal summary statistics, a comparison of daily assessments revealed considerable differences while it remained unclear which data source represented reality best. We discuss how snowpack simulations can add value to the forecasting process.
Simon Horton and Pascal Haegeli
The Cryosphere, 16, 3393–3411, https://doi.org/10.5194/tc-16-3393-2022, https://doi.org/10.5194/tc-16-3393-2022, 2022
Short summary
Short summary
Snowpack models can help avalanche forecasters but are difficult to verify. We present a method for evaluating the accuracy of simulated snow profiles using readily available observations of snow depth. This method could be easily applied to understand the representativeness of available observations, the agreement between modelled and observed snow depths, and the implications for interpreting avalanche conditions.
Florian Herla, Simon Horton, Patrick Mair, and Pascal Haegeli
Geosci. Model Dev., 14, 239–258, https://doi.org/10.5194/gmd-14-239-2021, https://doi.org/10.5194/gmd-14-239-2021, 2021
Short summary
Short summary
The adoption of snowpack models in support of avalanche forecasting has been limited. To promote their operational application, we present a numerical method for processing multivariate snow stratigraphy profiles of mixed data types. Our algorithm enables applications like dynamical grouping and summarizing of model simulations, model evaluation, and data assimilation. By emulating the human analysis process, our approach will allow forecasters to familiarly interact with snowpack simulations.
Simon Horton, Moses Towell, and Pascal Haegeli
Nat. Hazards Earth Syst. Sci., 20, 3551–3576, https://doi.org/10.5194/nhess-20-3551-2020, https://doi.org/10.5194/nhess-20-3551-2020, 2020
Short summary
Short summary
We investigate patterns in how avalanche forecasters characterize snow avalanche hazard with avalanche problem types. Decision tree analysis was used to investigate both physical influences based on weather and on snowpack variables and operational practices. The results highlight challenges with developing decision aids based on previous hazard assessments.
Simon Horton, Stan Nowak, and Pascal Haegeli
Nat. Hazards Earth Syst. Sci., 20, 1557–1572, https://doi.org/10.5194/nhess-20-1557-2020, https://doi.org/10.5194/nhess-20-1557-2020, 2020
Short summary
Short summary
Numeric snowpack models currently offer limited value to operational avalanche forecasters. To improve the relevance and interpretability of model data, we introduce and discuss visualization principles that map model data into visual representations that can inform avalanche hazard assessments.
M. Schirmer and B. Jamieson
The Cryosphere, 9, 587–601, https://doi.org/10.5194/tc-9-587-2015, https://doi.org/10.5194/tc-9-587-2015, 2015
Short summary
Short summary
Numerical Weather Prediction (NWP) models are rarely verified for mountainous regions during the winter season, although avalanche forecasters and other decision makers frequently rely on NWP models. We verified two NWP models (GEM-LAM and GEM15) and a precipitation analysis system (CaPA) at approximately 100 stations in the mountains of western Canada and northwestern USA. Ultrasonic snow depth sensors and snow pillows were used to observe daily precipitation amounts.
M. Schirmer and B. Jamieson
The Cryosphere, 8, 387–394, https://doi.org/10.5194/tc-8-387-2014, https://doi.org/10.5194/tc-8-387-2014, 2014
Related subject area
Mountain Processes
Quantifying frost-weathering-induced damage in alpine rocks
Subgridding high-resolution numerical weather forecast in the Canadian Selkirk mountain range for local snow modeling in a remote sensing perspective
Pressurised water flow in fractured permafrost rocks revealed by joint electrical resistivity monitoring and borehole temperature analysis
Rapid warming and degradation of mountain permafrost in Norway and Iceland
Improving climate model skill over High Mountain Asia by adapting snow cover parameterization to complex-topography areas
Brief communication: How deep is the snow on Mount Everest?
Snow sensitivity to temperature and precipitation change during compound cold–hot and wet–dry seasons in the Pyrenees
Mountain permafrost in the Central Pyrenees: insights from the Devaux ice cave
Glacier–permafrost relations in a high-mountain environment: 5 decades of kinematic monitoring at the Gruben site, Swiss Alps
Multi-scale snowdrift-permitting modelling of mountain snowpack
How much snow falls in the world's mountains? A first look at mountain snowfall estimates in A-train observations and reanalyses
Brief communication: The influence of mica-rich rocks on the shear strength of ice-filled discontinuities
Resolving the influence of temperature forcing through heat conduction on rock glacier dynamics: a numerical modelling approach
A temperature- and stress-controlled failure criterion for ice-filled permafrost rock joints
Quantifying irreversible movement in steep, fractured bedrock permafrost on Matterhorn (CH)
How much cryosphere model complexity is just right? Exploration using the conceptual cryosphere hydrology framework
Small-scale variation of snow in a regional permafrost model
Verification of analysed and forecasted winter precipitation in complex terrain
Soil erosion and organic carbon export by wet snow avalanches
Simulation of wind-induced snow transport and sublimation in alpine terrain using a fully coupled snowpack/atmosphere model
Influence of surface and subsurface heterogeneity on observed borehole temperatures at a mountain permafrost site in the Upper Engadine, Swiss Alps
The mass and energy balance of ice within the Eisriesenwelt cave, Austria
Rapid changes of the ice mass configuration in the dynamic Diablotins ice cave – Fribourg Prealps, Switzerland
Till Mayer, Maxim Deprez, Laurenz Schröer, Veerle Cnudde, and Daniel Draebing
The Cryosphere, 18, 2847–2864, https://doi.org/10.5194/tc-18-2847-2024, https://doi.org/10.5194/tc-18-2847-2024, 2024
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Frost weathering drives rockfall and shapes the evolution of alpine landscapes. We employed a novel combination of investigation techniques to assess the influence of different climatic conditions on high-alpine rock faces. Our results imply that rock walls exposed to freeze–thaw conditions, which are likely to occur at lower elevations, will weather more rapidly than rock walls exposed to sustained freezing conditions due to winter snow cover or permafrost at higher elevations.
Paul Billecocq, Alexandre Langlois, and Benoit Montpetit
The Cryosphere, 18, 2765–2782, https://doi.org/10.5194/tc-18-2765-2024, https://doi.org/10.5194/tc-18-2765-2024, 2024
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Snow covers a vast part of the globe, making snow water equivalent (SWE) crucial for climate science and hydrology. SWE can be inversed from satellite data, but the snow's complex structure highly affects the signal, and thus an educated first guess is mandatory. In this study, a subgridding framework was developed to model snow at the local scale from model weather data. The framework enhanced snow parameter modeling, paving the way for SWE inversion algorithms from satellite data.
Maike Offer, Samuel Weber, Michael Krautblatter, Ingo Hartmeyer, and Markus Keuschnig
EGUsphere, https://doi.org/10.5194/egusphere-2024-893, https://doi.org/10.5194/egusphere-2024-893, 2024
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We present a unique dataset of repeated electrical resistivity tomography and long-term borehole temperature measurements to investigate the complex seasonal water flow in permafrost rockwalls. Our joint analysis shows that permafrost rocks are subject to enhanced pressurised water flow during the melt period. In addition to slow thermal heat conduction, permafrost rocks are subject to push-like warming events, favouring accelerated permafrost degradation and reduced rockwall stability.
Bernd Etzelmüller, Ketil Isaksen, Justyna Czekirda, Sebastian Westermann, Christin Hilbich, and Christian Hauck
The Cryosphere, 17, 5477–5497, https://doi.org/10.5194/tc-17-5477-2023, https://doi.org/10.5194/tc-17-5477-2023, 2023
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Permafrost (permanently frozen ground) is widespread in the mountains of Norway and Iceland. Several boreholes were drilled after 1999 for long-term permafrost monitoring. We document a strong warming of permafrost, including the development of unfrozen bodies in the permafrost. Warming and degradation of mountain permafrost may lead to more natural hazards.
Mickaël Lalande, Martin Ménégoz, Gerhard Krinner, Catherine Ottlé, and Frédérique Cheruy
The Cryosphere, 17, 5095–5130, https://doi.org/10.5194/tc-17-5095-2023, https://doi.org/10.5194/tc-17-5095-2023, 2023
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This study investigates the impact of topography on snow cover parameterizations using models and observations. Parameterizations without topography-based considerations overestimate snow cover. Incorporating topography reduces snow overestimation by 5–10 % in mountains, in turn reducing cold biases. However, some biases remain, requiring further calibration and more data. Assessing snow cover parameterizations is challenging due to limited and uncertain data in mountainous regions.
Wei Yang, Huabiao Zhao, Baiqing Xu, Jiule Li, Weicai Wang, Guangjian Wu, Zhongyan Wang, and Tandong Yao
The Cryosphere, 17, 2625–2628, https://doi.org/10.5194/tc-17-2625-2023, https://doi.org/10.5194/tc-17-2625-2023, 2023
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There is very strong scientific and public interest regarding the snow thickness on Mountain Everest. Previously reported snow depths derived by different methods and instruments ranged from 0.92 to 3.5 m. Our measurements in 2022 provide the first clear radar image of the snowpack at the top of Mount Everest. The snow thickness at Earth's summit was averaged to be 9.5 ± 1.2 m. This updated snow thickness is considerably deeper than values reported during the past 5 decades.
Josep Bonsoms, Juan Ignacio López-Moreno, and Esteban Alonso-González
The Cryosphere, 17, 1307–1326, https://doi.org/10.5194/tc-17-1307-2023, https://doi.org/10.5194/tc-17-1307-2023, 2023
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This work analyzes the snow response to temperature and precipitation in the Pyrenees. During warm and wet seasons, seasonal snow depth is expected to be reduced by −37 %, −34 %, and −27 % per degree Celsius at low-, mid-, and high-elevation areas, respectively. The largest snow reductions are anticipated at low elevations of the eastern Pyrenees. Results anticipate important impacts on the nearby ecological and socioeconomic systems.
Miguel Bartolomé, Gérard Cazenave, Marc Luetscher, Christoph Spötl, Fernando Gázquez, Ánchel Belmonte, Alexandra V. Turchyn, Juan Ignacio López-Moreno, and Ana Moreno
The Cryosphere, 17, 477–497, https://doi.org/10.5194/tc-17-477-2023, https://doi.org/10.5194/tc-17-477-2023, 2023
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In this work we study the microclimate and the geomorphological features of Devaux ice cave in the Central Pyrenees. The research is based on cave monitoring, geomorphology, and geochemical analyses. We infer two different thermal regimes. The cave is impacted by flooding in late winter/early spring when the main outlets freeze, damming the water inside. Rock temperatures below 0°C and the absence of drip water indicate frozen rock, while relict ice formations record past damming events.
Isabelle Gärtner-Roer, Nina Brunner, Reynald Delaloye, Wilfried Haeberli, Andreas Kääb, and Patrick Thee
The Cryosphere, 16, 2083–2101, https://doi.org/10.5194/tc-16-2083-2022, https://doi.org/10.5194/tc-16-2083-2022, 2022
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We intensely investigated the Gruben site in the Swiss Alps, where glaciers and permafrost landforms closely interact, to better understand cold-climate environments. By the interpretation of air photos from 5 decades, we describe long-term developments of the existing landforms. In combination with high-resolution positioning measurements and ground surface temperatures, we were also able to link these to short-term changes and describe different landform responses to climate forcing.
Vincent Vionnet, Christopher B. Marsh, Brian Menounos, Simon Gascoin, Nicholas E. Wayand, Joseph Shea, Kriti Mukherjee, and John W. Pomeroy
The Cryosphere, 15, 743–769, https://doi.org/10.5194/tc-15-743-2021, https://doi.org/10.5194/tc-15-743-2021, 2021
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Mountain snow cover provides critical supplies of fresh water to downstream users. Its accurate prediction requires inclusion of often-ignored processes. A multi-scale modelling strategy is presented that efficiently accounts for snow redistribution. Model accuracy is assessed via airborne lidar and optical satellite imagery. With redistribution the model captures the elevation–snow depth relation. Redistribution processes are required to reproduce spatial variability, such as around ridges.
Anne Sophie Daloz, Marian Mateling, Tristan L'Ecuyer, Mark Kulie, Norm B. Wood, Mikael Durand, Melissa Wrzesien, Camilla W. Stjern, and Ashok P. Dimri
The Cryosphere, 14, 3195–3207, https://doi.org/10.5194/tc-14-3195-2020, https://doi.org/10.5194/tc-14-3195-2020, 2020
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The total of snow that falls globally is a critical factor governing freshwater availability. To better understand how this resource is impacted by climate change, we need to know how reliable the current observational datasets for snow are. Here, we compare five datasets looking at the snow falling over the mountains versus the other continents. We show that there is a large consensus when looking at fractional contributions but strong dissimilarities when comparing magnitudes.
Philipp Mamot, Samuel Weber, Maximilian Lanz, and Michael Krautblatter
The Cryosphere, 14, 1849–1855, https://doi.org/10.5194/tc-14-1849-2020, https://doi.org/10.5194/tc-14-1849-2020, 2020
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A failure criterion for ice-filled rock joints is a prerequisite to accurately assess the stability of permafrost rock slopes. In 2018 a failure criterion was proposed based on limestone. Now, we tested the transferability to other rocks using mica schist and gneiss which provide the maximum expected deviation of lithological effects on the shear strength. We show that even for controversial rocks the failure criterion stays unaltered, suggesting that it is applicable to mostly all rock types.
Alessandro Cicoira, Jan Beutel, Jérome Faillettaz, Isabelle Gärtner-Roer, and Andreas Vieli
The Cryosphere, 13, 927–942, https://doi.org/10.5194/tc-13-927-2019, https://doi.org/10.5194/tc-13-927-2019, 2019
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Rock glacier flow varies on multiple timescales. The variations have been linked to climatic forcing, but a quantitative understanding is still missing.
We use a 1-D numerical modelling approach coupling heat conduction to a creep model in order to study the influence of temperature variations on rock glacier flow. Our results show that heat conduction alone cannot explain the observed variations. Other processes, likely linked to water, must dominate the short-term velocity signal.
Philipp Mamot, Samuel Weber, Tanja Schröder, and Michael Krautblatter
The Cryosphere, 12, 3333–3353, https://doi.org/10.5194/tc-12-3333-2018, https://doi.org/10.5194/tc-12-3333-2018, 2018
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Most of the observed failures in permafrost-affected alpine rock walls are likely triggered by the mechanical destabilisation of warming bedrock permafrost including ice-filled joints. We present a systematic study of the brittle shear failure of ice and rock–ice contacts along rock joints in a simulated depth ≤ 30 m and at temperatures from −10 to −0.5 °C. Warming and sudden reduction in rock overburden due to the detachment of an upper rock mass lead to a significant drop in shear resistance.
Samuel Weber, Jan Beutel, Jérome Faillettaz, Andreas Hasler, Michael Krautblatter, and Andreas Vieli
The Cryosphere, 11, 567–583, https://doi.org/10.5194/tc-11-567-2017, https://doi.org/10.5194/tc-11-567-2017, 2017
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We present a 8-year continuous time series of measured fracture kinematics and thermal conditions on steep permafrost bedrock at Hörnligrat, Matterhorn. Based on this unique dataset and a conceptual model for strong fractured bedrock, we develop a novel quantitative approach that allows to separate reversible from irreversible fracture kinematics and assign the dominant forcing. A new index of irreversibility provides useful indication for the occurrence and timing of irreversible displacements.
Thomas M. Mosier, David F. Hill, and Kendra V. Sharp
The Cryosphere, 10, 2147–2171, https://doi.org/10.5194/tc-10-2147-2016, https://doi.org/10.5194/tc-10-2147-2016, 2016
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Our paper presents the Conceptual Cryosphere Hydrology Framework (CCHF), a tool to enable more rapid development and intercomparison of cryosphere process representations. Using the CCHF, we demonstrate that some common existing degree index cryosphere models are not well suited for assessing impacts across climates, even though these models appear to perform well under a common evaluation strategy. We show that more robust models can be formulated without increasing data input requirements.
Kjersti Gisnås, Sebastian Westermann, Thomas Vikhamar Schuler, Kjetil Melvold, and Bernd Etzelmüller
The Cryosphere, 10, 1201–1215, https://doi.org/10.5194/tc-10-1201-2016, https://doi.org/10.5194/tc-10-1201-2016, 2016
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In wind exposed areas snow redistribution results in large spatial variability in ground temperatures. In these areas, the ground temperature of a grid cell must be determined based on the distribution, and not the average, of snow depths. We employ distribution functions of snow in a regional permafrost model, showing highly improved representation of ground temperatures. By including snow distributions, we find the permafrost area to be nearly twice as large as what is modelled without.
M. Schirmer and B. Jamieson
The Cryosphere, 9, 587–601, https://doi.org/10.5194/tc-9-587-2015, https://doi.org/10.5194/tc-9-587-2015, 2015
Short summary
Short summary
Numerical Weather Prediction (NWP) models are rarely verified for mountainous regions during the winter season, although avalanche forecasters and other decision makers frequently rely on NWP models. We verified two NWP models (GEM-LAM and GEM15) and a precipitation analysis system (CaPA) at approximately 100 stations in the mountains of western Canada and northwestern USA. Ultrasonic snow depth sensors and snow pillows were used to observe daily precipitation amounts.
O. Korup and C. Rixen
The Cryosphere, 8, 651–658, https://doi.org/10.5194/tc-8-651-2014, https://doi.org/10.5194/tc-8-651-2014, 2014
V. Vionnet, E. Martin, V. Masson, G. Guyomarc'h, F. Naaim-Bouvet, A. Prokop, Y. Durand, and C. Lac
The Cryosphere, 8, 395–415, https://doi.org/10.5194/tc-8-395-2014, https://doi.org/10.5194/tc-8-395-2014, 2014
S. Schneider, M. Hoelzle, and C. Hauck
The Cryosphere, 6, 517–531, https://doi.org/10.5194/tc-6-517-2012, https://doi.org/10.5194/tc-6-517-2012, 2012
F. Obleitner and C. Spötl
The Cryosphere, 5, 245–257, https://doi.org/10.5194/tc-5-245-2011, https://doi.org/10.5194/tc-5-245-2011, 2011
S. Morard, M. Bochud, and R. Delaloye
The Cryosphere, 4, 489–500, https://doi.org/10.5194/tc-4-489-2010, https://doi.org/10.5194/tc-4-489-2010, 2010
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Short summary
We investigate how various meteorological and terrain factors affect surface hoar formation in complex terrain. We modelled the distribution of three surface hoar layers with a coupled NWP - snow cover model, and verified the model with field studies. The layers developed in regions and elevation bands with warm moist air, light winds, and cold snow surfaces. Possible avalanche forecasting applications are discussed.
We investigate how various meteorological and terrain factors affect surface hoar formation in...