Implications of mountain shading on calculating energy for snowmelt using unstructured triangular meshes

In many parts of the world, snowmelt energetics is dominated by solar irradiance. This is particularly the case in the Canadian Rocky Mountains, where clear skies dominate the winter and spring. In mountainous regions, solar irradiance at the snow surface is not only affected by solar angles, atmospheric transmittance, the slope and aspect of immediate topography but also by shadows from surrounding terrain. Accumulation of errors in estimating solar irradiation can lead to significant errors in calculating the timing and rate of snowmelt owing to the seasonal storage of internal energy in the snowpack. Gridded methods, which are often used to estimate solar irradiance in complex terrain, work best with high-resolution digital elevation models (DEMs), such as those produced using Light Detection and Ranging. However, such methods also introduce errors caused by the rigid nature of the mesh as well as limiting the ability to represent basin characteristics. Unstructured triangular meshes are more efficient in their use of DEM data than fixed grids when producing solar irradiance information for spatially distributed snowmelt calculations, and they do not suffer from the artefact problems of a gridded DEM. This paper demonstrates the increased accuracy of using a horizon-shading algorithm model with an unstructured mesh versus standard self-shading algorithms. A systematic over-prediction in irradiance is observed when only self-shadows are considered. The modelled results are diagnosed by comparison to measurements of mountain shadows by time-lapse digital cameras and solar irradiance by a network of radiometers in Marmot Creek Research Basin, Alberta, Canada. Results show that, depending on the depth and aspect of the snowpack of the Mount Allan cirque, 6.0 to 66.4% of the pre-melt snowpack could be prematurely melted. On average at a basin scale, there was a 14.4-mm SWE difference in equivalent melt energy between the two shading algorithms with maximum differences over 100% of the total annual snowfall. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  J. Corripio.  Snow surface albedo estimation using terrestrial photography , 2004 .

[2]  Christopher J. Duffy,et al.  International Journal of Geographical Information Science an Efficient Domain Decomposition Framework for Accurate Representation of Geodata in Distributed Hydrologic Models an Efficient Domain Decomposition Framework for Accurate Representation of Geodata in Distributed Hydrologic Models , 2022 .

[3]  Javier Chueca,et al.  Relationship between solar radiation and the development and morphology of small cirque glaciers (maladeta mountain massif, central pyrenees, spain) , 2004 .

[4]  V. Klemeš,et al.  Operational Testing of Hydrological Simulation Models , 2022 .

[5]  Richard P. Hooper,et al.  Moving beyond heterogeneity and process complexity: A new vision for watershed hydrology , 2007 .

[6]  Dara Entekhabi,et al.  Preserving high-resolution surface and rainfall data in operational-scale basin hydrology: a fully-distributed physically-based approach , 2004 .

[7]  J. Dozier,et al.  Rapid calculation of terrain parameters for radiation modeling from digital elevation data , 1990 .

[8]  H. Marchant.  Snow Ecology: An Interdisciplinary Examination of Snow-Covered Ecosystems , 2001 .

[9]  D. S. Munro,et al.  An operational net shortwave radiation model for glacier basins , 1982 .

[10]  Yumin Chen,et al.  Estimating surface flow paths on a digital elevation model using a triangular facet network , 2011 .

[11]  Jack Major,et al.  Handbook of Snow: Principles, Processes, Management and Use , 1983 .

[12]  R. Clarke.  A review of some mathematical models used in hydrology, with observations on their calibration and use , 1973 .

[13]  J. Dozier,et al.  A faster solution to the horizon problem , 1981 .

[14]  N. Kouwen,et al.  Proving WATFLOOD: modelling the nonlinearities of hydrologic response to storm intensities , 2001 .

[15]  M. Woo,et al.  Modeling arctic snow distribution and melt at the 1 km grid scale. , 2004 .

[16]  M. Sambridge,et al.  Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization , 1997 .

[17]  Donald K. McCool,et al.  Process-based snowmelt modeling: does it require more input data than temperature-index modeling? , 2005 .

[18]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[19]  Rafael Montenegro,et al.  Solar radiation and shadow modelling with adaptive triangular meshes , 2009 .

[20]  R. Rigon,et al.  GEOtop: A Distributed Hydrological Model with Coupled Water and Energy Budgets , 2006 .

[21]  Jim Ruppert,et al.  A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation , 1995, J. Algorithms.

[22]  Caren C. Dymond,et al.  Mapping vegetation spatial patterns from modeled water, temperature and solar radiation gradients , 2002 .

[23]  J. Pomeroy,et al.  Characteristics of the Near-Surface Boundary Layer within a Mountain Valley during Winter , 2012 .

[24]  J. Pomeroy,et al.  Estimating areal snowmelt infiltration into frozen soils , 2001 .

[25]  Jeff Dozier,et al.  Climate and energy exchange at the snow surface in the Alpine Region of the Sierra Nevada: 2. Snow cover energy balance , 1992 .

[26]  D. H. Gray,et al.  An evaluation of snow accumulation and ablation processes for land surface modelling , 1998 .

[27]  T. Meixner.  Spatial Patterns in Catchment Hydrology: Observations and Modelling , 2002 .

[28]  Daniel W. McKenney.  Calibration and sensitivity analysis of a spatially-distributed solar radiation model , 1999, Int. J. Geogr. Inf. Sci..

[29]  P. Brimblecombe,et al.  The Removal of Soluble Ions from Melting Snowpacks , 1987 .

[30]  M. Woo,et al.  Snowmelt Hydrology of two subarctic slopes, Southern Yukon, Canada , 1998 .

[31]  Grant W. Petty,et al.  A First Course in Atmospheric Radiation , 2004 .

[32]  Slobodan P. Simonovic,et al.  System dynamics model for predicting floods from snowmelt in North American prairie watersheds , 2002 .

[33]  Joseph Andrew Clarke,et al.  Energy Simulation in Building Design , 1985 .

[34]  Nicole M. Gasparini,et al.  An object-oriented framework for distributed hydrologic and geomorphic modeling using triangulated irregular networks , 2001 .

[35]  J. Wallace,et al.  Atmospheric Science: An Introductory Survey , 1977 .

[36]  Ming-ko Woo,et al.  The Mackenzie GEWEX Study: A Contribution to Cold Region Atmospheric and Hydrologic Sciences , 2008 .

[37]  Philip Marsh,et al.  Characterizing snowmelt variability in a land‐surface‐hydrologic model , 2006 .

[38]  C. Ryerson.  MAPPING SOLAR ACCESS IN HIGH RELIEF AREAS FOR REGIONAL ENERGY PLANNING , 1984 .

[39]  A FRAMEWORK FOR HYDROLOGICAL MODELLING IN MAGS , 2005 .

[40]  L. Paul Chew,et al.  Guaranteed-quality mesh generation for curved surfaces , 1993, SCG '93.

[41]  John W. Pomeroy,et al.  Estimating sub‐canopy shortwave irradiance to melting snow on forested slopes , 2007 .

[42]  R. Allen,et al.  Software for missing data error analysis of Penman-Monteith reference evapotranspiration , 2002, Irrigation Science.

[43]  J. Dozier,et al.  Climate and energy exchange at the snow surface in the Alpine Region of the Sierra Nevada: 1. Meteorological measurements and monitoring , 1992 .

[44]  Alain Pietroniro,et al.  On the importance of sublimation to an alpine snow mass balance in the Canadian Rocky Mountains , 2010 .

[45]  C. Hopkinson,et al.  The influence of DEM resolution on simulated solar radiation‐induced glacier melt , 2010 .

[46]  Richard Essery,et al.  Statistical representation of mountain shading , 2004 .

[47]  P. Dornes.  An approach for modelling snowcover ablation and snowmelt runoff in cold region environments , 2009 .

[48]  E. Nelson,et al.  Adaptive Tessellation Method for Creating TINs from GIS Data , 1999 .

[49]  E. Vivoni,et al.  On the effects of triangulated terrain resolution on distributed hydrologic model response , 2005 .

[50]  D. H. Male,et al.  Snow surface energy exchange , 1981 .

[51]  Richard Essery,et al.  Scaling and parametrization of clear-sky solar radiation over complex topography , 2007 .

[52]  Jr. James Edward Frew.  The image processing workbench , 1991 .

[53]  John W. Pomeroy,et al.  Modelling snow melt and snowcover depletion in a small alpine cirque, Canadian Rocky Mountains , 2009 .

[54]  Christopher B. Jones,et al.  The Implicit Triangulated Irregular Network and Multiscale Spatial Databases , 1994, Comput. J..

[55]  Kang-Tsung Chang,et al.  Introduction to geographic information systems (4. ed.) , 2008 .

[56]  Jay Lee,et al.  Comparison of existing methods for building triangular irregular network, models of terrain from grid digital elevation models , 1991, Int. J. Geogr. Inf. Sci..

[57]  I. Stewart,et al.  Changes in snowpack and snowmelt runoff for key mountain regions , 2009 .

[58]  Michel Gangnet,et al.  Shaded Display of Digital Maps , 1984, IEEE Computer Graphics and Applications.

[59]  B. J. Garnier,et al.  A Method of Calculating the Direct Shortwave Radiation Income of Slopes , 1968 .

[60]  Emilio L. Zapata,et al.  High-performance three-horizon composition algorithm for large-scale terrains , 2011, Int. J. Geogr. Inf. Sci..

[61]  L. Martz,et al.  A methodology for preserving channel flow networks and connectivity patterns in large‐scale distributed hydrological models , 2005 .

[62]  Alain Pietroniro,et al.  Influence of landscape aggregation in modelling snow-cover ablation and snowmelt runoff in a sub-arctic mountainous environment , 2008 .

[63]  Keith Beven,et al.  MODELLING SOLAR RADIATION IN STEEPLY SLOPING TERRAIN , 1996 .

[64]  M. Hayashi,et al.  Integrated hydrogeological and geophysical study of depression‐focused groundwater recharge in the Canadian prairies , 2004 .

[65]  Rachel Spronken-Smith,et al.  Spatial Variability of Surface Radiation Fluxes in Mountainous Terrain , 2003 .

[66]  Jonathan Richard Shewchuk,et al.  Delaunay refinement algorithms for triangular mesh generation , 2002, Comput. Geom..

[68]  C. Hopkinson,et al.  Relationships between snowpack depth and primary LiDAR point cloud derivatives in a mountainous environment , 2012 .

[69]  L.A Rasmussen,et al.  Estimation of atmospheric transmittance from upper-air humidity , 1998 .

[70]  M. Sivapalan.  Process complexity at hillslope scale, process simplicity at the watershed scale: is there a connection? , 2003 .

[71]  Alain Pietroniro,et al.  Development of the MESH modelling system for hydrological ensemble forecasting of the Laurentian Great Lakes at the regional scale , 2006 .

[72]  J. Pomeroy,et al.  Simulation of the snowmelt runoff contributing area in a small alpine basin , 2010 .

[73]  D. Eppstein,et al.  MESH GENERATION AND OPTIMAL TRIANGULATION , 1992 .

[74]  John F. O'Callaghan,et al.  The extraction of drainage networks from digital elevation data , 1984, Comput. Vis. Graph. Image Process..

[75]  Anthony B. Davis,et al.  3D Radiative Transfer in Cloudy Atmospheres , 2005 .

[76]  Richard C. Willson,et al.  Secular total solar irradiance trend during solar cycles 21–23 , 2003 .

[77]  Distributed estimation of incoming direct solar radiation over a drainage basin , 1995 .

[78]  Conrad Sanderson,et al.  Armadillo: An Open Source C++ Linear Algebra Library for Fast Prototyping and Computationally Intensive Experiments , 2010 .

[79]  A. James Stewart,et al.  Fast Horizon Computation at All Points of a Terrain With Visibility and Shading Applications , 1998, IEEE Trans. Vis. Comput. Graph..

[80]  D. Marks,et al.  Comparison of Snow Deposition, the Snow Cover Energy Balance, and Snowmelt at Two Sites in a Semiarid Mountain Basin , 2001 .

[81]  R. Granger,et al.  Variation in Surface Energetics during Snowmelt in a Subarctic Mountain Catchment , 2003 .

[82]  A. Pietroniro,et al.  Spatial–temporal variability in solar radiation during spring snowmelt , 2006 .

[83]  Y. Tachikawa,et al.  Development of a Basin Geomorphic Information System Using a TIN-DEM Data Structure , 1992 .

[84]  A. T. Young.  Air mass and refraction. , 1994, Applied optics.

[85]  G. Tucker,et al.  Modelling landscape evolution , 2010 .

[86]  Philip Marsh,et al.  Modelling spatially distributed snowmelt and meltwater runoff in a small Arctic catchment with a hydrology land‐surface scheme (WATCLASS) , 2005 .

[87]  C. Walcek.  Cloud Cover and Its Relationship to Relative Humidity during a Springtime Midlatitude Cyclone , 1994 .

[88]  Emilio L. Zapata,et al.  Fast clear-sky solar irradiation computation for very large digital elevation models , 2008, Comput. Phys. Commun..

[89]  William L. Quinton,et al.  The cold regions hydrological model: a platform for basing process representation and model structure on physical evidence , 2007 .