## Nomenclature

Symbol Description

Section Value

Units (SI)

a ai a2

c ci

csusp

Ccan cp,a

Parameter, saturation vapor pressure 2

Parameter, effective thermal 4 conductivity

Parameter, albedo weight function 4

Parameter, albedo weight function 4

Parameter, dimensionless sensible 3 heat flux

"Saltation efficiency" coefficient 3

Specific surface of snow 2

Parameter, saturation vapor pressure 2

Parameter, effective thermal 4 conductivity

Bowen ratio HS/HL 3

Lower limit for Bowen ratio 3

Parameter, saturation vapor pressure 2

Parameter, apparent change in roughness length New snow drift coefficient Mass concentration of suspended snow

Canopy closure

Specific heat of air at constant pressure and at 273.15 K

0.68

0.1203

1005

J kg-1K

Symbol Description

Section Value

Units (SI)

C Cd hq

Ch Cq

CQN d dopt

Dbs Dsalt D

susp

Esubl E

^evap

Ebs f

fs g

Specific heat of ice at constant pressure and at 273.15 K

Specific heat of water at constant pressure and at 273.15 K

Specific heat of snow at constant pressure

Shape factor

Bulk transfer coefficient

Bulk transfer coefficient for momentum

Bulk transfer coefficient for heat Bulk transfer coefficient for water vapor

Parameters, bulk transfer coefficients in terms of the bulk Richardson number Geometrical grain size or diameter Optical grain size

Diffusion coefficient of water vapor in air

Diffusion coefficient of water vapor in snow

Horizontal blowing snow transport Saltating transport of blowing snow Suspension transport of blowing snow

Sum of sublimation and evaporation rate at surface Surface sublimation rate Surface evaporation rate Sublimation rate of blowing snow Parameter, compaction Heat flux

Weight function for albedo Acceleration due to gravity

2114 4217

J kg-1K

1v-1

9.81

Wm-2

Symbol |
Description |
Section |
Value |
Units (SI) |

G |
Ground heat flux |
3 |
Wm-2 | |

Gg |
Enhancement factor for grain growth 2 |
m | ||

h |
Capillary rise |
2 |
m | |

hs,b |
Portion of bare ground sensible heat advected to a snow patch |
3 |
Wm-2 | |

h* |
Lower boundary for suspended snow 3 |
m | ||

(upper boundary for saltating snow) | ||||

h |
Mass transfer coefficient |
2 |
m s-1 | |

H |
Internal energy of the snowpack |
3 |
J m-2 | |

HL |
Latent heat flux |
3 |
W m-2 | |

HP |
Energy flux carried by precipitation and blowing snow |
3 |
Wm-2 | |

Hs |
Sensible heat flux |
3 |
W m-2 | |

Hs,b |
Sensible heat flux over bare ground |
3 |
W m-2 | |

Hs,s |
Sensible heat flux over a completely snow-covered fetch |
3 |
Wm-2 | |

H's |
Dimensionless sensible heat flux |
3 | ||

HNw |
New snow depth due to blowing and drifting snow |
3 |
m | |

HS, H |
Depth of snowpack, snow depth |
2, 3, 4, 5 |
m | |

I |
Snow interception |
3 |
kg m-2 | |

I1 |
Interception before unloading |
3 |
kg m-2 | |

k |
Thermal conductivity |
2 |
W m-1 K- | |

ka |
Thermal conductivity of air |
3 |
W m-1 K- | |

Ki |
Permeability of the interconnected water pathways in wet snow |
2 |
m2 | |

Kf |
Cryoscopic constant for water |
2 |
1.855 |
K kg mol-1 |

kcl |
Snow clump shape coefficient |
3 | ||

keff |
Effective thermal conductivity |
2 |
W m-1 K- | |

ki |
Thermal conductivity of ice |
4 |
W m-1 K- | |

K |
Intrinsic or saturated permeability |
2 |
m2 | |

Kk |
Permeability of phase k in unsaturated wet snow |
2 |
m2 | |

Krk |
Relative permeability of phase k in unsaturated wet snow (=Kk /K) |
2 | ||

Lu, Lu |
Latent heat of fusion for ice at 273.15 K |
2, 3 |
3.335 x 105 |
J kg-1 |

Symbol Description

Section Value

Units (SI)

Liv, Lvi

Ltv, Lvi

Li Ll

LL,b

Lf m

NRe p pa pe pk

Latent heat of sublimation for ice at 2, 3 273.15 K

Latent heat of evaporation for water at 273.15 K

Latent heat of phase change from phase j to phase i Snow load Initial snow load Maximum canopy snow load Maximum snow load per unit area of 3 branch

Obukhov length Net flux of longwave radiation, L4+Lf

Winter leaf and stem area index Maximum canopy snow load Downward component of longwave radiation

Upward component of longwave radiation

Parameter, water saturation (van Genuchten) Molality of species

Mass of single blowing snow particle 3

Mass growth rate of snow particle 2

Snow mass per unit surface area 3

Parameter, water saturation (van 2 Genuchten)

Nusselt number 3

Particle Reynolds number 3

Pressure 2

Atmospheric or air pressure 2

Air-entry pressure 2

Pressure of constituent k 2

Capillary pressure or pressure drop 2 (pa — pi) across air/water interface

2.838 x 106

2.505 x 106

Wm-2

Pa hPa or Pa Pa Pa Pa

Symbol Description

Section Value

Units (SI)

P Pe

Pbs q Q

Qo Ra rpt rpt,n rp rg

Racrit

Rf rm rn

Rrunoff

Pressure drop (pi - pj) across i/j interface

Saturation vapor pressure over a flat surface with respect to constituent k

Saturation vapor pressure over a curved surface with respect to constituent k

Precipitation rate

Accumulated precipitation

Peclet number

Probability of blowing snow occurrence

Phase change thermal source term Specific humidity

Specific humidity at the snow surface 3 Rayleigh number 2

Particle radius 3

Nominal snow particle radius 3

Tube radius or equivalent pore radius 2 Snow grain radius 2, 3

Critical Rayleigh number for onset 2 of convection Reynolds number Bulk Richardson number Gas constant for water vapor Freezing rate Melt rate

Net radiative flux at the snow surface, SN + LN

Runoff rate at snow-soil interface Liquid water saturation (0^/0) Irreducible or immobile liquid water 2 saturation

Effective liquid water saturation [(s - Si)/(1- Si)]

Phase change mass source term 2 Sherwood number 3

0.0005

461.50

kg m

Symbol |
Description |
Section Value |
Units (SI) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Stoa |
Solar radiation flux at the top of the |
3 |
Wm-2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

atmosphere | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

SCA |
Proportion of snow-covered area |
3 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Sn |
Net flux of shortwave radiation, |
3 |
Wm-2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

S| + St | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

SWE |
Snow water equivalent |
2, 3,4,5 |
kg m-2 (or | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

mm w.e.) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Si |
Downward component of solar |
3 |
Wm-2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

radiation | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

St |
Reflected component of solar |
3 |
Wm-2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

radiation | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

t |
Time |
2, 3, 4 |
s | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

th |
Snow surface age |
3 |
hours | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

T |
Temperature |
2, 3 |
Kor °C | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Td |
Melting point depression, 273.15 - T |
2 |
K | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

To |
Melting temperature 273.15 or 0 °C |
2 |
Kor °C | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

To, To |
Snow surface temperature |
3, 4 |
K or °C | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

o,sp |
Ice sphere surface temperature |
3 |
K | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

a |
Air temperature |
3, 4 |
K or °C | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Ts |
Snow temperature |
3 |
K or °C | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

T ' |
Snow temperature gradient |
2 |
K m-1 or | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

° Cm-1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Tmean |
Mean air temperature in layer of |
3 |
K | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

depth Z ref | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

u |
Wind speed |
3 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

uio |
Average hourly 1o-m wind speed |
3 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

u |
Mean wind speed |
3 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

ucrest |
Mean wind speed measured on a |
3 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

crest | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

u* |
Friction velocity |
3 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

u*n |
Friction velocity applied to |
3 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

small-scale non-erodible elements | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

u*t |
Threshold friction velocity |
3 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

tf/ |
Snow unloading coefficient |
3 |
s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Vi |
Velocity of ice matrix |
2 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Vk |
Flow (filter) velocity of fluid k |
2 |
m s-1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(a = air, i = water) |
Section Value Units (SI) zref zb zo, z0 a ab amax amin as At Ax Volume per unit mass or reciprocal density Vertical (wind) velocity Dimensionless vertical velocity Coordinate system with z positive upward relative to the ground Spatial coordinate along the direction of flow Parameters, similarity function Dimensionless distance downwind of snow patch Reference height above ground Upper boundary for suspended snow 3 Momentum (or aerodynamic) roughness length; surface roughness length Roughness length for heat Roughness length for water vapor Scale of roughness elements Snow (surface) albedo Albedo of snow-free (bare) surface Upper limit on snow albedo Lower limit on snow albedo Albedo of deep, homogeneous snow 4 Coefficient of solar absorption 2 Coefficient of thermal expansion 2 Parameters, similarity function 3 Parameter, similarity function, 3 Time interval 4 Characteristic distance 2 Parameters, similarity function 3 Standard deviation of wind speed 3 Snow infrared emissivity 3 Effective emissivity for the 3 atmosphere Exponent, phase permeability 2 Symbol Description Section Value Units (SI) Z ref Pv,a Pv,pt Height above snow surface 3 Reference height above snow 3 surface Radius of curvature of i/j interface 2 Newtonian viscosity of snow 2 Newtonian viscosity of snow at 2 T = 0 °C and ps = 0.0 kg m-3 Dynamic viscosity of fluid k 2 Contact angle between solid and 2 liquid Volume fraction of constituent k 2, 3 Von Karman constant 3 Turbulent diffusion coefficient for 3 snow particles Wavelength 2 Pore-size distribution index 2 Leaf area index 4 Kinematic viscosity of air (na / pa) 3 Density of air 2, 3 Reference density of air 2 Density of ice 2, 3 Density of fluid or solid k 2 Density of water 2, 3, 4 Maximum permitted snow density 4 Density of water vapor 2 Density of water vapor in air 3 Density of water vapor at particle 3 surface Saturation density of water vapor 2, 3 Stefan-Boltzmann constant 3 1000 Surface tension of air/water interface 2 Surface tension of ice/water interface 2 Surface tension of ice/vapor interface 2 Surface tension of i/j interface 2 Pa s Pas Pas rad. kg m
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