swe.delta.snow {nixmass}

SWE modeling from daily snow depth differences

Description

Model daily values of Snow Water Equivalent (SWE) solely from daily differences of snow depth.

Usage

swe.delta.snow(data, rho.max=401.2588, rho.null=81.19417, c.ov=0.0005104722, 
               k.ov=0.37856737,k=0.02993175, tau=0.02362476, eta.null=8523356,
               timestep=24, verbose=FALSE)

Arguments

data

A data.frame with at least two columns named date and hs. They should contain date and corresponding daily observations of snow depth hs \ge 0 measured at one site. The unit must be meters (m). No gaps or NA are allowed.

rho.max

Maximum density of an individual snow layer produced by the deltasnow model [kg/m3], rho.max > 0

rho.null

Fresh snow density for a newly created layer [kg/m3], rho.null > 0

c.ov

Overburden factor due to fresh snow [-], c.ov > 0

k.ov

Defines the impact of the individual layer density on the compaction due to overburden [-], k.ov \in [0,1].

k

Exponent of the exponential-law compaction [m3/kg], k > 0.

tau

Uncertainty bound [m], tau > 0.

eta.null

Effective compactive viscosity of snow for "zero-density" [Pa s].

timestep

Timestep between snow depth observations in hours. Default is 24 hours, i.e. daily snow depth observations.

verbose

Should additional information be given during runtime? Can be TRUE or FALSE.

Details

swe.delta.snow computes SWE solely from daily changes of snow depth at an observation site.
Compression of a snow layer without additional load on top is computed on the basis of Sturm and Holmgren (1998), who regard snow as a viscous fluid:

\rho_i(t_{i+1}) = \rho_i(t_i)*(1+(SWE*g)/\eta_0 * exp^{-k_2*\rho_i(t_i)})

with \rho_i(t_{i+1}) and \rho_i(t_i) being tomorrow's and today's respective density of layer i, the gravitational acceleration g = 9.8ms^{-2}, viscosity \eta_0 [Pa] and factor k2 [m^3kg^{-1}], determining the importance of today's for tomorrow's density.

Value

A vector with daily SWE values in mm.

Author(s)

Harald Schellander, Michael Winkler

References

Gruber, S. (2014) "Modelling snow water equivalent based on daily snow depths", Masterthesis, Institute for Atmospheric and Cryospheric Sciences, University of Innsbruck.

Martinec, J., Rango, A. (1991) "Indirect evaluation of snow reserves in mountain basins". Snow, Hydrology and Forests in High Alpine Areas. pp. 111-120.

Sturm, M., Holmgren, J. (1998) "Differences in compaction behavior of three climate classes of snow". Annals of Glaciology 26, 125-130.

Winkler, M., Schellander, H., and Gruber, S.: Snow water equivalents exclusively from snow depths and their temporal changes: the delta.snow model, Hydrol. Earth Syst. Sci., 25, 1165-1187, doi: 10.5194/hess-25-1165-2021, 2021.