A model which translates snow depth observations to snow water equivalents

Description

The HS2SWE model is based on similar principles as the delta.snow model. It is described in the following publication: Magnusson, J., B. Cluzet., L. Quéno, R. Mott, M. Oberrauch, G. Mazzotti, C. Marty, T. Jonas; 2025; Evaluating methods to estimate the water equivalent of new snow from daily snow depth recordings; Cold Regions Science and Technology, 233; 10.1016/j.coldregions.2025.104435.

Usage

hs2swe(
  data,
  RhoNew = 113.7,
  RhoMax = 571.6,
  SnoTemp = -0,
  Visc = 60510000,
  DQMultInc = 0.1,
  DQMultMax = 5,
  HsAcc = 2,
  c1 = 2.8e-06,
  c2 = 0.042,
  c3 = 0.046,
  c4 = 0.081,
  c5 = 0.018,
  g = 9.81,
  dt = 86400
)

Arguments

Details

The model is also available as matlab function, python package or as R function that accepts a slightly different input from https://github.com/oshd-slf/HS2SWE

Value

A numeric vector of simulated SWE in mm.

Examples

data(hsdata, package = "nixmass")

swe_deltasnow <- swe.delta.snow(hsdata)
swe_hs2swe <- hs2swe(hsdata)
plot(seq_along(hsdata$date), swe_deltasnow, type = "l", ylab = "SWE (mm) / hs (cm)", xlab = "day")
lines(seq_along(hsdata$date), swe_hs2swe, type = "l", col = "red")
lines(seq_along(hsdata$date), hsdata$hs * 100, type = "l", lty = 2, col = "grey30")
legend("topleft", legend = c("deltaSNOW", "HS2SWE", "HS"),
 col = c("black", "red", "grey30"), lty = c(1, 1, 2))

Daily snow depth data for a northern alpine station

Description

Gapless daily snow depth observations for a winter season from 1.8. - 31.7. from a station situated in the northern earstern alps at an altitude of 600 m. For anonymization the years are intentionally set to 1900 - 1901. This data series is free of gaps with a minimum of 0 and a maximum of 1.3 meters. It is intended to be used as is as input data for the package nixmass to calculate snow water equivalent and bulk snow density with the delta.snow method and several empirical regression models from the literature.

Usage

data(hsdata)

Format

A 'data.frame' named data with columns date and hs.

date

The date column contains character strings of the format "YYYY-MM-DD" and is of class character

.

hs

The hs column holds daily observed snow depths in meters and is of class numeric.

Examples

## Load example data
data("hsdata")

## explore dataset
head(hsdata)
plot(hsdata$hs, type="o")

## compute snow water equivalents
o <- nixmass(hsdata, model="delta.snow")
plot(o)

o1 <- nixmass(hsdata, alt=600, region.jo09 = 6, region.gu19 = "central",
snowclass.st10 = "alpine", verbose = FALSE)
plot(o1)
summary(o1)

SWE modeling with the delta.snow process based model and several empirical regression models.

Description

Snow Water Equivalent (SWE) is modeled either exclusively from daily snow depth changes or statistically, depending on snow depth, elevation, date and climate class.

Usage

nixmass(
  data,
  model = c("delta.snow", "delta.snow.dyn_rho_max", "hs2swe", "jo09", "pi16", "st10",
    "gu19"),
  alt,
  region.jo09,
  region.gu19,
  snowclass.st10,
  layers = FALSE,
  strict_mode = TRUE,
  verbose = FALSE
)

Arguments

Details

This function is a wrapper for the simulation of SWE with different models. The process based model delta.snow can be chosen in its original formulation (Winkler et al. 20219) and with a dynamically increasing maximum bulk snow density (Schroeder et al., 2024). The hs2swe model is an alternative formulation of the same physical concept used in delta.snow (Magnusson, et al., 2025). Some empirical regression models can also be chosen: Jonas,Pistocchi, Sturm and Guyennon. For the 'delta.snow' and 'hs2swe' models and the ones of 'Pistocchi' and 'Guyennon', the needed parameters and coefficients from the original references are set as default. They can however be changed according to results from other datasets. For the other models of 'Jonas' and 'Sturm' regression coefficients are fixed.

Computation is quite fast and there does not exist any restriction regarding the length of the data. However, if many years have to be modeled at once, it is recommended to split the computation into single years.

Value

A list of class nixmass with components:

Author(s)

Harald Schellander, Michael Winkler

References

Guyennon, N., Valt, M., Salerno, F., Petrangeli, A., Romano, E. (2019) 'Estimating the snow water equivalent from snow depth measurements in the Italian Alps', Cold Regions Science and Technology. Elsevier, 167 (August), p. 102859. doi: 10.1016/j.coldregions.2019.102859.

Jonas, T., Marty, C. and Magnusson, J. (2009) "Estimating the snow water equivalent from snow depth measurements in the Swiss Alps"", Journal of Hydrology, 378(1 - 2), pp. 161 - 167. doi: 10.1016/j.jhydrol.2009.09.021.

Pistocchi, A. (2016) "Simple estimation of snow density in an Alpine region", Journal of Hydrology: Regional Studies. Elsevier B.V., 6(Supplement C), pp. 82 - 89. doi: 10.1016/j.ejrh.2016.03.004.

Sturm, M. et al. (2010) "Estimating Snow Water Equivalent Using Snow Depth Data and Climate Classes", Journal of Hydrometeorology, 11(6), pp. 1380 - 1394. doi: 10.1175/2010JHM1202.1.

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.

Schroeder, M.et al. (2024) "CONTINUOUS SNOW WATER EQUIVALENT MONITORING ON GLACIERS USING COSMIC RAY NEUTRON SENSOR TECHNOLOGY A CASE STUDY ON HINTEREISFERNER, AUSTRIA", Proceedings: International Snow Science Workshop 2024, Tromsø, Norway, 1107 - 1114

Examples

# Load example data with realistic snow depth values
# from a station at 600 meters in the northern Alps
# Note that the winter season is set to an arbitrary date
# to mask its origin
data("hsdata")
o <- nixmass(hsdata, model="delta.snow",verbose=TRUE)
plot(o)

o1 <- nixmass(hsdata, alt=600, region.jo09=6, region.gu19 = "central",
              snowclass.st10 = "alpine", verbose = FALSE)
plot(o1)
summary(o1)

swe <- nixmass(hsdata, alt = 1000, region.jo09=1, snowclass.st10 = "tundra", region.gu19 = "italy")
summary(swe)

Plot modeled SWE values of a nixmass object.

Description

Plot modeled SWE values of a nixmass object.

Usage

## S3 method for class 'nixmass'
plot(x, title = NULL, density = FALSE, ...)

Arguments

Value

Does not return anything. A plot is produced.

Examples

data("hsdata")
plot(nixmass(hsdata, model = "delta.snow"))
plot(nixmass(hsdata, model = "delta.snow.dyn_rho_max", layers = TRUE), density = TRUE)

Print summary of a nixmass object.

Description

Print summary of a nixmass object.

Usage

## S3 method for class 'nixmass'
summary(object, ...)

Arguments

Value

Summary information of SWE values calculated with selected models is printed to the screen.

Examples

data("hsdata")
n <- nixmass(hsdata, model = c("delta.snow", "pi16"))
summary(n)

SWE modeling from daily snow depth differences

Description

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

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.

Usage

swe.delta.snow(
  data,
  model_opts = list(),
  dyn_rho_max = TRUE,
  layers = FALSE,
  strict_mode = TRUE,
  verbose = FALSE
)

Arguments

Details

If dyn_rho_max=TRUE, the bulk snow density varies with layer age. As activation function, atan is used, where the S-curve symmetrically transitions from the lower to the upper density bound. In that case, model_opts are extended by a lower density bound rho_l, an upper density bound rho_h, a slope sigma and a midpoint mu, which have been found via an optimization procedure (Winkler et al., 2021). Be aware that also the other model coefficients do slightly change.

The following model coefficients must be provided:

dyn_rho_max=FALSE:

• rho.max Maximum density of an individual snow layer produced by the delta.snow model (kg/m3), rho.max > 0

• rho.null Fresh snow density for a newly created layer (kg/m3), rho.null > 0. Currently optimized for daily snow depth observations.

• 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. No sub-daily values are allowed at the moment (see details).

dy_rho_max=TRUE:

Instead of a constant coefficient for rho.max, these four parameters describe the smooth S-curve approximated by the atan trigonometric function.

• sigma Steepness or slope of atan at its midpoint mu, (-), sigma > 0.

• mu Central midpoint in days, where the steepest transition occurs (days), mu > 0.

• rho_h Upper density bound for a single layer and the whole snow pack (kg/m3), rho_h > 0.

• rho_l Lower density bound for a single layer and the whole snow pack, where the transition begins (kg/m3), rho_l > 0.

All other coefficients are needed as well. Be aware however that they are slightly different.

The easiest way to call the original delta.swe model is swe.delta.snow(hsdata, dyn_rho_max = FALSE). Note that parameters intrinsic to the dynamic density model provided with the original model are silently ignored.

In principal, the model is able to cope with a sub-daily temporal resolution, e.g. hourly snow depth observations. However, the model was fitted to daily observations, and the model parameter rho.null reflects that. In other words, if the observation frequency changes, rho.null should change as well. Currently, no sub-daily resolution is allowed.

Value

If layers=FALSE, a vector with daily SWE values in mm. If layers=TRUE, a list with layerwise matrices of the parameters h (snow depth), swe and age is returned additionally to the SWE vector. The matrix rows correspond to layers, columns correspond to dates. swe is in mm, h in m and age in days.

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.

Schroeder, M.et al. (2024) "CONTINUOUS SNOW WATER EQUIVALENT MONITORING ON GLACIERS USING COSMIC RAY NEUTRON SENSOR TECHNOLOGY A CASE STUDY ON HINTEREISFERNER, AUSTRIA", Proceedings: International Snow Science Workshop 2024, Tromsø, Norway, 1107 - 1114

Examples

data(hsdata, package = "nixmass")

swe_dyn <- swe.delta.snow(hsdata)
swe <- swe.delta.snow(hsdata, dyn_rho_max = FALSE)
plot(seq_along(hsdata$date), swe_dyn, type = "l", ylab = "SWE (mm) / hs (cm)", xlab = "day")
lines(seq_along(hsdata$date), swe, type = "l", col = "red")
lines(seq_along(hsdata$date), hsdata$hs * 100, type = "l", lty = 2, col = "grey30")
legend(title = "delta.snow", "topleft", legend = c("SWE dyn", "SWE", "HS"),
 col = c("black", "red", "grey30"), lty = c(1, 1, 2))

Statistical SWE modeling based on a quadratic dependance on the day-of-year

Description

This model parameterizes bulk snow density with day-of-the-year as the only input similar to swe.pi16 but adds a quadratic dependance. It was calibrated for the regions of the whole Italian alps, and the subregions South-West, Central and South-East. By setting the coefficients of the empirical regression it can however be used with results from other datasets.

Usage

swe.gu19(data, region.gu19, n0 = NA, n1 = NA, n2 = NA)

Arguments

Details

swe.gu19 Similar to the model of Pistocchi (2016), this function uses only the day-of-year (DOY) as parameterization for bulk snow density and hence SWE. In contrast to the latter, here, a quadratic term for DOY was added, to reflect non-linearity in the snow bulk density variability. The datums in the input data.frame are converted to DOY as days spent since November 1st. Regression coefficients depend on regions defined in Guyennon et al. (2019), which are italy for the Italian Alps, southwest for the South-western Italian Alps, central for the Central Italian Alpes or southeast for the South-western Italian Alps.

If region.gu19 is set to myregion, the coefficients no, n1 and n2 must be set to values, obtained from a regression between densities and day-of-year from another dataset. It has to have the form density ~ DOY + DOY^2, where DOY is the day-of-year as defined in the original reference. Non computable values are returned as NA.

Value

A vector with daily SWE values in mm.

References

Guyennon, N., Valt, M., Salerno, F., Petrangeli, A., Romano, E. (2019) 'Estimating the snow water equivalent from snow depth measurements in the Italian Alps', Cold Regions Science and Technology. Elsevier, 167 (August), p. 102859. doi: 10.1016/j.coldregions.2019.102859.

Pistocchi, A. (2016) 'Simple estimation of snow density in an Alpine region', Journal of Hydrology: Regional Studies. Elsevier B.V., 6 (Supplement C), pp. 82 - 89. doi: 10.1016/j.ejrh.2016.03.004.

Examples

data(hsdata)
swe <- swe.gu19(hsdata, region = "italy")
summary(swe)

Statistical SWE modeling depending on month and climatic region in Switzerland

Description

Snow Water Equivalent (SWE) is modeled statistically depending on snow depth, altitude, date and region in Switzerland.

Usage

swe.jo09(data, alt, region.jo09)

Arguments

Details

swe.jo09 This model parameterizes bulk snow density using snow depth, season (i.e. month), site altitude and site location. The location is implemented by a density offset according to the region in Switzerland, where the station belongs to. Non computable values are returned as NA.

Value

A numeric vector with SWE values for each region in mm.

References

Jonas, T., Marty, C. and Magnusson, J. (2009) 'Estimating the snow water equivalent from snow depth measurements in the Swiss Alps', Journal of Hydrology, 378(1 - 2), pp. 161 - 167. doi: 10.1016/j.jhydrol.2009.09.021.

Examples

data(hsdata)
swe <- swe.jo09(hsdata, 1500, 1)
summary(swe)
plot(swe)

Statistical SWE modeling depending on the day-of-year

Description

This model parameterizes bulk snow density with day-of-the-year as the only input. It was calibrated for the region of South Tyrol, Italy, and is therefore called ST model in the original reference.

Usage

swe.pi16(data, rho_0 = 200, K = 1)

Arguments

Details

swe.pi16 This function uses only the day-of-year (DOY) as parameterization for bulk snow density and hence SWE. Here, the datums in the input data.frame are converted to DOY as defined in the original reference: negative values between 1.10. and 31.12. DOY=-92 at 1.10. In leap years 31.12. has DOY = 0, in non-leap years 31.12. has DOY = -1 with no day being 0. Non computable values are returned as NA.

Value

A vector with daily SWE values in mm.

References

Pistocchi, A. (2016) 'Simple estimation of snow density in an Alpine region', Journal of Hydrology: Regional Studies. Elsevier B.V., 6(Supplement C), pp. 82 - 89. doi: 10.1016/j.ejrh.2016.03.004.

Examples

data(hsdata)
swe <- swe.pi16(hsdata)
summary(swe)

Statistical SWE modeling depending on day of year and a climatic region

Description

The Sturm model parameterizes bulk snow density with day of the year and a snowclass.st10. It was trained on historical snow depth - density - SWE data from the United States, Canada, and Switzerland.

Usage

swe.st10(
  data,
  snowclass.st10 = c("alpine", "maritime", "prairie", "tundra", "taiga")
)

Arguments

Details

This model converts snow depth to SWE using snow depth, day of year and station location (from which a climate class of snow can be inferred. The day of year (DOY) is the day-number of in the season 1.10. - 30.6. The 1.10. refers to DOY = -92. The 1.2. would be DOY = 32, while 15.11. would be DOY = -47. The snowclass.st10 must be one out of the character strings "alpine","maritime","prairie","tundra" and "taiga". For the Alps probably "alpine" would be the most appropriate climate classification. Non computable values are returned as NA.

Value

A vector with daily SWE values in mm.

References

Sturm, M. et al. (2010) 'Estimating Snow Water Equivalent Using Snow Depth Data and Climate Classes', Journal of Hydrometeorology, 11(6), pp. 1380 - 1394. doi: 10.1175/2010JHM1202.1.

Examples

data(hsdata)
swe <- swe.st10(hsdata)
summary(swe)