Modelling snow

Structure of the snowpack

The density and temperature of snow is not usually uniform throughout the snowpack.  Density at all snow levels is related to how much air is trapped, the ice or water content, and also linked to the temperature of the snow itself.  The upper snow layer, especially if of fresh snow, is largely uncompressed and has relatively low density.  Lower layers in the snowpack generally have greater density due to compaction by the snow above.  

Heat flux differs through each layer of snow according to its density and temperature.  Snow, especially new dry snow, is a good thermal insulator.  Percolation, freezing and melting of water also has an effect upon the transfer, release and absorption of heat in each layer and on the surface.  Nevertheless, the flux of heat through the snowpack, though relatively small, is important.  In particular, upward heat flux from the ground through the layers of snow influences surface snowmelt and sublimation, and of course, surface temperature.

In snow-free areas, there is a ready exchange of heat, moisture and momentum between the atmosphere and underlying surface.   Snow-covered regions have reduced heat conductivity, higher surface albedo, and reduced roughness compared to areas without snow.  Thus for snowy areas there is an effective thermal, hydrological, and mechanical decoupling between the overlying atmosphere and underlying soil.     

Skin temperature of snow and the 2m temperature

The skin temperature of the upper snow layer is governed by the balance between:

Forecasts of air temperature at 2m are derived from the forecast temperature at the lowest level of the atmospheric model and the forecast temperature of the model surface (the skin temperature).  The skin temperature is itself derived using HTESSEL which employs one or more “tiles” to describe the characteristics of the land.  These “tiles” evaluate heat fluxes into and from the underlying surfaces.

Calculation of the skin temperature of snow is rather complex and depends upon the characteristics of the snowpack throughout its depth.

To address this, a multi-layer snow model is used in two “tiles” within HTESSEL:

Forecasts of air temperature at 2m use the skin temperature of the snow as if it were at the ground surface (rather than at the elevation of the snow surface).  This may lead to errors in forecast 2m temperatures in cases of deep snow.

The multi-layer snow model

The IFS multi-layer snow model uses up to five layers to represent the snowpack and the complex heat fluxes and interactions between them.   It represents the vertical structure and evolution of snow temperature, snow mass, density, and liquid water content in each layer.  The energy flux at the top of the snowpack is the balance of the upward and downward energy fluxes at the snow surface including the effect of any snow evaporation.   Albedo and surface fluxes vary according to the snow extent, depth and ground coverage (with account taken of trees in areas of forest), and age of the snow.  Heat flux from the underlying ground is also incorporated.  The fluxes are illustrated and explained in Figs1A to 1C.

The multi-layer snow model has a fairly realistic representation of the vertical density and temperature profiles of the snowpack which allows a good representation of its thermal properties.  

The model represents:

When fresh snow falls or melts away, it is added to or subtracted from the top of the snowpack.  Then the layers are reanalysed such that relatively shallow layers of snow are maintained at the top (5cm thick) and at the base (15cm thick) so that the atmosphere/snow and soil/snow heat fluxes can be best modelled.

The skin temperature (Tskin) over snow cannot rise above 0°C and any net positive heat flux at this temperature is used to warm or melt the snow layer.    The flux of heat might be:

Vertical discretisation over flat terrains:


Fig1A: Schematic representation of the multi-layer snow scheme. Shallow snow layer.  Snow depth <12.5cm.  (Note: Snow depth < 10cm implies only a partial cover of snow) 


Fig1B: Schematic representation of the multi-layer snow scheme. Deep snow. Snow depth >27.5cm. Any additional snow accumulation is added into the fourth snow layer in order to preserve the characteristics and thermal flux qualities of thinner layers at base and top of the snowpack.  For snow depths between 12.5cm and 27.5cm additional snow is added proportionately to the layers as they are introduced.


Fig1C: Schematic representation of the multi-layer snow scheme for permanent snow (e.g. Greenland, Antarctica) and for glaciers.  Snow depth is defined as ≥10m.  Any additional snow accumulation is added into the fifth snow layer in order to preserve the characteristics and thermal flux qualities of thinner layers at the top of the snowpack.  



rsnowConductive resistance between exposed snow and atmosphere


rforestConductive resistance between forest snow and atmosphere


KSDownward short wave radiation
TiTemperature of snow layer i
LSDownward long wave radiation
ρiDensity of snow layer i
HSSensible heat flux
SiMass of frozen water in snow layer i
ESLatent heat flux
WiMass of liquid water in snow layer i
RSNet (precipitation and evaporation) water flux at the surface
didepth of I-layer in the snowpack
aSAlbedo of exposed snow
KiShort wave radiation between snow layers I and I+1
aFAlbedo of forest snow
GiConductive heat flux between snow layers I and I+1



RiLiquid water flux between snow layers I and I+1
TSOTemperature of uppermost soil layer
GBConductive heat flux at snow-soil surface
WSOLiquid water of uppermost soil layer
KBShort wave radiation at snow-soil surface
dSODepth of uppermost soil layer
RBLiquid water flux at snow-soil surface
rsoilConductive resistance between snow and soil


Table1: List of symbols for parameters shown in Figs1.

Complex terrain areas:

A different algorithm is applied to define the snow layers in regions of complex or mountainous terrain where snow depth >25 cm.  These layers are thicker than used for a snowpack with same depth over a flat region (e.g. in complex terrain an 85cm deep snowpack is discretised with layer depths: 16.00cm, 17.25cm, 17.25cm, 17.25cm, 17.25cm).

Complex terrain is defined as regions where the standard deviation of the sub-grid-scale orography is greater than 50 m.   Ground height data from internationally available datasets at 1km resolution are interpolated to model resolution but smoothing misses important detail.   Statistical parameters (e.g. standard deviations of the mean height, slopes, and direction of unresolved orography) are fed into the model via the sub-grid-scale parametrisation of orography. 

Permanent snow areas:

In permanent snow areas (e.g. Greenland, Antarctica and glaciers) a fixed snow layering it is used. The top four layers (counting from the one in contact with the atmosphere) have a constant depths of 50 cm, whereas any additional snow accumulation is added into the bottom layer (Fig1C). 

Sea ice:

There is no representation of snow on top of sea ice or ice on lakes.  Snow cover on ice acts to increase its persistence by increasing the albedo and reducing the heat flux into the modelled ice.  Thin sea ice or lake ice covered by thin snow grows or melts much faster than does thick ice with deep snow.  

Snow depth

The snow depth in the model changes when fresh snow falls or when snow on the ground melts, evaporates or is compressed.  The response in dry periods at different altitudes is shown in Fig2.1.12D. 

Fresh snowfall is added to the top layer, with a new snow density depending on air temperature and wind speed.  Melted snow is removed from the top layer.  The snow mass is then redistributed across the different layers but relatively shallow layers of snow are maintained at the top and at the base so that the atmosphere/snow and soil/snow heat fluxes can be best modelled. 

Liquid water from rainfall onto snow or melting percolates downwards and can refreeze on a different level, releasing latent heat.

Snow depth water equivalent is the sum of frozen and liquid water within the snowpack.  Snow density considers meltwater refreezing, so the density will vary but the snow water equivalent should not change.

The snow depth of each layer is calculated by snow depth water equivalent divided by snow density for each layer.  

Snow depth is computed using:

The total snow depth is the sum of the snow depth of each layer.

When snow depth is:

For permanent snow areas (e.g.Greenland, Antarctica) and over mountain glaciers:

It is common for snow depth to be extremely high at grid points within these areas of permanent snow .  

Snow cover

Snow cover is diagnosed from the water equivalent of the modelled snow: 

Data assimilation for snow on the ground

Snow cover, snow depth and snow compaction affect all IFS atmospheric forecast models.  It is important the IFS monitors actual values and updates the background fields accordingly.  Any discrepancy will cause errors in the forecast as several physical properties of snow influence:

Model variables of snow need to be reanalysed at each analysis cycle.  These are:

Snowfields are initialized every day at 00UTC from continuous offline data.  

Snow data assimilation at ECMWF relies on:

Incorrect analyses and forecasts of snow are possible:

At high levels (altitudes >1500m) IMS data is not used and observations of snow depth are sparse or non-existent.  In these cases snow depth prediction depends only upon the short range IFS evolution.  Thus there can be little or no decrease in snow water equivalent (if it remains cold enough), though an increase after further forecast or actual snowfalls.   Snow depths may also reduce because the density of the snow tends to increase with time through compaction in the model (and also in reality).  Snow depths in such regions rise in response to forecast snowfall but may not decrease sufficiently at other times (See example in Fig2.1.12D).

Lake ice and sea ice do not have snow cover in the model.      

Fig1D:. Weather station at Røldalsfjellet (Norway).  The temperature sensor is mounted at 5m above the ground (left picture) to allow sufficient clearance beneath the sensor with high snow accumulation (right picture). Photos:MET Norway.


 

Fig2.1.12A: Snow depth (cm) and sea-ice cover (%) in the high resolution forecast (HRES).  DT 12UTC 07 Feb 2023 T+00.  Note frozen lakes (e.g. NW Russia, north Caspian Sea, Uzbekistan) are also plotted as "sea ice".  FLake represents or generates ice on coastal or inland  water.  


Fig2.1.12B: Conversion of background and forecast snow water equivalents to snow cover.  Forecast snow water equivalents of 10cm or greater are considered as associated with full cover of snow on the ground; snow water equivalent of 5cm is considered to be associated with half cover.


Fig2.1.12C: Conversion of IMS information into an estimate of snow water equivalent for data assimilation.   IMS delivers binary information on the presence of snow for each grid cell but does not give information on snow depth.

IMS strongly impacts upon any updates to the background snow depth field.  Only if both IMS and background fields indicate snow is the IMS information not used.


Fig2.1.12D: Forecast snow water equivalent at high level stations (blue) and low level stations (red) during the winter of 2019/20.

At low levels background fields are updated using IMS data and numerous observations of snow depth.  Forecasts show a gradual decrease in snow water equivalent during a dry period.

At high levels observations are more sparse and IMS data is not used (>1500m).  Background fields rely on earlier snow depth forecasts.  Forecasts show constant snow water equivalent during a dry period.


Considerations interpreting snow forecast information

Users should be aware of possible impacts on model forecasts, especially where snow cover and associated colder surface temperatures may persist for longer than they should and influence other parameters too.

Additional sources of information

(Note: In older material there may be references to issues that have subsequently been addressed)