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:

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 Figs1.

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:

Over flat terrains:

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 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.  At snow depths between 12.5cm and 27.5cm additional snow is added proportionately to the layers as they are introduced.  Where the snow depth is >27.5cm, only the layer 4 is used as the snow accumulation layer.



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.



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. 

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 analysis and forecast of snow depth, snow compaction and snow cover are important.  They affect all IFS atmospheric forecast models and several physical properties of snow control the energy and water exchanges between snow surface and atmosphere.

Snowfields are initialized every day at 00UTC from continuous offline data.  Snow temperature, water equivalent of snow, and liquid water content are prognostic variables in IFS and need to be reanalysed at each analysis cycle. 

Snow depth is computed using the liquid water equivalent of snow lying on the ground and the density in the model snow layers.  The snow depth in the model changes when fresh snow falls or when snow on the ground melts, evaporates or is compressed.  At some high-latitude or ‘glacial’ grid points it is common for snow depth to be extremely high.

Snow cover

Depth of snow is diagnosed from the water equivalent of the modelled snow. 

See the section Prognostic variables that affect energy fluxes for more information on snow data and its assimilation into the model.

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)



Fig2.1.xx: Example Surface snow and ice chart.