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:

  • sensible heat fluxes and latent heat fluxes
  • downward long wave and shortwave radiation
  • upward fluxes of heat through the layer(s) in the snowpack from the underlying ground.

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:

  • exposed snow - for areas without vegetation above the snowpack, and therefore without interference to the weak incoming and outgoing heat and momentum fluxes.
  • forest snow - for areas where there is tree cover sufficient to interfere with incoming and outgoing heat and momentum fluxes.   The heat flux at the snow/atmosphere interface is rather larger than over exposed snow. 

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 Fig2.1.4.4-1, Fig2.1.4.4-2, Fig2.1.4.4-3.

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:

  • thermal coupling across the snow-atmosphere interface and within the thin top snow layer.  This allows a realistic representation of sporadic surface snow melt and is especially important for warmer sites with wet snow.
  • variations in snow density with depth in thick and cold snowpacks.
  • percolation, freezing and melting of water which has an effect upon the transfer, release and absorption of heat in each layer and on the surface.
  • heat fluxes across the snow-soil interface and within the thin bottom snow layer.  This allows a representation of changes in permafrost.   

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:

  • downwards from the atmosphere (e.g. by advection of warmer air,  by insolation, or by underlying an area of warm based cloud). 
  • upwards from lower in the snowpack, though this could be offset by latent heat extraction where melting of snow occurs.

Vertical discretisation over flat terrains:

  • for snow depth <12.5cm only only one snow layer is modelled (Fig2.1.4.4-1).  Note: Partial cover of the 'tile' is assumed if snow depth is less than 10cm. 
  • for snow depth >12.5cm the number of snow layers varies up to a maximum of 5 layers according to the total snow depth (Fig2.1.4.4-2).
  • permanent snow is defined as snow water equivalent >= 10m with 5 snow layers (Fig2.1.4.4-3).

Fig2.1.4.4-1: 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) 

Fig2.1.4.4-2: 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.

Fig2.1.4.4-3: 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

Table2.1.4.4-1: List of symbols for parameters shown in Fig2.1.4.4-1, Fig2.1.4.4-2, Fig2.1.4.4-3.

Vertical discretisation over 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.  The spectral nature of model orography may mean that in rugged mountainous areas, where there are large variations in altitude over short distances, mountain peaks may be under-represented and narrow valleys may not be represented at all.

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 (Fig2.1.4.4-3 and Fig2.1.4.4-4).

Fig2.1.4.4-4: Permanent snow and glacier grid points. These are predominantly in Greenland and other Arctic mountainous island areas.  Permanent snow is located in the Himalayan region. Isolated locations are in the Alpine region, Caucasus mountains and southern Norway.  Many coastal regions of Greenland, Ellesmere Island and Baffin Island have less permanent snow allowing snowmelt and warming of the rock to allow modelling of temperature and precipitation changes. 

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 Fig2.1.4.4-8. 

Fresh snowfall is added to the top layer, with a new snow density depending on air temperature and wind speed.  Both convective and dynamic snowfall is considered to be homogenous over the grid box.  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.  If snow already exists on the ground then freezing rain and ice pellets are accounted for as rainfall that has frozen.

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 liquid water equivalent of snow lying on the ground
  • the average density of the snow layer (typically lower for fresh uncompacted snow, higher for compacted old snow).

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

When snow depth is:

  • < 12.5cm, additional snow is added to the single snow layer.
  • 12.5cm < 27.5cm additional snow is added proportionately to the layers as they are introduced.
  • >27.5cm, only the layer 4 is used as the snow accumulation layer.

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

  • the snow depth is defined as 10m of water equivalent.
  • there is a fixed snow density for all 5 layers.
  • the depth of each of the upper four layers is 0.50m; fresh snowfall is added the bottom layer (i.e. layer 5 is used as an accumulation layer). See Fig2.1.4.4-3.

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

Fresh snow seems to be too dense and compacted in the model.  As a rough rule of thumb:

  • generally 10mm of precipitation approximates to 10cm of snow depth. 
  • for less dense newly fallen snow, 10mm of precipitation approximates to 10-15cm of snow depth.
  • with wind effects the density of snow increases quite quickly, 10mm of precipitation approximates to 7cm of snow depth.  
  • very low negative temperatures are required to considerably decrease the density and increase the equivalent snow depth in cm.

The current snow scheme tends to melt snow too slowly.

Snow cover

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

  • Total snow cover is assumed where snow depth is diagnosed as >10cm.  Only snow or forest snow "tiles" are used by HTESSEL.
  • Partial snow cover is assumed where snow depth is diagnosed as <10cm.  A snow water equivalent of 6cm is considered to be associated with 60% snow cover (Fig2.1.4.4-6).   Other "tiles" which describe the location are used by HTESSEL in addition to the snow or forest snow "tiles".

Snow is not intercepted by a tree canopy and will accumulate on the ground.  Snow does not accumulate on sea ice or lake ice. 

The albedo of snow in forested areas is given by a look-up table depending on (high) vegetation type (Table  The albedo of exposed snow decays with time between 0.85 for fresh white snow to 0.5 for .  It is reset to 0.85 after large snowfall events.

Table2.1.4.4-2: Mean values of Northern Hemisphere five-year (2000-2004)  broad band surface albedo (in the presence of snow) aggregated by high vegetation type.

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:

  • the energy and water exchanges between snow surface and atmosphere.
  • the upward heat flux from the ground into the atmosphere, which in turn influences surface snowmelt and sublimation.
  • the albedo.

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

  • snow temperature,
  • water equivalent of snow,
  • liquid water content.

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

Snow data assimilation at ECMWF relies on:

  • an Optimal Interpolation method which adjusts the model-analysed snow water equivalent and snow density prognostic variables.
  • conventional measurements of snow depth (from SYNOP and other national networks) with additional national snow depth observations, particularly in Europe and North America.  These are generally an important and reliable source of information.  However, snow depth observations from many other regions of the world remain unavailable to IFS.  Thick hoar frost (which can look like a dusting of snow) can be incorrectly reported as very shallow snow.  This can be assimilated by the model despite no supporting evidence from other sources.  
  • snow extent data from the NOAA/NESDIS Interactive Multi-sensor Snow and Ice Mapping System (IMS).  This combines satellite visible and microwave data with weather station reports to give snow cover information and sea ice extent over the northern hemisphere at 4km resolution.  There is some manual intervention and quality control.  The IMS product only shows where at least 50% of the grid cell is covered by snow and is converted to snow depths using relationships shown in  Fig2.1.4.4-7 and Fig2.1.4.4-8.  IMS data is not currently used by the IFS at altitudes above 1500m.

Incorrect analyses and forecasts of snow are possible:

  • in data sparse areas and the representativeness of observations.
  • after a prolonged period without observations.
  • at altitudes above 1500m.
  • near glaciers.  Glaciers are considered as very deep snow rather than ice - this can cause nearby correct observations to be rejected.
  • at some high-latitude grid points in the model it is common for snow depth to be extremely high and may not be assimilated.

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 Fig2.1.4.4-5 and Fig2.1.4.4-9).

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

Fig2.1.4.4-5:. 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.


Fig2.1.4.4-6: 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.  

Fig2.1.4.4-7: 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.

Fig2.1.4.4-8: 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.

  • If the background snow water equivalent is 0cm and IMS shows snow cover then the updated snow water equivalent is set to 5cm.
  • If IMS shows no snow cover then the updated snow water equivalent is set to 0cm.

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.

Fig2.1.4.4-9: 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.

  • High impact considerations

    • Cloud and freezing fog strongly influence the energy fluxes into and from the snowpack.  The IFS may not correctly capture or forecast the extent or thickness of cloud.   It is very important to consider the possible formation, persistence or clearance of cloud and to assess the possible changes in energy transfer between cloud and snowpack.  Thick cloud at any level will reduce solar radiation, but low cloud could be warmer than the underlying snow surface resulting in a net increase in downwards long wave radiation.

    • The characteristics of each grid box and areal extent of each tile type are updated through the forecast period and can vary in a rapid and interactive way.

      • model forecast snowfall might increase the area or depth of snow cover incorrectly.  Partial cover of snow may become full cover as the accumulated model snow depth becomes >10cm.  This means "tiles" in HTESSEL describing land surfaces may incorrectly cease to be used.

      • snow may accumulate then melt (e.g. with rain, or as as a warm front advances over a cold area).

    • Differing snowfall among the ENS members can cause increasing differences in evolution during the remainder of the model forecast period.  Nevertheless each member remains equally probable.

    • The statistical information on the slope and aspect of orography within each grid box (e.g. south-facing, steepness) is not detailed enough for forecasts at an individual location.  This can be important in mountainous areas and HTESSEL may under- or over-estimate solar heating and runoff.  Incorrect analyses and forecasts of snow are quite possible at altitudes above 1500m in data sparse areas, or after a prolonged period without observations.  Forecasts of snow depths can be too great at altitudes above >1500m due to insufficient melting of snow more especially at very high locations (e.g. Tibet).

    • Incorrectly reported shallow snow (say by thick deposition of frost) that has been assimilated can be persistent in the model and give misleading forecasts.
  • Snow temperature considerations

    • Variation in the surface reflectance (snow-albedo) can influence surface heat flux and skin temperatures (by 1°C-4°C).  Fresh (white) snow has high albedo reflecting much of the incoming radiation.  Dirty or older (greyer) snow absorbs more radiation with greater heat flux into the snowpack.  The sun's elevation at high latitudes is limited (and non-existent in winter) which reduces the availability of solar radiation to the snow surface.  
    • Snow surfaces are likely to melt a little more readily in forests as the heat flux at the snow/atmosphere interface is rather larger than with exposed snow.
    • Phase changes can cause a delay in warming during melting or sublimation of snow.  In IFS, airborne snow tends to sublimate much more readily than the undisturbed snow on the ground.
    • If ground surface temperatures are above 0°C, shallow surface snow often takes too long to melt.  This can have an adverse impact on albedo and radiation fluxes.
    • Thermal properties of the snow can cause heat and moisture transfers to be effectively de-coupled.  Snow, especially new dry snow, is a good thermal insulator.
    • Snow depths may reduce gradually because the density of the snow has increased through compaction in the model (and also in reality) as the days progress.
    • Forest snow night time temperatures fall too low.  Even if the forest is dominant, the vertical interpolation to evaluate T2m is done as for an exposed snow tile (because verifying SYNOP stations are always in a clearing).  In reality, forest generated turbulence maintains turbulent exchange over the clearing and prevents extreme cooling.

    • Forecast 2m temperatures over deep snow:
      • have good agreement with observations between −15°C and 0°C.
      • tend to be too warm by around 3-5°C compared to observations when T2m <-15°C.   Large night time errors of forecast temperatures, even by as much as 10°C too warm, are more likely under clear skies, even when this has been correctly simulated by the model. 
      • have a relatively constant cold bias during the day of ~1.5°C compared to observations.
      • the amplitude of the forecast diurnal cycle of T2m underestimates the amplitude of the observed diurnal cycle by between ~10% to 30%.  Forecast minima tend to be warmer and daytime maxima colder than observations. 
      • verification of temperatures can be difficult.  This is due to variations in the height that temperature observations are made.  Some countries and locations:
        • maintain the sensors 2m above the snow surface, adjusted after every fall of snow.
        • have sensors higher than 2m above the ground to ensure measurement of air temperature throughout the year even after large accumulations of snow.  High snow depths in late winter mean a short distance between snow surface and the sensor, while the sensor will be in a greater distance than usual to the ground surface during the warm period of the year.  See Fig2.1.4.4-5. 
  • Snow depth and coverage considerations

    • The smooth nature of the snow surface can cause momentum fluxes to be decoupled and winds increase in the absence of friction.  
    • Strong winds can alter snow depth and snow compaction.  Transport of snow can bring areas of drifting with snow compaction and associated increase in density.  This can be particularly effective for polar snow, where snow temperature is extremely low throughout the winter and compaction due to other processes is limited.  Conversely, strong winds can carry away dry surface snow and reduce snow depth in exposed areas.  The user should consider this effect in periods of strong winds or in generally windy regions.
    • Bias in snow depths:
      • Short-range snow depth forecasts, when compared with independent observations, on average show high quality but with a slight overestimation of snow depth in the background and analysis fields.
      • There is a tendency towards underestimation of snow depth in central Eurasia implying either melting or compaction is overestimated for these forested areas.
  • Ice

    • There is no representation or forecast of snow on sea ice, lake ice or glaciers.  If considering ice cover and thickness, thin sea ice or lake ice that is covered by thin snow grows or melts much faster than does thick ice with deep snow.

Additional sources of information

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