  | 
      | 
      | 
      | 
      | 
      | 
      | 
      | 
      | 
      | 
      | 
      | 
   
   
    There are four steps to assimilate SWE observation at a given
    time step: 
     | 
     | 
   
   
     | 
   
   
    (1)
    Forecasting step:
    the SWE states evolve nonlinearly 
    according to model 
     | 
   
   
    dynamics; its
    covariances are propagated linearly with time. 
     | 
     | 
   
   
     | 
   
   
    (2)
    Updating step: the SWE of each
    layer is updated using the Kalman filter 
     | 
     | 
   
   
    equations. 
     | 
     | 
   
   
     | 
   
   
    (3)
    Analysis step:
    Snow depth and heat content are calculated using SWE, 
     | 
     | 
   
   
    snow density and
    snow temperature. When the model predicts no snow and 
     | 
     | 
   
   
    the updated SWE
    being non-zero, snow density is 150 km/g3 and the air 
     | 
     | 
   
   
    temperature at 2
    m  is assigned to snow temperature.
    Otherwise, snow 
     | 
     | 
   
   
    density and
    temperature predicted by model are used. 
     | 
     | 
   
   
     | 
   
   
    (4) Repartition step: At this step, the total snow depth is
    evaluated and the 
     | 
     | 
   
   
    thickness of each
    layer is reassigned to ensure a layer 1 thickness of 5 cm. 
     | 
     | 
   
   
    The SWE and heat
    content are calculated accordingly. 
     | 
     |