  Forecasting of future snow depths is useful for many applications like road
safety, winter sport activities, avalanche risk assessment and hydrology.
Motivated by the lack of statistical forecasts models for snow depth, in this
paper we present a set of models to fill this gap. First, we present a model to
do short term forecasts when we assume that reliable weather forecasts of air
temperature and precipitation are available. The covariates are included
nonlinearly into the model following basic physical principles of snowfall,
snow aging and melting. Due to the large set of observations with snow depth
equal to zero, we use a zero-inflated gamma regression model, which is commonly
used to similar applications like precipitation. We also do long term forecasts
of snow depth and much further than traditional weather forecasts for
temperature and precipitation. The long-term forecasts are based on fitting
models to historic time series of precipitation, temperature and snow depth. We
fit the models to data from three locations in Norway with different climatic
properties. Forecasting five days into the future, the results showed that,
given reliable weather forecasts of temperature and precipitation, the forecast
errors in absolute value was between 3 and 7 cm for different locations in
Norway. Forecasting three weeks into the future, the forecast errors were
between 7 and 16 cm.
