109
consists of dividing at each time step the total snow depth H sn in a pre-selected number
of layers N sn . The depth of the t.op layer h~n is assumed to be constant and the depth of
the remaining layers is given by
(55)
In this way, the depth of the layers varies wit.h time depending on Hsn. Hsn is calculated
from Eq. (53) and the temperature of the snow layers is calculated from a vertical diffusion
equation similar to Eq. (25) forced at the top by t.he net energy flux (r.h.s. of Eq. (54))
and at thc bottom by the conductive energy flux between snow and underlying soil.
When at a given layer the snow temperature goes above the melting point., snow melt is
calculated as the amount of melted snow necessary to bring the temperature of the layer
back to aoc.
This model also requires calculation of a fractional snow cover isn' which is calculated
by assuming a minimum total snow depth of (N sn x h;~), i.e. Isn = min[l., H.m/Nsnh;nl.
When isn is less than 1, H sn is set. to N sn x h;n. 'When it is snowing, t.he quantity
6.
_ Psn6.t
isn - N hi
Srt sn
(56)
is appended to the side of existing snow at each t.ime step 6.( When t.he fractional
snow cover is equal to 1, further snow is accumulat.ed on top of exist.ing one. Different
calculations of fractional snow cover as a function of snow depth and surface characteristics
can also be found in other schemes (e.g Dickinson et al. 1993). Snow density is mostly
assumed constant, except for a few schemes which include a snow density prognostic
equation based on self-loading densification (e.g. Pitman et al. 1991). Snow albedo is
assumed to either be constant or a function of snow age (Dickinson et al. 1993) and snow
granular structure (Pitman et al. 1991).
3.2.4. Surface runoff sub-component
Surface runoff Rn is one aspect of present ESEMs which is still highly parameterized in
ways not very dissimilar from those of early bucket models. This is mostly because of the
complexity of the surface runoff process, which depends critically on t.he forcing climate,
terrain morphology and soil water movement within t.he soil. Therefore, many ESEMs
still treat surface runoff essentially as a residual t.erm necessary t.o balance the water
budget. A typical example of the crudeness of the runoff parameterization in ESEMs
used for climate studies is t.hat of HATS, in which the runoff rate is simply assumed to
be proportional to the rainfall t·snowmelt rate times a power function of the soil water
content relative to saturation.
Only recently, more elaborate representations of the surface runoff process, based more
firmly on surface hydrologic principles, have been included in ESEMs. A representative
consists of dividing at each time step the total snow depth H sn in a pre-selected number
of layers N sn . The depth of the t.op layer h~n is assumed to be constant and the depth of
the remaining layers is given by
(55)
In this way, the depth of the layers varies wit.h time depending on Hsn. Hsn is calculated
from Eq. (53) and the temperature of the snow layers is calculated from a vertical diffusion
equation similar to Eq. (25) forced at the top by t.he net energy flux (r.h.s. of Eq. (54))
and at thc bottom by the conductive energy flux between snow and underlying soil.
When at a given layer the snow temperature goes above the melting point., snow melt is
calculated as the amount of melted snow necessary to bring the temperature of the layer
back to aoc.
This model also requires calculation of a fractional snow cover isn' which is calculated
by assuming a minimum total snow depth of (N sn x h;~), i.e. Isn = min[l., H.m/Nsnh;nl.
When isn is less than 1, H sn is set. to N sn x h;n. 'When it is snowing, t.he quantity
6.
_ Psn6.t
isn - N hi
Srt sn
(56)
is appended to the side of existing snow at each t.ime step 6.( When t.he fractional
snow cover is equal to 1, further snow is accumulat.ed on top of exist.ing one. Different
calculations of fractional snow cover as a function of snow depth and surface characteristics
can also be found in other schemes (e.g Dickinson et al. 1993). Snow density is mostly
assumed constant, except for a few schemes which include a snow density prognostic
equation based on self-loading densification (e.g. Pitman et al. 1991). Snow albedo is
assumed to either be constant or a function of snow age (Dickinson et al. 1993) and snow
granular structure (Pitman et al. 1991).
3.2.4. Surface runoff sub-component
Surface runoff Rn is one aspect of present ESEMs which is still highly parameterized in
ways not very dissimilar from those of early bucket models. This is mostly because of the
complexity of the surface runoff process, which depends critically on t.he forcing climate,
terrain morphology and soil water movement within t.he soil. Therefore, many ESEMs
still treat surface runoff essentially as a residual t.erm necessary t.o balance the water
budget. A typical example of the crudeness of the runoff parameterization in ESEMs
used for climate studies is t.hat of HATS, in which the runoff rate is simply assumed to
be proportional to the rainfall t·snowmelt rate times a power function of the soil water
content relative to saturation.
Only recently, more elaborate representations of the surface runoff process, based more
firmly on surface hydrologic principles, have been included in ESEMs. A representative