99
where SH and LH are given by Eqs. (18) and (19) of section 2.1.2. Note that a term
accounting for the exchange with a deeper soil reservoir is not included in Eq. (22), so that
this equation yields realistic average skin temperatures only in the absence of a diurnal
insolation cycle. Eq. (22) is of the form f(Tg) = 0 and was usually solved via NewtonRaphson iterative procedures. The surface hydrologic cycle was not explicitly described,
the specified surface wetness factor f3 (see Eq. (19)) being specified and essentially treated
as a tuning parameter.
Inclusion of the diurnal cycle in AMs required the use of an energy exchange term
with a deeper soil reservoir, since the direct use of Eq. (22) would yield excessively large
diurnal temperature excursions. One of the most efficient and accurate ways of including
this process is the force-restore method originally proposed by Bhumralkar (1975). In
this approach a reservoir temperature Td is introduced and the surface skin temperature
is calculated from the system of equations
(23)
aTd
(Td - Tg)
- = - C 3 [
+c4(Td -Tref )]
(24)
at
Tl
where P.C. is the soil specific capacity, G. is the net surface heating, Tl is the period of
surface heating (i.e. 1 day), d1 is the soil depth influence by diurnal heating (typically of
the order of a few tens of cm), Tref is an annual mean reference temperature and Cl - C4
are constants. Eqs. (23) and (24) express the condition that the surface temperature is
forced by the diurnal surface heating and restores to the reservoir temperature Td, which
in turn restores to the annual mean TreJ. The parameters Cl - C4 can be chosen such
that Tg follows a diurnal cycle and Td follows a seasonal cycle. The force restore method
is rather accurate and highly efficient when compared to more complex soil layer models
(Deardorff 1978), and still today it is used in advanced surface process schemes.
iFrom the viewpoint of surface hydrology, the use of specified surface wetness factors
presents a strong constraint, because it prevents the surface hydrology to reach a dynamical equilibrium with the forcing climate. In particular, this precludes the use of AMs
for simulations of climate and hydrologic regimes different from present and the study of
atmosphere-hydrology feedbacks mechanisms. The simplest model of interactive surface
hydrology was introduced in the late sixties by Manabe et al. (1969) with the concept
of "bucket" model. In this approach it is assumed that the hydrologically active region
of soil can be described as a bucket of given water capacity (e.g. 15-20 cm). The bucket
fills up if precipitation exceeds evaporation and it is depleted if the opposite occurs. The
wetness factor, fl, increases linearly with water content until a critical value is reached
and then it is equal to 1. If the maximum capacity of the bucket is reached, the excess
water is removed as runoff. The empirical basis for the bucket parameterization resides in
where SH and LH are given by Eqs. (18) and (19) of section 2.1.2. Note that a term
accounting for the exchange with a deeper soil reservoir is not included in Eq. (22), so that
this equation yields realistic average skin temperatures only in the absence of a diurnal
insolation cycle. Eq. (22) is of the form f(Tg) = 0 and was usually solved via NewtonRaphson iterative procedures. The surface hydrologic cycle was not explicitly described,
the specified surface wetness factor f3 (see Eq. (19)) being specified and essentially treated
as a tuning parameter.
Inclusion of the diurnal cycle in AMs required the use of an energy exchange term
with a deeper soil reservoir, since the direct use of Eq. (22) would yield excessively large
diurnal temperature excursions. One of the most efficient and accurate ways of including
this process is the force-restore method originally proposed by Bhumralkar (1975). In
this approach a reservoir temperature Td is introduced and the surface skin temperature
is calculated from the system of equations
(23)
aTd
(Td - Tg)
- = - C 3 [
+c4(Td -Tref )]
(24)
at
Tl
where P.C. is the soil specific capacity, G. is the net surface heating, Tl is the period of
surface heating (i.e. 1 day), d1 is the soil depth influence by diurnal heating (typically of
the order of a few tens of cm), Tref is an annual mean reference temperature and Cl - C4
are constants. Eqs. (23) and (24) express the condition that the surface temperature is
forced by the diurnal surface heating and restores to the reservoir temperature Td, which
in turn restores to the annual mean TreJ. The parameters Cl - C4 can be chosen such
that Tg follows a diurnal cycle and Td follows a seasonal cycle. The force restore method
is rather accurate and highly efficient when compared to more complex soil layer models
(Deardorff 1978), and still today it is used in advanced surface process schemes.
iFrom the viewpoint of surface hydrology, the use of specified surface wetness factors
presents a strong constraint, because it prevents the surface hydrology to reach a dynamical equilibrium with the forcing climate. In particular, this precludes the use of AMs
for simulations of climate and hydrologic regimes different from present and the study of
atmosphere-hydrology feedbacks mechanisms. The simplest model of interactive surface
hydrology was introduced in the late sixties by Manabe et al. (1969) with the concept
of "bucket" model. In this approach it is assumed that the hydrologically active region
of soil can be described as a bucket of given water capacity (e.g. 15-20 cm). The bucket
fills up if precipitation exceeds evaporation and it is depleted if the opposite occurs. The
wetness factor, fl, increases linearly with water content until a critical value is reached
and then it is equal to 1. If the maximum capacity of the bucket is reached, the excess
water is removed as runoff. The empirical basis for the bucket parameterization resides in