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**Basic Structure**

Atmospheric GCMs solve the three-dimensional, time-dependent equations for the rates of change of surface pressure, wind components, temperature, and moisture content, taking account of sources and sinks of heat, moisture, and momentum. These equations are usually expressed either in finite-difference form for a three-dimensional array of points or in spectral form in each layer of the model. Whichever form is used, the source and sink terms, representing the physical parametrizations, are calculated at grid points. As the land surface processes, which are central to this review, are part of these, the distinction between spectral and finite-difference models need not concern us further. The basic equations with the source and sink terms on the right-hand side may be written:

(1)

Here t , H. E are the vertical fluxes (positive
upward) of momentum, heat, and moisture due to vertical
subgrid-scale eddies (turbulence and convection), R. is the net
downward radiative flux, P is the precipitation or net sink of
moisture, and a is the vertical coordinate, being p/r _{*},
or pressure normalized by surface pressure r _{*}.
Other notation is conventional as given in the list of symbols.

**Fluxes at the Land-Atmosphere Interface**

The land surface affects the
atmosphere through the fluxes R_{N}, t , H. and E at
the bottom boundary (s = 1) of the atmospheric model. The
treatment of these fluxes in GCMs has been reviewed by Carson
(1982). Though an attempt to emulate Carson's review would be too
lengthy for the present purpose and an unnecessary duplication, a
summary of the present state of the art may be useful, especially
as some information not available to Carson can be included. In
this section, we shall first present and discuss the basic
formulation for each of the fluxes and then summarize the
parametrizations in the main GCMs in current use, as known to the
reviewer. These models are listed in table 1. Some models for
which no new information is available are omitted here. These
include the Australian Numerical Meteorology Research Centre
model, now adopted, with some changes, as the NCAR (National
Centre for Atmospheric Research) "Community Climate
Model," and the Oregon State University (OSU), Siberian
Academy of Sciences Computing Centre, and Main Geophysical
Observatory models. These have only low vertical resolution and
cannot be expected to give a realistic representation of the
near-surface processes important in assessing the response to
surface perturbations. However, brief descriptions of the OSU
model and also the ECMWF (European Centre for Medium Range
Weather Forecasting) forecast model are at the end of this paper.

*Radiative Fluxes*. (A)
Basic formulations. The net downward radiative flux at the land
surface

(2)

where is the emissivity or absorptivity of the surface for radiation of wavelength and and B(l ) represent the downward and black body fluxes at wavelength lambda. However, in atmospheric radiative transfer, we are concerned mainly with two principal streams of radiation, solar radiation at l = 0.2µm-4µm and terrestrial radiation at l = 3µm-100µm (these wavebands contain over 99% of the radiation from each source). It is therefore convenient to make the twostream approximation and write:

(3)

where s _{s} is Stefan's constant and T_{0}
the surface temperature (degrees Kelvin). R_{s}(0) is the
downward solar radiation and a _{*} R_{s}(0) is the
reflected solar flux. Note that a _{*}, the albedo, is not a
constant for a given surface but depends on the spectral
distribution of the incoming solar radiation, which will depend
on atmospheric constituents, including cloud, and on the zenith
angle of the sun. Thus, formally

(4)

Similarly, the emissivities for terrestrial radiation are means over the appropriate range of wavelengths weighted by the intensity at each wavelength. For the downward flux, this is again dependent on the atmospheric structure (temperature, humidity, and cloud), whilst for the upward radiation it is, for given surface conditions, dependent only on the surface temperature because of the Planck function's temperature dependence.

**TABLE 1. GCM models**

Label |
Centre |
Vertical resolution |
Horizontal
representation |
Reference |

AES | Atmospheric Environment Service, Downsview, Ontario, Canada | 5-layer | Spectral 20 wave rhomboidal | Boer and McFarlane 1979 |

EERM | l'Etablissement d'Etudeset de Recherches Météorolo- giques, Toulouse, France | 10-layer | Spectral 10-13 waves trapezoidal | Royer et al. 1981 |

GFDL | Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey, USA | 9-layer (also 11 and 18) | Spectral 15, 21, or 30 waves rhomboidal (also gridpoint versions) | Manabe et al. 1979 |

GISS | Goddard Institute for Space Studies, New York, New York, USA | 9-layer | Grid point 4° latitude x 5° longitude (also 8° x 10°, 12° x 15°) | Hansen et al. 1983 |

GLAS | Goddard Laboratory for Atmospheric Sciences, Greenbelt, Maryland, USA | 9-layer | Grid point 4° latitude x 5° longitude | Randall 1983a |

LMD | Laboratoire de Meteorologie Dynamique, Paris, France | 11-layer | Grid point 5.6° east-west 50 point pole-pole (cost coordinate) | Sadourny 1983 |

MO | Meteorological Office, Bracknell, England | 11-layer | Grid point 2.5° latitude x 3.75° longitude | Mitchell and Bolton 1983 |

NCAR | National Center for Atmospheric Research, Boulder, Colorado, USA | 9-layer | Spectral 15 waves rhomboidal | Pitcher et al. 1983 |

^{a}Randall describes two
versions of the GLAS model, referred to in this paper as GLAS
1980 and GLAS 1982.

(B) Surface albedo in GCMs. We
shall discuss here only the snow-free albedo; snow cover is
allowed to increase the albedo in all the GCMs except that the
LMD model prescribes a geographical variation taking account of
the climatological snow cover. For snow-free albedo, many models,
including the AES, GFDL, GLAS, and NCAR models, use the
geographical distribution specified by Posey and Clapp (1964),
who specified a low albedo (0.07) for tropical forests. As
discussed by Rowntree (1975) and Dickinson (1980), this is due to
the use of a visible albedo, but there is a strong spectral
variation with much larger values for infrared wavelengths, and
the mean value for the whole spectrum is about 0.125. Other
geographical distributions, used in the LMD model due to Bartman
(1981) and the ECMWF model due to Preuss and Geleyn (1980), using
satellite data, also have values below 0.1 over parts of the
tropical continents. Probably the most satisfactory treatment is
that in the GISS model, with a detailed specification of albedos
for eight land surface types as classified by Matthews (1983). It
allows for seasonal variation and separate values for the visible
and nearinfrared. The desert albedo has a moisture dependence
that can halve the albedo to 0.175 for a moist surface.
Relatively simple formulations are used in the EERM model, with a _{*}
= 0.31-0.17 h_{u} where h_{u} is a non-linear
function of soil moisture content, and in the MO model, with a. =
0.2, though a vegetation-dependent variation due to M. F. Wilson
(personal communication) has recently been tested in the latter.

(C) Surface emissivity in GCMs. Generally a value of 1.0 has been used for emissivity in GCMs. However, the model II of GISS (Hansen et al. 1983) uses realistic emissivities for deserts, snow, and ice. The NCAR model uses values less than unity at 812 µm; the EERM model uses 0.95.

*Surface Turbulent Fluxes*.
(A) Basic formulations. The turbulent fluxes at the surface may
be formally written

(5)

Here the formal definition of the
flux of a quantity X is given first as , where the primes (') indicate deviations
from a time-mean, then the formulation commonly used in GCMs , with C_{x}
being a turbulent transfer coefficient depending on surface
roughness and atmospheric stability; ro and are near-surface
density and windspeed and OX is an estimate of the excess of a
surface value X_{0} over the nearsurface atmospheric
value is
generally taken as zero.

The right-hand terms in equation
5 for heat and moisture transfer are alternative expressions for
the fluxes in resistance form. For heat this combines an
atmospheric resistance r_{H} and the temperature gradient
d q ; setting q _{0}
at the surface temperature is observed to give reasonable
estimates. With a wet surface such as a lake, the same is true of
the moisture flux with the same, purely atmospheric, resistance r_{E}
and with q_{0} = q_{sat} (T_{0}), the
saturation specific humidity at the surface temperature. However,
for moisture transfer over land there is often an additional
surface resistance due to the vegetation's stomata! resistance to
transfer from moist surfaces within the leaf. This resistance is
very large in arid regions and also at certain times in other
regions (e.g. at night).

(B) GCM specifications of
transfer coefficients. As discussed by Carson (1982), there is a
wide range of complexity in the specifications of transfer
coefficients. The GFDL and AES models use very simple forms (C_{D}
= C_{H} = C_{E} = 2 and 3 x 10^{-3}
respectively) and do not distinguish between land and sea;
similarly simple roughness and stability dependent formulations
are used in the EERM, GISS, and MO models. Intermediate,
relatively simple forms that depend only on surface type (land or
sea) and windspeed are used in the NCAR and LMD models. The
roughness lengths (z_{0}) used in the MO and EERM models
over land are fixed (10 and 16 cm respectively), whilst in the
GISS model they depend not only on the vegetation type but also
on the orographic roughness.

(C) GCM specifications of
near-surface variables. The models may be divided into two groups
by their specifications of the near-surface values of V_{s}.
q _{s},
q_{s}. The simplest approach of taking the values for the
lowest model level is used in the GFDL, NCAR, and MO models; for
all of these this level is at 70-100 metres above the surface (s = .987-.991).

Values for the EERM model's lowest level (s = .95) are also used directly, except that the wind is turned through an angle dependent on thermal stability, wind speed, and Coriolis parameter. Some such turning is probably beneficial to the accuracy of the surface stress computation even with the lowest level at nearly 100 m. Hansen et al. (1983) found that with realistic cross-isobar angles of surface flow, the ITCZ was sharpened, with decreased rainfall over the southern Sahara and increased Hadley cell mass flux.

Apart from the Randall (GLAS
1982) version of the GLAS model (see Randall 1982), the other
models (GLAS 1980, AES, GISS) derive the near-surface values of q_{s},
and tetas by assuming that the surface flux (eqn. 5) equals a
diffusive flux, which, for specific humidity q_{s} is of
the form , with K
a stability dependent diffusion coefficient and expressed as the
gradient between q_{s} and the value for the lowest
level. One might expect the form for temperature to be , but for the AES model
it is with c =
5° C km^{-1}, whilst for the GISS model it is said to be
. In the AES model
V_{s} is also obtained by flux continuity, while in the
GLAS 1980 and earlier GISS models, downward extrapolation is
used. In the latest GISS model, an Ekman formulation is used with
explicit allowance for turning of the wind as discussed above. In
middle latitudes this formulation gave increased eddy kinetic
energies with warming of high latitudes.

(D) GCM specifications of surface
variables. The surface temperature T_{0} derived from the
subsurface thermal parametrization discussed in the next section,
is used for q _{c} in all the models. The
limitation of evaporation in arid conditions is usually allowed
for by calculating a potential evaporation E_{p} from
equation (5c) with q_{0} = q_{sat}(T_{0})
and obtaining the actual evaporation E from

(6)

with b a function of W the normalized soil
moisture content W = (m/m_{crit}), where m is the soil
moisture content for the top soil layer, and mcrit the lowest m
for which E = E_{p}, and b = 1 for W>1. The calculation of m is
discussed under (B) in Subsurface Processes. In the GFDL, MO,
LMD, GISS, and AES models b = W, whilst in the EERM model, a weighted
combination of two calculations of E is used, the weights
depending on the vegetative cover such that with full vegetation
cover b = h_{u} = 0.9 W^{2}
(3-2W). In the NCAR model, b is set to a constant value (0.25). The
linear formulation (b = W) has been criticized by Mintz
(personal communication) because in arid conditions it gives an
excessive value for E_{p}. To appreciate the problem, it
is instructive to consider an alternative formulation of
evaporation, that using the PenmanMonteith equation (e.g.
Monteith 1973). Equation is written in the resistance form

(7)

Here r_{aE} is the
atmospheric resistance and r_{s} is the surface
resistance (for water vapour).

Because of the difficulty of
observing T_{0}, it is desirable to eliminate it from
equation (7). In the Penman-Monteith approach, this is achieved
by using the surface energy balance:

(8)

where d T = T_{0} - T(z_{e}), G
is downward heat flux into the soil, and r_{aH} is an
atmospheric heat resistance analogous to r_{aE}.

By defining

so that d T (and so T_{0}) can be
eliminated to give the Penman-Monteith equation:

Priestley and Taylor (1972) analysed observations of drying surfaces using equation (9) and obtained a formulation like (6). However, it differs from (6) because their estimate of the potential evaporation in

(10)

depends only weakly on T_{0}
and hence on soil moisture. In contrast, in GCMs T_{0},
and hence qsat (T_{0}) and so also E_{ps}, all
increase rapidly as the soil dries, so (6), as used in GCMs, is
not consistent with observations. One solution to this problem,
as proposed by Mintz and Serafini (1981) and used in the 1982
version of the GLAS model, is to use a separate wet surface
energy balance to compute the surface temperature needed for the
calculation of E_{p}. Randall (1983) used b = 1 - exp ( -
6.8 W) with this formulation. Randall reports that this
formulation gave a considerable reduction in evaporation over
subtropical deserts. In the GCM experiments with the 1982 GLAS
model, the ground wetness data were based on climatology instead
of depending on modelled precipitation and evaporation.

An alternative solution to Mintz
and Serafini's may be to introduce the surface resistance r_{s}
explicitly in equation (5c). In one practical application of this
approach with observed data, Thompson, Barrie, and Ayles (1982)
allow r_{s} to depend on the minimum stomatal resistance,
leaf area index, and available water capacity of different types
of vegetation as well as on soil moisture. Evaporation of
precipitation intercepted by vegetation is included. An approach
of this kind could be used in a GCM. It would allow incorporation
of geographical distributions of vegetation characteristics and
soil types and the use of multilayer soil models.

*Subsurface Processes. *(A)
Basic formulations. To specify the surface temperature and soil
moisture variables needed for calculating the surface turbulent
fluxes, some representation of subsurface processes is needed.
For a layer of ground between depths z and z + d z, neglecting
horizontal subsurface transfers of heat and water, and defining
z, G, and the water flux M as positive downward

(11)

(12)

where m is the soil water
content, Q_{g} and N are source and sink terms. For the
heat budget (11), the only significant heat sources are due to
moisture phase changes. In the moisture budget (12), provided we
consider m (and M) to refer to the sum of water vapour and liquid
water contents (and flux), there are no sources and sinks except
those associated with melting and freezing. With this definition,
the "surface" is strictly the interface between
vegetation and air and it is there that the surface boundary
condition

(13)

applies. The terms in parentheses
represent the net contribution of surface and atmospheric
processes (rainfall P_{R} and snowmelt M_{S} less
surface runoff Y(0)) to the downward water flux in the soil,
whilst E(0) is the evapotranspiration, which may be partly a sink
at the soil surface but in the presence of vegetation also takes
water out of the soil throughout the root zone and transfers it
to the atmosphere throughout the canopy. For GCMs, with a lowest
layer of order 100 m in depth, it is probably unnecessary to
apply the boundary condition for the atmospheric model so as to
allow for this. However, the distribution of the sink in the soil
needs to be taken into account by allowing direct transfer of
water to the atmosphere from layers throughout the root zone.

With heat fluxes the heat capacity of the vegetation is probably small enough to justify use of

(14)

as the surface boundary condition.

The treatment of the subsurface moisture fluxes is discussed in the paper by Dooge chap 7). The subsurface heat flux G(z) can be represented by a diffusive term of form

(15)

Typical values of the heat capacity C and conductivity lambdag are given by Geiger (1965); both depend markedly on moisture content so that changes in moisture content due to changes in vegetation or climate can affect G(0). In the tropics G(0) is generally small on seasonal time scales but its diurnal variation can be large for dry surfaces.

(B) GCM treatments of subsurface
hydrological processes. Most models represent subsurface water
content, generally called soil moisture, by a single variable
that is updated according to equation (13), with surface runoff
generally represented by limiting the soil moisture to a maximum
value (field capacity), generally 100 to 200 kg m^{-2}.
Exceptions to this are the NCAR model (no surface hydrology) and
the GLAS and GISS models, with more elaborate parametrizations.

The GISS model has two layers
whose water capacities depend on the vegetation characteristics,
with diffusion between the layers. During development of the
model the upward diffusion coefficient was made infinite during
the mid-latitude growing season and all the year in lower
latitudes (except deserts) to represent the ready accessibility
of water in the deeper soil to vegetation. Together with more
rapid downward diffusion of water to the lower layer, this change
delayed the limitation of evaporation due to soil dryness by
about two months. Runoff is allowed before field capacity is
reached, with runoff taken as 0.5 WP_{R}. The model was
quite sensitive to variations in the coefficient; doubling it to
unity reduced summer continental temperatures by 7-8 K and
increased global mean runoff by 70 mm y^{-1}.

The 1980 version of the GLAS model treats soil moisture in a way similar to other models but allows runoff of a fraction of the precipitation, this fraction being a nonlinear function of the soil moisture deficit (see Carson 1982).

(C) GCM treatments of subsurface
thermal processes. The treatment of subsurface thermal processes
in GCMs may be conveniently described in terms of a thermal
capacity C. equal to p_{g}CD as obtained by vertical
integration of equation (11) through a depth D. For the GFDL and
NCAR models, C_{*} = 0, so that the substantial diurnal
variation of heat storage cannot be represented. Most other
models (see Carson 1982 for more details) use a value of C_{*}
roughly appropriate for the diurnal variation of surface
temperature by taking , where is the e-folding depth of the diurnal temperature
wave (v _{0} = 2p per day). In
the MO model, D = d is used, which, with a typical value of C_{*}
gives C_{*} ~ 21 J cm^{-2} K^{-1}. The
LMD model uses C_{*} ~ 18 J cm^{-2} K^{-1},
whilst in the AES model, l _{g} and C are specified
functions of soil moisture.

Two of the models (EERM and GISS) use two layer treatments with thermal capacity (and also conductivity in the GISS model) dependent on soil moisture. These two-layer treatments allow representation of the seasonal cycle of soil heat flux, though this is unlikely to affect simulations significantly in the tropics.