United Kingdom Meteorological Office: Model UKMO
HadAM1 (2.5x3.75 L19) 1993
Dr. Vicky Pope, Hadley Centre for Climate Prediction and Research, United
Kingdom Meteorological Office, London Road, Bracknell, Berkshire RG12 2SY,
United Kingdom; Phone: +44-1344-854655; Fax: +44-1344-854898; e-mail: firstname.lastname@example.org;
World Wide Web URL: http://www.met-office.gov.uk
UKMO HadAM1 (2.5x3.75 L19) 1993
The UKMO HadAM1 model is the first of a line of Unified Models (UM)
intended to provide a common framework for forecasting and climate applications
(cf. Cullen 1993 ). The dynamical formulations
are those described by Bell and Dickinson (1987) ;
the physical parameterizations are substantially modified from those of
an earlier UKMO model documented by Slingo (1985)
Cullen (1993)  gives an overview
of the UKMO Unified Model. Key documentation of different model features
is provided by Cullen (1991) , Cullen
et al. (1991) , Ingram (1993)
, Gregory (1990) , Gregory and
Smith (1990) , Smith (1990a
 , b ), Smith(1993)
, Smith and Gregory (1990) ,
Wilson (1989) , and Wilson and Swinbank
Fourth-order finite differences on a B-grid (cf. Arakawa and Lamb 1977
, Bell and Dickinson 1987 )
in spherical polar coordinates. Mass-weighted linear quantities are conserved,
and second moments of advected quantities are conserved under nondivergent
2.5 x 3.75-degree latitude-longitude grid.
Surface to about 5 hPa; for a surface pressure of 1000 hPa, the lowest
atmospheric level is at about 997 hPa.
Finite differences in hybrid sigma-pressure coordinates after Simmons
and Strüfing (1981) . Mass and
mass-weighted potential temperature and moisture are conserved. See also
There are 19 unevenly spaced hybrid levels. For a surface pressure of
1000 hPa, 4 levels are below 800 hPa and 7 levels are above 200 hPa.
The AMIP simulation was run on a Cray Y/MP computer using two processors
in a UNICOS environment.
For the AMIP experiment, about 4.7 minutes Cray Y/MP computation time
per simulated day (about half this time being associated with output postprocessing).
For the AMIP experiment, the model atmosphere, soil moisture, and snow
cover/depth were initialized for 1 December 1978 from a previous model
simulation. Snow mass for areas of permanent land ice was initially set
to 5 x 10^4 kg/(m^2). The model was then integrated forward to the nominal
AMIP start date of 1 January 1979.
Time Integration Scheme(s)
Time integration proceeds mainly by a split-explicit scheme, where the
solution procedure is split into "adjustment" and "advection"
phases. In the adjustment phase, a forward-backward scheme that is second-order
accurate in space and time is applied. The pressure, temperature, and wind
fields are updated using the pressure gradient, the main part of the Coriolis
terms, and the vertical advection of potential temperature. In the advective
phase, a two-step Heun scheme is applied. A time step of 30 minutes (including
a 10-minute adjustment step) is used for integration of dynamics and physics,
except for full calculation of shortwave/longwave radiation once every
3 hours. In addition, an implicit scheme is used to compute turbulent vertical
fluxes of momentum, heat, and moisture in the planetary boundary layer
(PBL). Cf. Cullen et al. (1991) for
further details. See also Diffusion,
Planetary Boundary Layer, and Surface
To prevent numerical instability, the orography is smoothed in high
latitudes (see Orography), and Fourier
filtering is applied to mass-weighted velocity and to increments of potential
temperature and total moisture. Negative values of atmospheric moisture
are removed by summing the mass-weighted positive values in each horizontal
layer, and rescaling them to ensure global moisture conservation after
the negative values are reset to zero.
For the AMIP simulation, the model history is written once every 6 hours.
(All average quantities in the AMIP monthly-mean standard output data are
computed from samples taken at every 30-minute time step.)
Primitive-equation dynamics, formulated to ensure approximate energy
conservation, are expressed in terms of u and v winds, liquid/ice water
potential temperature, total water, and surface pressure (cf. White and
Bromley 1988 ).
- Linear conservative horizontal diffusion is applied at fourth-order
(del^4) to moisture, and at sixth-order (del^6) to winds and to liquid
water potential temperature (cf. Cullen et al. 1991).
- Stability-dependent, second-order vertical diffusion of momentum and
of conserved cloud thermodynamic and water content variables (to include
the effects of cloud-water phase changes on turbulent mixing), operates
only in the PBL. The diffusion coefficients are functions of the vertical
wind shear (following mixing-length theory), as well as surface roughness
length and a bulk Richardson number that includes buoyancy parameters for
the cloud-conserved quantities (cf. Smith 1990b
). See also Cloud Formation,
Planetary Boundary Layer, and Surface
The parameterization of orographic gravity-wave drag follows a modified
Palmer et al. (1986)  scheme, as
described by Wilson and Swinbank (1989) .
The drag is given by the vertical divergence of the wave stress. Near the
surface, the stress is equal to the product of a representative mountain
wave number, the square of the wave amplitude (taken to be the subgrid-scale
orographic variance--see Orography),
and the density, wind, and Brunt-Vaisalla frequency evaluated in near-surface
layers. At higher levels, the stress is given by this surface value weighted
by the projection of the local wind on the surface wind. If this projection
goes to zero, the stress is also zero; otherwise, if the minimum Richardson
number falls below 0.25, the gravity wave is assumed to break. Above this
critical level, the wave is maintained at marginal stability, and a corresponding
saturation amplitude is used to compute the stress.
The solar constant is the AMIP-prescribed value of 1365 W/(m^2). Both
seasonal and diurnal cycles in solar forcing are simulated. The seasonal
cycle of solar insolation is based on a 360-day year (each month 30 days
in length), with the date of perihelion adjusted to minimize discrepancies
(cf. Ingram 1993).
The carbon dioxide concentration is the AMIP-prescribed value of 345
ppm. Zonally averaged monthly ozone profiles are specified from the climatology
of Keating et al. (1987)  above hybrid
level 0.0225 (see Vertical Representation),
and from satellite data of McPeters et al. (1984)
 below this level. Radiative effects of water vapor and clouds,
but not those of aerosol, are also included (see Radiation).
- The radiation schemes are as described by Ingram (1993)).
Incoming insolation is based on a 360-day year (see Solar
Constant/Cycles). Shortwave computations follow Slingo (1985))
, extended to include 4 spectral intervals (with boundaries at 0.25,
0.69, 1.19, 2.38, and 4.0 microns) and the interactive cloud optical properties
of Slingo (1989) . Rayleigh scattering
is represented by reflection of 3 percent of the incoming insolation before
any interaction with the atmosphere. Shortwave absorption (by ozone, carbon
dioxide, and water vapor) is treated by use of look-up tables. The effects
of pressure broadening on carbon dioxide and water vapor absorption bands
are included; the overlap of these bands is assumed to be random within
each spectral interval.
- Calculation of longwave fluxes follows the method of Slingo and Wilderspin
(1986) . Absorption by water vapor,
carbon dioxide, and ozone is treated in 6 spectral bands (with boundaries
at 0.0, 4.0x10^4, 5.6x10^4, 8.0x10^4, 9.0x10^4, 1.1x10^5, and 1.2x10^5
m^-1), using exponentials for the water vapor continuum and look-up tables
otherwise. The temperature dependence of e-type absorption in the water
vapor continuum is after Roberts et al. (1976)
. Pathlengths of gaseous absorbers are scaled to account for pressure-broadening
effects(and for carbon dioxide, also for temperature-broadening effects).
- The convective cloud in each grid box is confined to a single tower
(with full vertical overlap). All absorption of shortwave radiation by
the convective cloud occurs in its top layer, with the remainder of the
beam passing unimpeded through lower layers. In each vertical column, the
shortwave radiation interacts only with 3 stratiform clouds defined by
vertical domain: low (levels 1 to 5), middle (levels 6 to 9), and high
(levels 10 to 18), all randomly overlapped. The cloud with the greatest
area in each domain interacts with the shortwave radiation, and it is assigned
the cloud water content of all the layer clouds in the domain. (Neither
the shortwave nor longwave scheme allows cloud in the top layer, however.)
In the longwave, similar to the formulation of Geleyn and Hollingsworth
(1979) , clouds in different layers
are treated as fully overlapped if there is cloud in all intervening layers,
while clouds separated by cloud-free layers are treated as randomly overlapped.
- Sunlight reflected from a cloud is assumed to pass directly to space
without further cloud interactions, but with full gaseous absorption; the
surface albedo (see Surface Characteristics)
is adjusted to account for the increased absorption due to multiple reflections
between clouds and the surface. Cloud shortwave optical properties (optical
depth, single-scattering albedo, and asymmetry factor) are calculated from
the cloud water path (CWP), the effective radius of the drop-size distribution
(7 microns for water and 30 microns for ice), and the sun angle, following
the Practical Improved Flux Method of Zdunkowski et al. (1980)
. Cloud longwave emissivity is a negative exponential function
of CWP, with absorption coefficient 65 m^2/kg for ice clouds and 130 m^2/kg
for water clouds. See also Cloud Formation
- Moist and dry convection are both simulated by the mass-flux scheme
of Gregory and Rowntree (1990)) that
is based on the bulk cloud model of Yanai et al. (1973)
. Convection is initiated if a parcel in vertical layer k has a
minimum excess buoyancy beta that is retained in the next higher level
k + 1 when entrainment effects and latent heating are included. The convective
mass flux at cloud base is taken as proportional to the excess buoyancy;
the mass flux increases in the vertical for a buoyant parcel, which entrains
environmental air and detrains cloud air as it rises. Both updrafts and
downdrafts are represented, the latter by an inverted entraining plume
with initial mass flux related to that of the updraft, and with detrainment
occurring over the lowest 100 hPa of the model atmosphere.
- When the parcel is no longer buoyant after being lifted from layer
m to layer m + 1, it is assumed that a portion of the convective plumes
has detrained in layer m so that the parcel in layer m + 1 has minimum
buoyancy b. Ascent continues until a layer n is reached at which an undiluted
(without entrainment) parcel originating from the lowest convectively active
layer k would have zero buoyancy, or until the convective mass flux falls
below a minimum value. Cf. Gregory (1990)
 and Gregory and Rowntree (1990) 
for further details.
- The convection scheme (see Convection)
determines the vertical extent of subgrid-scale convective cloud, which
is treated as a single tower in each grid box. The convective cloud base
is taken as the lower boundary of the first model layer at which saturation
occurs, and the cloud top as the upper boundary of the last buoyant layer.
The fractional coverage of each vertical column by convective cloud is
a logarithmic function of the mass of liquid water condensed per unit area
between cloud bottom and top (cf. Gregory 1990).
- Large-scale (stratiform) cloud is prognostically determined in a similar
fashion to that of Smith (1990a) .
Cloud amount and water content are calculated from the total moisture (vapor
plus cloud water/ice) and the liquid/frozen water temperature, which are
conserved during changes of state of cloud water (i.e., cloud condensation
is reversible). In each grid box, these cloud-conserved quantities are
assumed to vary (because of unresolved atmospheric fluctuations) according
to a top-hat statistical distribution, with specified standard deviation.
The mean local cloud fraction is given by the part of the grid box where
the total moisture exceeds the saturation specific humidity (defined over
ice if the local temperature is < 273.15 K, and over liquid water otherwise).
See also Radiation for treatment of
- Large-scale precipitation forms in association with stratiform cloud
(see Cloud Formation). For purposes
of precipitation formation and the radiation calculations (see Radiation),
the condensate is assumed to be liquid above 0 degrees C, and to be ice
below -15 degrees C, with a liquid/ice fraction obtained by quadratic-spline
interpolation for intermediate temperatures. The rate of conversion of
cloud water into liquid precipitation is a nonlinear function of the large-scale
cloud fraction and the cloud-mean liquid water content, following Sundqvist
(1978 , 1981
) and Golding (1986) . The
precipitation of ice is a nonlinear function of the cloud-mean ice content,
as deduced by Heymsfield (1977) .
Liquid and frozen precipitation also form in subgrid-scale convection (see
- Evaporation/sublimation of falling liquid/frozen precipitation are
modeled after Kessler (1969)  and
Lin et al. (1983) . Frozen precipitation
that falls to the surface defines the snowfall rate (see Snow
Cover). For purposes of land hydrology, surface precipitation is assumed
to be exponentially distributed over each land grid box, with fractional
coverage of 0.5 for large-scale precipitation and 0.1 for convective precipitation.
Cf. Smith and Gregory (1990) and Dolman
and Gregory (1992) for further details.
Planetary Boundary Layer
Conditions within the PBL are typically represented by the first 5 levels
above the surface (centered at about 997, 975, 930, 869, and 787 hPa for
a surface pressure of 1000 hPa), where turbulent diffusion of momentum
and cloud-conserved thermodynamic and moisture variables may occur (see
Cloud Formation and Diffusion).
The PBL top is defined either by the highest of these layers, or by the
layer in which a modified bulk Richardson number (that incorporates buoyancy
parameters for the cloud-conserved variables) exceeds a critical value
of unity. Nonlocal mixing terms are included for heat and moisture. See
also Surface Characteristics, Surface
Fluxes, and Land Surface Processes.
Orography obtained from the U.S. Navy 10-minute resolution dataset (cf.
Joseph 1980 ) is grid-box averaged,
and is further smoothed with a 1-2-1 filter at latitudes poleward of 60
degrees. The orographic variances required by the gravity-wave drag parameterization
are obtained from the same dataset (see Gravity-wave
AMIP monthly sea surface temperature fields are prescribed, with daily
values determined by linear interpolation.
AMIP monthly sea ice extents are prescribed. The ice may occupy only
a fraction of a grid box, and the effects of the remaining ice leads are
accounted for in the surface roughness length, shortwave albedo and longwave
emission, and turbulent eddy fluxes (see Surface
Characteristics and Surface Fluxes).
The spatially variable sea ice thickness is prescribed from climatological
data. Snow falling on sea ice affects the surface albedo (see Surface
Characteristics), but not the ice thickness or thermodynamic properties.
Ice temperature is prognostically determined from a surface energy balance
(see Surface Fluxes) that includes a
conduction heat flux from the ocean below. Following Semtner (1976)
, the conduction flux is proportional to the difference between
the surface temperature of the ice and the subsurface ocean temperature
(assumed to be fixed at the melting temperature of sea ice, or -1.8 degrees
C), and the conduction flux is inversely proportional to the prescribed
Surface snowfall is determined from the rate of frozen large-scale and
convective precipitation in the lowest vertical layer. (Snowfall, like
surface rainfall, is assumed to be distributed exponentially over each
land grid box--see Precipitation.) On
land only, prognostic snow mass is determined from a budget equation that
accounts for accumulation, melting, and sublimation. Snow cover affects
the roughness and heat conduction of the land surface, and it also alters
the albedo of both land and sea ice (see Surface
Characteristics). Snow melts when the temperature of the top soil/snow
layer is > 0 degrees C, the snowmelt being limited by the total heat
content of this layer. Snowmelt augments soil moisture, and sublimation
of snow contributes to the surface evaporative flux over land. See also
Surface Fluxes and Land
- Surface types include land, ocean, sea ice, and permanent land ice.
Sea ice may occupy a fraction of a grid box (see Sea
Ice). On land, 15 different soil/vegetation types are specified from
the 1 x 1-degree data of Wilson and Henderson-Sellers (1985)
. The effects of these surface types on surface albedo (see below)
and on surface thermodynamics and moisture (see Land
Surface Processes) are treated via parameters derived by Buckley and
Warrilow (1988) .
- On each surface, roughness lengths are specified for momentum, for
heat and moisture, and for free convective turbulence (which applies in
cases of very light surface winds under unstable conditions). Over oceans,
the roughness length for momentum is a function of surface wind stress
(cf. Charnock 1955 ), but is constrained
to be at least 10^-4 m; the roughness length for heat and moisture is a
constant 10^-4 m, and it is 1.3 x 10^-3 m for free convective turbulence.
Over sea ice, the roughness length is a constant 3 x 10^-3 m, but it is
0.10 m for that fraction of the grid box with ice leads (see Sea
Ice). Over land, the roughness length is a function of vegetation and
small surface irregularities; it is decreased as a linear function of snow
cover, but is at least 5 x 10^-4 m. Cf. Smith (1990b)
for further details.
- The surface albedo of open ocean is a function of solar zenith angle.
The albedo of sea ice varies between 0.60 and 0.85 as a linear function
of the ice temperature above -5 degrees C, and it is also modified by snow
cover. Where there is partial coverage of a grid box by sea ice, the surface
albedo is given by the fractionally weighted albedos of sea ice and open
ocean. Surface albedos of snow-free land are specified according to climatological
vegetation and land use. Snow cover modifies the albedo of the land surface
depending (exponentially) on the depth (following Hansen et al. 1983
) and (linearly) on the snow temperature above -2 degrees C (following
Warrilow et al. 1990 ), as well as
on the background vegetation (following Buckley and Warrilow 1988
). Cf. Ingram (1993) for further
- Longwave emissivity is unity (blackbody emission) for all surfaces.
Thermal emission from grid boxes with partial coverage by sea ice (see
Sea Ice) is calculated from the different
surface temperatures of ice and the open-ocean leads, weighted by the fractional
coverage of each.
- Surface solar absorption is determined from the surface albedos, and
longwave emission from the Planck equation with constant emissivity of
1.0 (see Surface Characteristics).
- Turbulent eddy fluxes are formulated as bulk formulae in a constant-flux
surface layer, following Monin-Obukhov similarity theory. The momentum
flux is expressed in terms of a surface stress, and the heat and moisture
fluxes in terms of cloud-conserved quantities (liquid/frozen water temperature
and total water content) to account for effects of phase changes on turbulent
exchanges (see Cloud Formation). These
surface fluxes are solved by an implicit numerical method.
- The surface atmospheric variables required for the bulk formulae are
taken to be at the first level above the surface (at 997 hPa for a 1000
hPa surface pressure). (For diagnostic purposes, temperature and humidity
at 1.5 m and the wind at 10 m are also estimated from the constant-flux
assumption.) Following Louis (1979) ,
the drag/transfer coefficients in the bulk formulae are functions of stability
(expressed as a bulk Richardson number) and roughness length, and the same
transfer coefficient is used for heat and moisture. In grid boxes with
fractional sea ice, surface fluxes are computed separately for the ice
and lead fractions, but using mean drag and transfer coefficients obtained
from linearly weighting the coefficients for ice and lead fractions (see
- The surface moisture flux also is a fraction beta of the local potential
evaporation for a saturated surface. Over oceans, snow and ice, and where
there is dew formation over land, beta is set to unity; otherwise, beta
is a function of soil moisture and vegetation (see Land
- Above the surface layer, momentum and cloud-conserved variables are
mixed vertically within the PBL by stability-dependent diffusion. For unstable
conditions, cloud-conserved temperature and water variables are transported
by a combination of nonlocal and local mixing. Cf. Smith (1990b,
1993 ) for further details. See also
Diffusion and Planetary
Land Surface Processes
- A vegetation canopy model (cf. Warrilow et al. 1986
 and Shuttleworth 1988 )
includes effects of moisture condensation, precipitation interception,
direct evaporation from wet leaves and from surface ponding, and evapotranspiration
via root uptake of soil moisture. The fractional coverage and water-storage
capacity of the canopy vary spatially by vegetation type (see Surface
Characteristics), with a small storage added to represent surface ponding.
The canopy intercepts a portion of the precipitation, which is exponentially
distributed over each grid box (see Precipitation).
Throughfall of canopy condensate and intercepted precipitation occurs in
proportion to the degree of fullness of the canopy; evaporation from the
wet canopy occurs in the same proportion, as a fraction of the local potential
evaporation. Cf. Gregory and Smith (1990)
for further details.
- Soil moisture is predicted from a single-layer model with spatially
nonuniform water-holding capacity; it is augmented by snowmelt, precipitation,
and the throughfall of canopy condensate. This moisture infiltrates the
soil at a rate depending on saturated soil hydraulic conductivity enhanced
by effects of root systems that vary spatially by vegetation type (see
Surface Characteristics). The noninfiltrated
moisture is treated as surface runoff. Subsurface runoff from gravitational
drainage is also parameterized as a function of spatially varying saturated
soil hydraulic conductivity and of the ratio of soil moisture to its saturated
value (cf. Eagleson 1978 ). Soil
moisture is depleted by evaporation at a fraction beta of the local potential
rate (see Surface Fluxes). The value
of beta depends on the ratio of soil moisture to a spatially varying critical
value, and on the ratio of the stomatal resistance to aerodynamic resistance
(cf. Monteith 1965 ). The critical
soil moisture and stomatal resistance vary spatially by soil/vegetation
type (see Surface Characteristics).
Cf. Gregory and Smith (1990)  and Smith
(1990b)  for further details.
- Soil temperature is predicted after Warrilow et al. (1986)
 from heat conduction in four layers. The depth of the topmost
soil layer is given by the penetration of the diurnal wave, which depends
on the spatially varying soil heat conductivity/capacity (see Surface
Characteristics). The lower soil layers are, respectively, about 3.9,
14.1, and 44.7 times the depth of this top layer. The top boundary condition
for heat conduction is the net downward surface energy balance (see Surface
Fluxes), including the latent heat of fusion for snowmelt (see Snow
Cover); the bottom boundary condition is zero heat flux. Heat insulation
by snow (see Snow Cover) is modeled
by reducing the thermal conductivity between the top two soil layers; however,
subsurface moisture does not affect the thermodynamic properties of the
soil. Cf. Smith (1990b) for further
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Last update May 27, 1998. For further information, contact: Tom Phillips