Ž in mid-latitudes, land-surface conditions are anthropogenically altered e.g., through
urbanization, deforestation and afforestation, subsidy politics, open-pit mining and .
recultivation of open-pit mines, etc. . These land-use changes go along with modifica- tions of surface heterogeneity. Since low extended stratus may significantly alter
Ž .
photolysis rates Molders et al., 1995 as well as evapotranspiration, and, thus, ground-
¨
Ž water recharge, land-use changes may not only affect the water and energy cycle e.g.,
. Molders, 1998 , but also the trace gas concentrations. Moreover, since in mid-latitudes,
¨
extended low stratus is often supercooled, here, land-use changes that contribute to enhance stratus should be avoided in areas of airports due to the danger of icing.
2. Model description and initialization
The nonhydrostatic meteorological model GEesthacht’s SImulation Model of the Ž
. Atmosphere GESIMA, Kapitza and Eppel, 1992; Eppel et al., 1995 is used in our
study. Its dynamical part is based on the anelastic equations. The physical features of the cloud module are based upon a five water-class
Ž .
cloud-parameterization scheme Molders et al., 1997 . In this scheme, saturation adjust-
¨
Ž .
ment follows Lord et al. 1984 . Note that, in the case of low extended stratus, as investigated in our study, condensation and evaporation of cloud-water are the cloud-mi-
crophysical processes of most importance. In the long-wave spectral range, the radiative transfer equation is solved in a
simplified two-stream approximation that transforms the radiation flux into an upward Ž
. and downward one Eppel et al., 1995 . These fluxes are coupled by their values at the
upper and lower boundaries. To get reliable upper model boundary fluxes, 10 additional model layers are added at the top of the computational domain of the model. The mean
spectral heating is calculated by the divergence of the net long-wave radiation flux Ž
. Ž
. Eppel et al., 1995 . The spectral extinction coefficients depend on pressure height and
Ž .
temperature. In accord with Buykov and Khvorostyanov 1977 , a wavelength-indepen- dent value is assumed for the extinction coefficients of liquid water. Outside the window
region, water vapor and liquid-water absorption are taken into account. The transmission is approximated by a sum of exponential terms adjusted to the results of a statistical
Ž .
band model for more details, see Eppel et al., 1995 . In the short-wave spectral range, only scattering processes are considered, leading to a simple parameterization of the
Ž .
solar flux at the surface see Claussen, 1988; Eppel et al., 1995 . In the case of clouds, Ž
. the transmission function is formulated in accord with Stephens 1978 . In doing so, the
optical thickness of a cloud is considered as a function of liquid-water path by Ž
integrating the cloud substance densities which are predicted by the cloud-parameteriza- .
tion scheme from the surface to model top. Ž
. The treatment of the soilrvegetationratmosphere interaction follows Deardorff 1978
Ž .
see also Eppel et al., 1995; Molders, 1998 . Herein, homogeneous soil- and land-surface
¨
characteristics are assumed within a grid cell. A force-restore method determines soil-wetness factors. At the surface, the fluxes of sensible and latent heat are calculated
applying a bulk formulation. Transpiration of plants is considered by a Jarvis-type Ž
. approach Jarvis, 1976 . The soil heat fluxes and soil temperatures are determined by a
K. Friedrich,
N. Molders
r Atmospheric
Research 54
2000 59
– 85
¨
62
Table 1 Plant- and soil-specific parameters as used in this study
Surface Thermal
Heat Emissivity
Albedo Roughness
Field Capillary
Max. evaporative
y3 3
Ž .
type diffusivity
capacity length
capacity 10
kgrm s conductivity
y6 2
6 3
Ž .
Ž .
Ž . Ž .
Ž .
10 m rs
10 Jrm K m
m mrs
Grass 0.56
2.1 0.95
0.25 0.02
0.010 8.0
0.04 Sand
0.84 2.1
0.90 0.3
0.0004 0.002
0.9 –
Ž .
diffusion equation Claussen, 1988; Eppel et al., 1995 where, at 1-m depth, soil temperature is held constant at the climatological value. The plant- and soil-specific
parameters used in this study are listed in Table 1. The surface stress and near-surface fluxes of heat and water vapor are expressed in terms of dimensionless drag-and-transfer
Ž .
coefficients utilizing a parametric model Kramm et al., 1995 . The turbulent flux of momentum for the region above the surface layer is calculated
by a one-and-a-half-order closure scheme. The elements of the eddy-diffusivity tensor are expressed by the vertical eddy diffusivity, K
, and horizontal diffusivity, K .
M, V M,H
The latter is also related to K by the simple linear relationship, K
s 2.3 K .
M, V M,H
M,V
Ž .
K is expressed by the turbulent kinetic energy TKE and mixing length, l, using the
M, V
Kolmogorov–Prandtl relation where the mixing length is parameterized by Blackadar’s Ž
. Ž
. 1962 approach, slightly modified by Mellor and Yamada 1974 . The turbulent fluxes
of sensible heat and water vapor for that region are expressed as functions of K and
M, V
the turbulent Prandtl number, Pr s K rK
, and turbulent Schmidt number, Sc s
t M,V
H,V t
K rK
, respectively. These characteristic numbers depend on the thermal stratifica-
M, V E,V
Ž .
tion. They are derived from the local stability functions of Businger et al. 1971 and the assumption that Sc s Pr . To determine the TKE, an additional budget equation for that
t t
Ž quantity is solved, where the energy production due to horizontal shear is neglected for
. more detail, see Kapitza and Eppel, 1992 .
The model is initialized using profiles of air temperature and humidity typical for a Ž
. day with extended low stratus in spring Fig. 1 . Surface pressure is 1031.2 hPa. In the
calculation of radiation, a geographical latitude of 51.58N and the 15 May are assumed. Initial soil wetness factor is set equal to 0.5. Soil temperature of 1-m depth is set equal
to 280.1 K.
The simulations are integrated for 24 h where the first 6 h serve as the adjusting Ž
.
2
phase. The inner model domain s test domain encompasses 75 = 75 km with a
horizontal grid resolution of 5 = 5 km
2
. The vertical resolution varies from 20 m close
Ž .
Ž Fig. 1. Initial profiles of specific humidity q
in grkg, u- and Õ-component of wind vector in mrs upper
v
. Ž .
Ž .
x-axis , and air temperature T in 8C lower x-axis .
to the ground to 1 km at the top, which is located in 12-km height. Eight levels are located below the 2-km height and nine are above. Homogeneously flat terrain is
assumed for all simulations.
3. Design of the study
