Idealized numerical simulations of atmospheric
convection in 2D
Fantini ISAC-CNR Bologna Italy
Poster 2010-2437 AS1.10
EGU General Assembly
Vienna 2-7 May 2010
We use a two-dimensional (x-z ) non-hydrostatic model, with periodic
boundary conditions, to perform an ensemble of experiments on the
generation and intensity of atmospheric convection. The model is a 2D
version of the model MOLOCH, designed at ISAC-CNR and described in
the literature (Malguzzi et al., 2006). It is the same model that was used in
Fantini and Malguzzi (2008) except that rotation is disabled (f=0 ), and the
solar cycle is activated, with the same phase over the entire domain, in order
to maintain spatial homogeneity of the forcing. The model integrates the
fully compressible set of equations, with pressure, temperature, specific
humidity, horizontal and vertical velocity components, and five water
species as prognostic variables. The model is run with a horizontal grid
spacing of 0.01 degrees (1.11 km) and 1024 grid points, 50 vertical levels
with exponentially increasing separation with height (150 m near the ground,
600 m at 10 km).
This paper reports on the early stages of a project intended to perform
ensemble simulations in three dimensions and look for quantitative
relationships between the characteristics of convection and the physical
parameters of the environment in which it develops. Although not
necessarily accompanied by detailed description of the events, or of the
physical processes taking place in the model simulations, such relations could
be used for the formulation and verification of convective parameterization
schemes. As a way of testing the model and at the same time obtain
preliminary indications on the viability of this approach, we run this twodimensional version in different conditions of environmental shear and
verify its influence on total precipitation.
The typical time scale of convective cells is a few hours, and to obtain
average properties and their relations with the environment one could
perform many short-time simulations, each of which may suffer from the
arbitrariness of the initialization. Alternatively, we exploit the cyclic nature
of accumulation-release of convective energy (CAPE) driven by the solar
cycle, and generate model trajectories, of the duration of a few days, that
include several instances of convective cells and precipitation events. This
procedure has the advantage that after the first few hours the simulated fields
are self-consistent, avoiding the repeated adjustments that would be needed
by individual, short-term experiments. It has the disadvantage that it gives
little control after initialization – the environment of each new convective
episode is redefined by the previous history of the simulation, in addition to
the solar forcing. In this way we follow long trajectories in phase space that,
after an initial transient of as yet undetermined duration, should lie entirely
on an `attractor’ of the system, hopefully giving us robust statistical
information on its behaviour.
We perform 21 sets of experiment, each set characterized by an imposed
initial zonal wind UINI, vertically uniform, assuming values from –50 to 50
m/s in steps of 5 m/s. Low-level shear of the wind is created letting model
physics modify the profile in a consistent way. For each of these sets, defined
by the same UINI, eight different experiments are performed with slightly
different initial conditions, generated by inserting different random
perturbations of surface temperature in eight different locations. The initial
thermodynamic profile is not linearly unstable, therefore the initial
perturbation does not determine the location of convective initiation. The
random initial condition only defines a member of an ensemble of initially
very close trajectories, which will diverge as soon as convection takes place.
Meteorological fields are shown below at three different times for one
individual experiment.
Initial thermodynamic profile, common to all
experiments, on a skew T-log p diagram
Evolution of mean wind for experiment
initialized at 30 m/s. Each red curve is the
profile averaged over the domain and over
eight different initial conditions. One profile
per hour. Horizontal lines at 1,3,5 km. Ticks
mark model levels.
Hourly accumulated precipitation vs time.
Precipitation is averaged over the domain
and over the eight different initial conditions
for the same mean initial wind UINI. Green:
|UINI| > 30 m/s. Red: all others
Accumulated precipitation vs low-level shear.
Solid: Day 2, short dash: day 1, long dash:
day 3, dots: day 4
Space- and time-lagged autocorrelation of
accumulated precipitation in days 2,3,4 for
four initial with mean wind values UINI, as
labeled. Lowest contour 0.2, interval 0.2. Thick
black line is advection at speed UINI. The
hourly modulation of the contours is only due
to the time resolution of the data.
Width of the autocorrelation region shown in
the figure above, evaluated at time lag =0, for
the values labeled on the left of the curves, for
all UINI
Domain averaged CAPE vs time. Green: |UINI|
< 15 m/s; Blue |UINI| > 30 m/s; Red: all others
Evolution of precipitation and shear for all the
experiments. Each point represents the average
over a 32-grid-points sub-domain, every hour.
Red: all events regardless of precipitation. Green:
precipitation higher than 0.1 mm/h. Blue:
precipitation higher than 1.25 mm/h
Time evolution of lowest 3 km shear. Red: all
experiments. Green: UINI = -50 m/s, blue: UINI
= -30m/s, violet: UINI=-15 m/s, cyan: UINI=0.
At the initial time of the experiments, solar time is 12 noon. Daily
accumulations are computed from 12 to 12. The effect of solar heating is an
increase of temperature and moisture near the ground (not shown) with
consequent destabilization of the profile, but the remaining hours of daytime
in day 1 are not enough to induce a start-up of convection. Precipitation
begins around 24 hours, i.e. noon of the following day, except for the highshear cases. The first cycle of precipitation (day 2) is the most intense. All
experiments seem to produce an initial burst of convection, that reduces the
amount of moisture subsequently available, and precipitation maxima
decrease from day 2 to the next. Moisture removed by precipitation is partly
replenished by surface fluxes (not shown). The wind profile can be seen to
evolve, because of surface drag in the first few time steps, and then by
vertical transfer of momentum carried both by parameterized boundary-layer
turbulence and explicit convection. Wind profiles in days 3 and 4 are almost
stationary, at least in domain average. Domain-accumulated precipitation is
also shown, for the four days, as a function of wind shear in the lowest 3 km.
Maxima of precipitation at intermediate shear values can be seen, except for
day 1 when the dynamical fields are presumably not well adjusted. The
imperfect symmetry between positive and negative shear values suggests
that the number of experiments is not large enough to yield smooth statistics,
or that the experiments are not independent.
In order to obtain an estimate of the typical size of convective formations, we
performed a time- and space-lagged autocorrelation of the hourly
accumulated precipitation field, starting at 24 hours and with a maximum
time lag of 12 hours. Results show spatial size and life-span increasing with
increasing shear of the wind, in a uniform manner, and a translation speed
slightly slower than the advection by the mean wind.
More details on the system evolution can be seen in the averages on 32 grid
points (approx. 35.5 km) shown in a shear vs time representation. The more
intense precipitation events occur nearly at the same time, and repeated
every day, for intermediate values of low-level shear, but only at day two,
with a slightly earlier startup, for low shear. A spread in shear values for each
set of experiments having the same UINI is also seen to coincide with the
initiation of convection. Finally domain averaged CAPE vs time shows
different overall tendency for the high- and low-shear cases.
The figures here displayed show some of the features of the experiments
performed, which we consider a reference for a study of sensitivity to
changes in environmental and model characteristics. This study still lacks a
full physical interpretation of some of the features exhibited, but our primary
concern at this point is to identify variables that characterize convection and
examine their quantitative dependence on environmental parameters.
Experiments being performed at this time include variation of surface
exchange coefficients of momentum, heat and moisture, horizontal
resolution, initial thermodynamic profile and latitude. Verification of the
dependence on the details of numerical procedures, such as turbulence and
microphysical parameterization and advection scheme, might have to be
done in comparison with different models. Finally, we are aware that any
useful application of this approach has to come from an extension to full
three-dimensional models, but a preliminary exploration of the phase space
of two- dimensional convection should give useful indications for the
preparation and interpretation of the more realistic, and more complex,
cases.
One run with UINI=30m/s. Fields at 31 hours. Left: color: equivalent
potential temperature, dist 1 K, arrows: u-w vectors. Center:color: cloud
water, dist 0.1, contours: cloud ice, dist 0.1. Right: color: rain, dist 0.25;
contours: precipitating ice, dist 0.5.
the same at 55 hours
the same at 81 hours