Analysis, Geometry and Stochastics for Planet Earth
Date: September 29, 2015
Location: Room Lyle G74 CDT-Suite, University of Reading
Supported by: London Mathematical Society Institute and EPSRC-CDT Mathematics of
Planet Earth
Speaker: Prof Darryl Holm (Imperial College London)
Title: “Stochastic Variational Principles for Geophysical Fluid Dynamics (GFD)”
Abstract: Abstract: Suppose your data for a GFD system had some noisy-looking,
complicated, small-scale motions (variability); but it also had some large-scale spatial
correlations, as seen, for example, in the Figure below (courtesy of E Van Sebille, Grantham
Institute, Imperial College) showing thirty years worth of satellite measurements of the
paths of drifters in the Pacific Ocean in the region between Australia and New Zealand. How
could you modify your deterministic basic GFD equations to incorporate into them the
randomness and statistics you have seen in your data; so that numerical simulations of your
modified GFD equations would reproduce the same sort of randomness and statistics as
seen in your data? Hint: you would want to do it in an optimal way, so that some kind of
variational principle would be needed, and you would need to constrain your variations to
be consistent with the statistics of your data. This talk will discuss a mathematical approach
via stochastic variational principles for solving such problems, in examples ranging from
wobbling rotating bodies in classical mechanics, to realistic GFD models.
Speaker: Dr Glenn Shutts (MetOffice)
Title: "Physical parametrization of unresolved and partially-resolved phenomena in weather
forecast models."
Abstract: Current Numerical Weather Prediction (NWP) models have sufficiently fine grid
meshes to be able to resolve the rotationally- and hydrostatically-balanced atmospheric
flow that achieves the required energy and moisture transport from the tropics to the Polar
Regions (i.e. planetary Rossby waves, cyclone waves and fronts). The success of NWP
(mainly outside of the tropics) comes from the strong constraint placed upon large-scale
airflows of the Earth's rotation and manifest in the geostrophic wind approximation and
balanced forms of the potential vorticity (which determine the flow through elliptic
equations). Theories of geostrophic turbulence explain the tendency for steep energy
spectra (k^(-3) ) and for energy to be locked into the largest permissible scales on the planet
for which solar forcing dominates. The transport of moisture takes place in narrow
'atmospheric rivers' ahead of cold fronts and it appears that gridlengths finer than 30 km are
required to capture these. Unfortunately, this mathematically-elegant view leaves out a
very important meteorological phenomenon that atmospheric physicists call 'convection'
which takes the form of cumulus clouds of varying scale and intensity. They transport heat,
moisture and momentum vertically through the buoyancy forces that accompany water
phase changes (dominated by latent heat release in updraughts). These unbalanced motions
are most unstable at horizontal scales of the order of 100 metres and limited by turbulence
at smaller scales. Small cumulus clouds are composed of ensembles of these narrow
convective plumes thereby giving them their cauliflower appearance. Severe convective
storms have tilted airflows (in the vertical plane) that are organized so that hydrometeors
(rain, snow, hail etc) fall into dry air and the resultant cooling due to evaporation and
melting drives strong downdraughts. Some of the most intense convective storms occur in
mid-latitudes and the associated upward transport of mass and subsequent horizontal
spreading in the upper troposphere disturbs the position of jetstreams and creates pools of
zero absolute vorticity. These Mesoscale Convective Systems (MCSs) are responsible for
forecast errors since their updraughts are sub-grid-scale and so rely on a parametrized
representation of their effect. The balanced flow picture of global atmospheric flows is also
upset by the presence of mountain ranges. For the highest mountains, much of the airflow
is around rather than over the mountain but the air that does flow over generates internal
gravity waves that typically radiate their energy vertically upwards into the stratosphere.
This wave motion is accompanied by a wave stress on the mountain and an opposite stress
is transmitted upwards with the wave. The air that flows around the mountain may
generate wakes and eddies which in turn cause a drag force on the mountain. These
stresses/drag forces exert a powerful influence on the balanced flow and also require
parametrization. Along with the representation of boundary layer turbulence and cloud
microphysical processes, these parametrizations for convection and mountain waves are
semi-empirical and assume a unique relationship between the statistical mean of the
relevant process and the instantaneous state of a model grid column. My talk will reflect on
the challenges of parametrization and forecast model improvement.
Speaker: Caroline Muller (Ecole Polytechnique)
Title: Spatial organization of clouds in the tropical atmosphere
Abstract: Clouds have been recognized as a key source of uncertainty for climate
predictions. In particular, cloud feedbacks are responsible for a large fraction of the intermodel scatter in climate sensitivity. One source of uncertainty is the spatial distribution of
deep convection, and its response to warming.
We will analyze the properties of deep convection in idealized high-resolution simulations of
homogeneous radiative-convective equilibrium. The numerical results will be linked to
theoretical expectations based on the physics of clouds. We will also compare the numerical
and theoretical results to observations of deep clouds over the tropical oceans.
Under certain conditions, the homogeneous radiative-convective equilibrium has been
shown to be unstable to large-scale overturning circulations. The resulting new equilibrium
is a spatially organized atmosphere composed of two distinct areas: a moist area with
intense convection, and a dry area with strong radiative cooling. In nature, the organized
state can take the form of cloud clusters or tropical cyclones. We will investigate the
physical processes responsible for the spontaneous organization of deep clouds.