Greet de Graaf / Brigitta Kamphuis
Monitoring atmospheric analyses
Statistical mechanical approach to 2D coherent structures
Low order statistical-dynamical climate models
Contour dynamics
In the summer of 1999 the post-doctoral research project `The predictability
of two-layer contour
dynamics systems', funded by NWO came to an end by the departure of Dr.
Trieling to the Vortex Dynamics Group of the Technical University Eindhoven.
The project aimed at investigating to which extent it is possible to describe
the process of atmospheric cyclogenesis (synoptic development) using isentropic
contour dynamics models. In isentropic contour dynamics models the vertical
structure of the atmosphere is represented by one or more layers of uniform
potential temperature (isentropic layers) and the horizontal structure (within
the layers) by two or more regions of uniform potential vorticity (PV). Assuming
hydrostatic and geostrophic equilibrium, the models are defined completely in
terms of the positions of the potential vorticity fronts and can be integrated
in time using the technique of contour dynamics.
The work has evolved into a state in which it has become clear that a so called two-and-a-half layer contour dynamics model with a single front of potential vorticity in each of the two active layers is sufficiently versatile to produce cyclogenesis. This model, consisting of three layers of uniform potential temperature - the upper layer assumed to be at rest - was investigated extensively. The project has resulted in two studies on baroclinic life cycles in a two-and-a-half layer contour dynamics system: one on infinitesimal perturbations of zonal flows and another on finite-amplitude perturbations of zonal flows.
Monitoring atmospheric analyses
This project,
begun in the summer of 1998, was funded by the BCRS (Netherlands Remote Sensing
Board). The aim of the project was to devise a method by means of which it should
be possible, using a graphical interaction procedure, to modify the analysis
of HIRLAM (High Resolution Limited Area Model) used at KNMI and to study the
consequences of the modification in terms of the resulting forecast. The analysis
is adjusted in terms of PV (potential vorticity) and a three-dimensional variational
data-assimilation system (3DVAR) is used to obtain a dynamically consistent
modified analysis from the modified PV.
In December 2000 the project was completed in terms of the BCRS report 'Manually adjusting a numerical weather analysis in terms of potential vorticity using three-dimensional variational data-assimilation'. The project has resulted in a system that, although it needs further fine-tuning and optimisation, functions as expected. It has been established that the concept of potential vorticity in combination with variational data-assimilation can handle human interventions in the numerical forecasting process in a natural and effective way. It is intended to continue the work by testing the system on a few selected meteorological cases and to optimise the system in terms of computational speed and user-friendliness. In the future we expect to test the system in an operational forecasting environment to assess its effectiveness in daily operational practice.
Isentropic models
The main goal of this project is to provide a solid physical foundation for
isentropic contour dynamics models of the atmosphere. The study of the dynamics
of an isentropic layer in hydrostatic equilibrium - with the emphasis on the
vertical profile of vertical velocity - appeared in the January 2000 issue of
the Quarterly Journal of the Royal Meteorological Society. As a result of a
referee's suggestion it was shown that the derived profile of vertical velocity
is an exact solution of Richardson's equation when specialised to an isentropic
layer.
In contrast with hydrostatic balance, geostrophic balance is not trivially applied to flow on a global domain. The problem was studied in the context of the simplest isentropic model that one can imagine: a single hydrostatic layer of air with uniform potential temperature. Such a model behaves very much like a single-layer shallow water model, but is more appropriate as a simplified model of the atmosphere than a shallow-water (constant-density) model. The assumption that deviations of the Montgomery potential (or geopotential) from the state of rest are equal to the Coriolis parameter times the streamfunction was found to give a form of geostrophic balance that can be used globally. This simplification of linear balance can be used to derive, e.g., the equivalent barotropic vorticity equation on the sphere in a conceptually clear and physically consistent way.
The form of balance just mentioned was also used as a starting point in a Hamiltonian method, developed by Salmon, to construct global balanced models of the atmosphere that conserve energy, mass and potential vorticity. The method was applied to the single-layer isentropic model mentioned above. A comparison of the balanced model with the original unbalanced model makes clear that the balanced model is a very accurate approximation of the original model. The corresponding paper is now in press at the Quarterly Journal of the Royal Meteorological Society. It is planned to apply the method to isentropic models with more than one layer including the case in which the lowest layers are infinitesimally thin locally.
Statistical mechanical approach to 2D coherent structures
This concerns the study of the effects of the ever present and often neglected
microscopic fluctuations on the macroscopic behaviour of the system under consideration.
Three papers were published on the so-called statistical mechanics approach
to the coherent structures observed in the asymptotic regime of two-dimensional
flows. A fourth paper is in preparation. In this paper it is explained how and
when it is possible that the inviscid theory correctly predicts the coherent
structures generated by viscous two-dimensional flows. This represents an important
step in bridging the gap between the theory and the behaviour of realistic,
dissipative flows.
Low order statistical-dynamical climate models
For two reasons it is an interesting objective to formulate low-dimensional
models of the atmosphere which, in spite of their simplicity, retain a considerable
degree of realism in the description of mean states as well as internal variability.
First, they are more transparent than the ever more complex state-of-the-art
GCM's and thereby serve as tools for deepening our understanding of the behaviour
of GCM's and the atmosphere itself. Furthermore, they are fast so that they
can be used as part of intermediate complexity models by which we can examine
the ultra-long timescales of the climate system. With this in mind, and based
on previous encouraging work during the stay of Achatz
at KNMI and after his return to the Leibniz-Institut für Atmosphärenphysik
(Germany), a reduced model has been developed which is based on empirical orthogonal
functions (EOF). Such models are able to describe complex systems with high
efficiency. The novelty
of the work undertaken here was that the non-linear dynamics of the model is
based on the primitive equations (PE) so that also tropical dynamics is captured
well. Furthermore the model goes beyond previous counterparts by also describing
a seasonal cycle. Basis is a new numerical PE algorithm, which retains internal
gravity waves but is filtered with respect to the external wave type. This serves
as framework for the definition of a PE-based total energy metric for the determination
of the EOF's from some data set. The dataset used is a long run of ECHAM3 (Hamburg
Version of the ECMWF Model). External forcing and linear dynamics of the model
are empirical. They optimise instantaneous tendencies in the ECHAM3 data. Investigations
of the behaviour of the model show good simulations of first and second moments
in the ECHAM3 data and their respective seasonal cycles. Recurrent anomalies
can be reproduced. This is especially the case for a small model version, based
on as few as 30 patterns. The model is presently employed in studies on atmospheric
dynamics. The possibility of using them as a dynamical core of an intermediate
complexity climate model is presently under investigation.
By studying the properties of a two-layer quasi-geostrophic version of a low order dynamical-empirical EOF model a link is established between atmospheric ultra-low frequency variability (ULFV) and the occurrence of homoclinic dynamics. Uncoupled atmosphere models possess significant variability on very long time scales (years to decades), which must be generated by internal atmospheric dynamics. The mathematical structure of this long-timescale variability is investigated. The ten-dimensional (10D) version of the model possesses both nonzero ultra-low frequency variability and some realistic short timescales. The essence of the ultra-long timescale behaviour of the 10D model, which manifests itself as bursts in the atmospheric turbulent energy, can be represented by a 4D subsystem. In this subsystem, strong evidence for the existence of a homoclinic orbit is found. The chaotic dynamics generated by the homoclinic orbit explains the observed long-timescale features of the model. It is shown that hints of homoclinic dynamics can also be found in more complex models.
Greet de Graaf / Brigitta
Kamphuis
Updated on July 10, 2002