ELFT HÍRADÓ

[StatFizSzeminar <statfiz AT glu.elte.hu>]

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             ELTE TTK Fizikai Intézet
         STATISZTIKUS FIZIKAI SZEMINÁRIUM


                PÁROS SZEMINÁRIUM

                2018. április 18.
                  szerda, 11.00 


                  Gábor Drótos

            University of the Balearic
                Islands and CSIC



   "A coarse-grained finite-time description of 
        open flows, with an  introduction
    to the conceptof Lagrangian flow networks"

In fluid flows, or in the phase space of any dynamical
system, the time evolution of the trajectories can be 
regarded as a transport phenomenon, described by the 
Perron--Frobenius operator. Its discretized version gives
the amount of (phase space) volume transported from one
box of the domain to another. The recognition that this
discretized operator can be considered to be the connec-
tivity matrix of a weighted directed network, a Lagrangian
flow network, led to particularly successful applications
of this coarse-grained description. Beyond identifying 
relationships between traditional quantifiers of chaos and
network characteristics, techniques developed for the inves-
tigation of networks, like community detection, have proven
to be remarkably useful from a dynamical systems point of
view, like for the identification of coherent regions.

The focus has so far been almost exclusively on volume-pre-
serving closed flows. In one of our research directions, we
study how characteristics of open flows can be defined in a
coarse-grained finite-time description. In particular, we
consider the escape rate and the fractal dimension beyond
the finite-time largest Lyapunov exponent, and illustrate
numerically that the Kantz--Grassberger relation, linking
these quantities on infinitesimally small spatial scales for
asymptotically long times, is approximately satisfied by the
coarse-grained finite-time counterparts of these quantities.
What is interesting is that these quantities have a spread
throughout the domain of the flow, but such that the Kantz-
Grassberger relation is approximately fulfilled.


                 2018. április 18.
                  szerda, 12.10 


                   Tamás Bódai

               University of Reading

        "Linear response theory applied to
                 geoengineering"



We investigate in an intermediate-complexity cli-
mate model (I) the applicability of linear response
theory to a geoengineering problem and (II) the suc-
cess of the considered geoengineering method. The 
geoengineering method is framed here as a special 
optimal control problem, which leads mathematically
to the following inverse problem. A given rise in 
carbon dioxide concentration would result in a 
global climate change with respect to an appropriate
ensemble average of the surface air temperature. We
are looking for a suitable modulation of solar forcing
which can cancel out the said global change, or mod-
ulate it in some other desired fashion. It is rather
straightforward to predict this solar forcing, consid-
ering an infinite time period, and we will spell out an 
iterative procedure suitable for numerical implementa-
tion that applies to finite time periods too.

Regarding (I), we find that under geoengineering, i.e.
the combined greenhouse and solar forcing, the actual
global mean surface temperature response asymptotically
is not zero, indicating that the linear susceptibility
is not determined correctly. This is due to a signifi-
cant quadratic nonlinearity of the response under system
identification achieved by a forced experiment. This non-
linear contribution can in fact be easily removed, which 
results in much better estimates of the linear suscepti-
bility, and, in turn, in a five-fold reduction in a resi-
dual global mean surface temperature response under geo-
engineering. Regarding (II), however, we diagnose this 
geoengineering method to result in a considerable spatial
variation of the surface temperature anomaly, reaching more 
than 2 K at polar/high latitude regions upon doubling 
the carbon dioxide concentration, even in the ideal case 
when the geoengineering method was successful in cancel-
ing out the response in the global mean. In the same 
time, a new climate is realised also in terms of e.g. an
up to 4 K cooler tropopause or drier/disrupted Tropics,
relative to unforced conditions.

https://arxiv.org/abs/1803.09606



1117, Budapest, Pázmány P. sétány 1/A, Északi tömb 2.54
        honlap: http://glu.elte.hu/~statfiz

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