Geoscience Reference
In-Depth Information
Since the entropic balance theory is found to fit well with all analyzed results of
tornado and visual observations, it is suggested to use the entropic balance equation
as a constraint for variational data assimilation in future development as a challenge.
18.1
Introduction
Tornado data assimilation requires an appropriate dynamical model and observa-
tional input data. The dynamical model utilized in current applications is a full set
of governing equations of motion, mass continuity, thermodynamics, and cloud-
physics. The dynamical model has been tested by tornado simulations. Starting from
the numerical simulation of a supercell storm by
Klemp and Wilhelmson
(
1978
),
many simulations were successful in reproducing supercells and mesocyclones, but
not tornadoes. Indeed,
Burgess
(
1997
) concluded from his analysis that tornadoes
developed from only 20 % of mesocyclones, suggesting that tornadogenesis is
still unsolved. Recent advanced observations and successful computer simulations
of tornadogenesis (
Wilhelmson and Wicker 2001
;
Noda 2002
) clearly suggested
super high spatial resolution and the associated temporal resolution are required to
solve a full set of governing equations of motion, mass continuity, thermodynamics
and cloud-physics by computer. For example, in the first successful simulation of
tornadogenesis for a few hours of evolution time, Noda used ARPS (Advanced
Regional Prediction System, Version 4.5;
Xue et al. 1995
) with horizontal grid
size of 70 m, not nested, and 45 levels of vertical grid, with 10-m spacing near
the ground, with associated time increments on the time split integration scheme
(
Klemp and Wilhelmson 1978
;
s, 0.18 s; the former is for sound wave and
the latter for others). The simulation took about 720 h on the IBM Regatta computer
of 16 nodes at Tokyo University. It will take several days or weeks of computer
execution time to simulate tornado evolution of a few hours by the supercomputers
currently available for weather forecasting. These requirements prohibit direct
application of the current full simulation model for practical operational use under
present computing availability.
Also, recent advanced observations such as phased-array Doppler radar and
mobile X-band radars have revealed spatial and temporal details of similar high
resolutions that are important for tornadogenesis and should be properly reflected in
data assimilation. However, again, the presently-available computing power is not
sufficient for practical operational forecasting of tornadoes with numerical models.
So, it became the first author's motivation to develop a simple but accurate theory
that captures all essential processes of tornadogenesis.
The molecular Reynolds number is extremely large (normally
t D
0:03
>10
7
/
for most
of atmospheric weather systems, and the molecular viscosity is neglected. It allows
us to define an appropriate Lagrangian based on the variational principle instead
of use of all governing equations of motion, mass continuity, thermodynamics,
and cloud physics. It leads to a sole diagnostic Euler-Lagrange (E-L) equation
among all other prognostic E-L equations. The diagnostic E-L equation, first
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