Synoptic-scale kinetic energy budgets are being computed for three cases when large areas of intense convection occurred over the Central United States. Major energy activity occurs in the storm areas

Fuelberg, H. E.

English

NASA Technical Reports Server

Paper No. 4
KINETIC ENERGY BUDGET STUDIES OF AREAS OF CONVECTION
Henry E. Fuelberg, St. Louis University, St. Louis, MO
ABSTRACT
Synoptic-scale kinetic energy budgets are being com-
puted for three cases when large areas of intense con-
vection occurred over the Central United States. Ma-
Jor energy activity occurs in the storm areas.
INTRODUCTION
Kinetic energy budget studies have been performed mostly
on synoptic-scale systems such as cases of cyclogenesls; few
studies have dealt with mesoscale phenomena. Fuelberg (1977) and
Fuelberg and Scogglns (1978) studied the energy variability of
the synoptic-scale flow in which convection was imbedded. Large
areas of intense thunderstorms seemed to influence the surround-
ing synoptic-scale environment. The present research involves
additional studies of synoptic-scale kinetic energy variability
during periods of intense thunderstorms.
THEORY
The kinetic energy equation in isobaric coordinates is :
DE _0k
f f : Tp + : f
op op op op
(a) (b) (c) (d) (e)
1
where f f = _ fff dxdydp, _ is the frictional force, k is hor-
op
izontal kinetic energy per unit mass, and A is the area of com-
putation O. Local changes in kinetic energy for a fixed volume,
term (a) above, are due to four processes. Term (b) represents
kinetic energy generation due to cross contour flow. Terms (c)
and (d) are horizontal and vertical flux divergence of kinetic
energy. Term (e), called the dissipation term, represents a
transfer of energy between resolvable and unresolvable scales of
mot ion.
PROCEDURES
Rawinsonde data are objectively analyzed onto a grid system
that encloses the area of study. Gridded fields of the input
data are obtained at the surface, and then at 50 mb intervals up
21
https://ntrs.nasa.gov/search.jsp?R=19790012466 2020-03-20T18:23:06+00:00Z
to I00 mb. Vertlcal motions are computed uslng the klnematlc
method. By using finite difference techniques, values of the
budget terms are computed at individual grid points at 50 mb
intervals. Grid point fields of the budget terms are related to
storm location, and the grid point values can be averaged In
various ways.
Three case studies are being investlgated--the first and
second Atmospheric Varlabillty and Severe Storm Experiments
(AVSSE I, 27-28 April 1975; and AVSSE If, 6-7 May 1975) and the
seventh Atmospheric Variability Experiment (AVE VII, 2-3 May
I_78).
RESULTS
Kinetic energy budgets have already been computed for the
AVSSE I and II periods. Brief results of these studies wlll be
described.
a. The AVSSE II Period. During AVSSE II, intense thunder-
storm activity formed in the Midwest and in central Texas along
a dry llne. To isolate energy processes near the convection from
processes in non convection areas, grid point budget values were
averaged to give kinetic energy budgets overs mall areas that Just
enclosed the convection. The budget areas moved as the convec-
tion moved.
Thunderstorm activity began near 1500 GMT 6 May 1975,
reached peak intensity (18.6 km tops) and areal coverage near
2100 GHT, and had dissipated by 0300 GMT 7 May. The pressure-
time cross-sectlon of Fig. i indicates that average synoptic-
scale vertical motion wlthln the area was a maxlmum upward value
(_<0) at 2100 GMT and later changed to downward motion. The llt-
erature suggests that dlabatlc heating associated with convectlon
is probably responsible for inducing these changes. Flg. i also
reveals that kinetic energy from the lower and mlddle troposphere
is transported to hlgher levels of the atmosphere.
Dramatic changes in the kinetic energy budget also occur.
Destruction of kinetic energy by cross contour flow (- values)
near the level of the Jet stream changes to strong generation of
kinetic energy near 2100 GMT and then tapers off and changes
sign (Fig. 2). Fuelberg and Scogglns (1978) observed slmilar
variations in energy generation during AVE IV. Using mesoscale
data, Tsul and Kung (1977) found that periods of active convec-
tion were times of strong generation of kinetic energy, but that
destruction of kinetic energy was dominant near the tlme of
storm passage.
The profile of horlzontal flux divergence of kinetic energy
at peak storm intensity (2100 GMT) is conslderably different from
that at earlier and later times (Fig. 3). Strong upper level
export of energy (+ values) is dominant at 2100 GMT. The fluc-
tuatlons in the transport term seen in the present case are sim-
ilar to those observed during the AVE IV squall llnes (Fuelberg
and Scoggins, 1978).
22
100
20¢
3O(
400
SO0
GOO
TOO
8O©
90C
0
/ !, / ..: _ ....-.- .S
o t t _/2".\t ...,_.o
-I ........ ',. !; .'/.,' ".'..'4. i _ !
•.,,.......-,.._ ,,;.:.,...............,...:,,.,,.,.,,_III/_2
.. _ i .5
. .S............ :5 ...... _ ......... - .S "" .S
' 6/12 ' e#15 6#10 6121 7/00 7/03
Fig. 2. Pressure-time c_o_s
section of term -V.V_
for the Texas convec-
tion area. W m-2(lO0
mb) -i
10(]
20C
3oc
40O
Soo
600
#00
80o
90C
Fig. i. Pressure-time cross
section of vertical
motion (u) for the Tex-
as convection area.
_b S -| •
l -30-2CI40 0 10 10 0 ' 1
:::::::::::::::::::::::::::::::::::::::..........:
.o.I-,o....======================
6112 6/15 6/111 8#21 7100 7/03
23
-1S -10 0 10 0
....-............. _ :, _/ ..::.:::!::::...........
./' ., ",. ,....,.- ,.... , .
:....... -: :, _.."--':::--_..-_i'o:" / ............ ' .......... :'.,. "--..-::':::':. _-_lS
- 5 --.. "'::::_-::.---" ....................... :::::::::::::::::::::::::
0
0
6112 6115 6118 6121 7/00 7103
1001
200
30O
Fig. 4. Pressure-ti_e cros_4oo
section of the dis- soo
slpatiou term for 6ooI
the Texas convection
area. W m -2(I00 mb)-_°°
tO0
goo
Fig. 3. Pressure-time _ro_s
section of term V.kV
for the Texas convec-
tion area. W m-2(lO0
rob}-i .
10 20 30 2010 0 -10 -20 -25 -20 -15
,".::"/:"::_-,il//
('f: !,",,.,'/.' -'..,.,'...,,,..:::..'...._---_:,,, ,. ,,,., ,. ...... -: ::,-.y-
7103
-- 6112 6115 6118 6121 7100
The dissipation term reveals that energy transfer between
resolvable and unresolvable scales of motion is large in the syn-
optlc-scale environment of the storms (Fig. 4). The net effect
of all motions is a transfer of energy from resolvable to un-
resolvable scales (- values) after 1800 GMT. Before maximum
storm intensity, the unresolvable scales of motion are a source
of synoptlc-scale kinetic energy.
A tabulated kinetic energy budget of this convection area
is given in Table 1. Generation of kinetic energy by cross
contour flow and dissipation to subgrld scales of motion are the
two most important processes. The magnitudes of the energy pro-
cesses occurring in the synoptic-scale environment of the convec-
tion are larger than those observed near many mature cyclones.
Table 1. Average kinetic energy budget for the limited
area enclosing the convection in Texas at 2100 GMT 6
,X_y 1975. The area is 1.5 x 10" m2.
Layer K _K/_t V. kV _k/_ -V.V_ D
(mb) (105jm -2 ) (Wm -2 ) (Wm -2 ) (Wm -2 ) (Wm -2 ) (Wm-2 )
Sfc-700 0.5 -0.9 -1.2 2.0 1.0 -I.i
700-400 6.5 8.5 i0.0 8.4 31.8 -4.9
400-100 24.1 2.6 5.9 -10.4 52.4 -54.4
Total 31.1 10.2 14.7 0.0 85.2 -60.4
b. The AVSSE I Period. A llne of severe thunderstorms
stretching from Nebraska into Texas formed along a cold front
during the AVSSE I period. The results of this section demon-
strate a different procedure by which the kinetic energy budget
of storm areas is being investigated.
Values of Manually Digitized Radar (MDR) data are assigned
to each grid point at each observation time. The average of each
budget term is computed for various categories of MDR intensity
by combining all observation times.
The average budget for grid points having no convection
during AVSSE I is given in Table 2A while the average budget for
grid points of moderate and intense convection (MDR 4-9 of the
old MDR scheme) is given in Table 2B. Energy processes occurring
during convection are much larger than those observed for non
convection. The grid points associated with convection are char-
acterized by strong destruction of kinetic energy by cross-con-
tour flow and by transfer of energy from subgrid to grid-scale
motions (positive dissipation).
c. Other Studies. Beside the results presented in this
brief report, spatial fields of the energy budget terms are being
examined for continuity and their relation to storm activlty and
other map features. Energy budgets for individual times of each
case study are being compiled and examined for temporal vat-
24
Table2-A. Averagekinetic energybudgetfor grid points
havingno convection during AVSSE I (26-27 April 1975).
The number of grid points is 138.
-4. -4. -_ -4,
Layer K _K/_t V •kV _k/_p -V •V_ D
(mb) (lOSjm -2) (Win-2) (_hn-2) (WN-2) (Win"L) (Win-2)
Sfc-700 2.7 -1.2 0.7 0.6 2.4 -2.3
700-400 7.1 1.5 8.1 0.6 9.2 1.0
400-100 14.4 4.4 -8.1 -1.2 -13.2 8.3
Total 24.2 4.7 0.7 0.0 -1.6 7.0
B. Kinetic energybudget for MDR 4-9 (43 grid points).
Sfc-700 2.7 -0.8 0.0 2.6 -3.9 5.7
700-400 9.9 7.0 -7.6 9.4 -2.8 11.6
400-100 19.1 9.4 -4.8 -12.1 -35.6 28.1
Total 31.7 15.6 -12.4 0.0 -42.3 45.4
lability. Results of the AVE 7 period (May 2-3, 1978) also are
being compiled.
CONCLUSIONS
The synoptic-scale kinetic energy budget of large areas
of intense convection is considerably different from that of
areas of non convection. Time series analysis of some budget
terms suggests thatthe energy variability is closely related to
the llfe cycle of the storms.
ACKNOWLEDGEMENTS
This research is sponsored by NASA under Contract NAS8-32838
and is under the auspices of the Aerospace Environment Division,
NASA Marshall Space Flight Center.
REFERENCES
Fuelberg, H. E., 1977: Atmospheric energetlcs in regions of
intense convective activity. NASA CR-2826 Marshall Space
Flight Center, Alabame, 136 pp.
, and J. R. Scogglns, 1978: Kinetic energy budgets
during the llfe cycle of intense convective activity. Mo___n_n.
Wea. Rev., i06, 637-653.
Tsul, T. L., and E. C. Kung, 1977: Subsynoptlc-scale energy trans-
formations in various severe storm situations. J. Atmos.
Sci., 3__4,98-110.
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Kinetic energy budget studies of areas of convection

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