Infrared geosynchronous satellite data with an interval of five minutes between images are used to estimate thunderstorm top ascent rates on two case study days. A mean vertical velocity of 3.5/ms for 19 clouds is calculated at a height of 8.7 km. This upward motion is representative of an area of approximately 10km on a side. Thunderstorm mass flux of approximately 2x10 to the 11th power/gs is calculated, which compares favorably with previous estimates. There is a significant difference in the mean calculated vertical velocity between elements associated with severe weather reports (w bar=4.6/ms) and those with no such reports (2.5/ms). Calculations were made using a velocity profile for an axially symmetric jet to estimate the peak updraft velocity. For the largest observed w value of 7.8/ms the calculation indicates a peak updraft of approximately 50/ms

Adler, R. F.

Fenn, D. D.

English

NASA Technical Reports Server

Paper No. 2
THUNDERSTORM VERTICAL VELOCITIES AND MASS FLUX ESTIMATED
FROM SATELLITE DATA
Robert F. Adler, Laboratory for Atmospheric Sciences, Goddard Space Flight
Center, NASA, Greenbelt, Maryland and Douglas D. Fenn, GE/MA TSCO, Belts-
ville, Maryland
ABSTRACT
Infrared geosynchronous satellite data with an interval of five
minutes between images are used to estimate thunderstorm
top ascent rates on two case study days. A mean vertical velocity
of 3.5ms -1 for 19 clouds is calculated at a height of 8.7km. This
upward motion is representative of an area of approximately 10kin
on a side. Thunderstorm mass flux of approximately 2 x 1011 gs -1
is calculated, which compares favorably with previous estimates.
There is a significant difference in the mean calculated vertical ve-
locity between elements associated with severe weather reports
(_= 4.6ms -1) and those with no such reports (2.5ms-I).
Calculations were made using a velocity profile for an axially
symmetric jet to estimate the peak updraft velocity. For the larg-
est observed w value of 7.8ms -1 the calculation indicates a peak
updraft of approximately 50ms -1.
1. INTRODUCTION
In the current paper we present the results of using a simple method to estimate
thunderstorm cloud-top vertical velocity from SMS/GOES rapid-scan (5 minute inter-
val) window channel infrared (IR) data. Time rate of change of cloud-top minimum
equivalent blackbody temperature (TBB) is converted to vertical velocity w by
(0T)-' dTBBw = -- --, (1)0z dt
where the lapse rate is determined from rawinsonde data. In the following sections
the calculated vertical velocities are compared for clouds with associated severe
weather reports and for those with no such reports, and the computed values are also
compared with previous estimates of thunderstorm vertical velocities.
2. DESCRIPTION OF ANALYSIS TECHNIQUE
The analysis of the digital satellite data was performed on the Atmospheric
and Oceanic Information Processing System (AOIPS), an interactive image analysis
system described by Billingsley (1976). Sequences of images are enhanced, ele-
ments are isolated and identified, and their maximum gray level (minimum TBB)
recorded. The analysis of the thunderstorms used in this study (on April 24, 1975
and May 6, 1975) was part of a larger effort (see Adler and Fenn, 1978). On each
https://ntrs.nasa.gov/search.jsp?R=19790012464 2020-03-20T18:22:58+00:00Z
of thesestudydays an area of convection was monitored during a set period of
time (approximately 4 hours). Thunderstorm elements were defined by the tech-
nique described by Adler and Fenn (1976, 1978) and time histories of each ele-
ment were determined.
It should be emphasized here that not all thunderstorms can be observed at
middle tropospheric heights. This is because they are often hidden by dense cirrus
clouds produced by previous convection. In the two case studies that will be de-
scribed here, of the thunderstorm elements defined above 10km (Taa = 226K), only
about 25-30% could be detected at lower heights.
3. VERTICAL VELOCITY ESTIMATES
a. Sources of Error
The vertical velocity estimates presented in this paper are subject to error be-
cause of errors in the satellite radiance measurements and possible unrepresentative-
ness of the data. A possible source of error is in the cloud emissivity. For thick
water clouds such as we are dealing with, the emissivity (e) is very close to unity.
In order to use TBB in place ofT in Equation (1), e = 1 must be assumed. For
ice clouds, especially thin cirrus clouds, emissivity can be substantially less than
1.0. As the thunderstorm top glaciates, the change from water to ice may reduce
the cloud top emissivity and TaB will be larger than T, the cloud top temperature.
This effect, however, appears to be small and will not affect the vertical velocity
calculations. This conclusion is based on calculations made with the help of tables
presented by Hunt (1973) and on results presented by Cox (1977).
The most serious source of error stems from the satellite data itself. The IR
channel has an instantaneous field of view (IFOV) of 8km on a side at the sub-
satellite point and approximately 10km at 40N. As noted by Negri, et al., (1976)
the use of SMS/GOES IR temperatures to determine thunderstorm height results
in underestimates, especially for small elements. In comparison with radar meas-
urement of thunderstorm tops, the satellite underestimation is approximately 2kin.
This effect is related to two factors. First, the satellite, because of its rather large
IFOV, is averaging over an area approximately 100km 2 compared with the radar
observation, which is applicable to an area closer to I km2. Thus the radar will be
identifying smaller, higher features, because of its better resolution. The second
factor is inadequate sensor response when going from a warm (low) to a cold (high)
target (Negri, et al., 1976). In general, the bias in the estimation of storm height
will not affect the vertical velocity calculation. However, it may affect the height
to which the velocities are assigned.
Other errors might arise from the use of inaccurate lapse rates in Equation (1).
In the calculations to follow we use a smooth profile which is a mean of the am-
bient and the moist adiabatic lapse rate. The calculations can be shown to be
rather insensitive to variations in the lapse rate. Using either the moist adiabatic
or the ambient lapse rate instead of the average of the two produces only 10% dif-
ferences in the calculated velocities. The final validation of the calculated vertical
velocities must come through a careful comparison with radar, aircraft or satellite
stereo observations.
b. Vertical Velocity Results
Fourteen elements on May 6, 1975 and ten on April 24, 1975 were analyzed.
Minimum TBB as a function of time for each element was plotted and dTaa/dt
valueswerecalculated.Thewarmestor lowest of the monitored elements was at
TBB = 260K (about 6kin). Not all thunderstorms could be observed from that
point upward through the remainder of the troposphere. Some elements were
blocked out by other storms; other elements were not detected until they pene-
trated middle level cloud fields.
Vertical velocities were calculated every 5 K in the vertical for each cloud ele-
ment or thunderstorm using Equation (1) and a lapse rate halfway between ambi-
ent and moist adiabatic. The mean w was then calculated for various categories of
clouds to produce composite profiles. The results for the May 6 case are shown
in Figure 1. Profiles are shown for thunderstorms associated with severe weather
reports (based on National Severe Storms Forecast Center logs) and those with no
accompanying reports. The numbers in parentheses indicate the number of cases
constituting each mean or composite vertical velocity. The mean profile of all
cases is also shown.
The vertical velocities in Figure 1 and the calculated divergence noted above
are applicable to an area of about 10km on a side. The calculated vertical veloci-
ties do not represent updraft core velocities, which could be an order of magnitude
larger when measured on a horizontal scale of 1 km (see Section 5).
A similar diagram for April 24, 1975 case is given in Figure 2. The convection
of interest on this day was centered in southwestern Missouri. The composite w
profiles for three categories are displayed. The additional category is for weak ele-
ments which did not reach a height of 10kin (as determined by the TBB values).
In the layer from 7 to 9km the average w is approximately 1.Sms -1 for those
storms. This is significantly lower than the composite for "non-severe" elements
in either Figure 1 or 2.
The 235-240K level (_8.7km) is representative of the layer of relatively large
vertical velocities on both days. Figure 3 shows the frequency distribution of the
19 elements or clouds for these two days. The hatched portion of the histogram
contains the values for the severe weather elements. The average w for all 19 cases
is 3.5 ms -1. The severe and non-severe elements have average values of 4.6 and
2.5 ms -1, respectively. The severe thunderstorms dominate the high end of the dis-
tribution where six out of seven cases with w )- 4ms -l are associated with severe
weather reports.
c. Mass Flux Calculation
Because of the values of w calculated in the last section are representative of
an area larger than a typical thunderstorm updraft, vertical volume or mass flux
calculations can be simply made through the formula,
4
F m = pAw, (2)
where F m is the vertical mass flux, p is the density, and A is the area. For the
235-240K layer (_8.7km) p is assumed to be 5 x 10-4gcm -3, and A is assigned
a value of 100km 2 for the area of the satellite IFOV.
With the given values for p and A the mean w for all storms of 3.Sms -1 is
converted to a mass flux of 1.8 x 101tgs -1. The mean w of severe elements
(4.6ms -1) is equivalent to a mass flux of 2.3 x 1011gs -l. These magnitudes are
for the mass flux through a given layer associated with a growing thunderstorm
top. The calculated values compare favorably with results presented by other in-
vestigators. Kropfli and Miller (1976) calculate a value of 1.9-2.0 x 10 llgs'l be-
tween 8-9km for a northeast Colorado storm calculated using vertical velocity
9
inferredfromdual-Dopplerradardata.AuerandMarwitz(1968)presentresultsof
thecloudbasemassfluxinto18hailstormsonthehighplainsdeducedfromair-
craftmeasurements.Theiraveragevalueis2.3x 1011gs-1.Therefore,it appears
thattheupwardflowdeducedfromthesatelliteobservationsisof areasonable
magnitudewhencomparedto calculationsandobservationsonapproximatelythe
samescale.Inferencesabouthemagnitudeof themaximumupdraftarepresented
inSection5.
4. EXAMPLEOFINTENSETHUNDERSTORM
OnApril24,1975aseverethunderstormcomplexdevelopedoverextreme
northeasternOklahomain thelateafternoonandmovedintosouthwesternMis-
souriaroundsunset.Themostsignificantsevereweatherassociatedwiththesys-
temwastheNeosho,Mo.tornadowhichtouchedownatapproximately0040
GMT,April25. Byfollowingtheevolutionof thestormsystembackwardsintime,
theinitialintenseconvectioncanbedetectedanditsassociatedrapidcloudtop
growthcalculated.
TheNeoshocloudsystemwasdesignatedcloud18aspartofa largerstudy
of thisday.Figure4 exhibitsminimumcloudtopTBBasafunctionof timefor
cloud18in itsearlystages.Thetemperaturedropsprecipitouslybetween2200
and2220GMTwithamaximumcalculatedrateof4K min-l. Thedropin tem-
peraturebetween260Kand220Ktakesonlyalittlemorethan15minutes.This
typeof rapidchangemphasizestheimportanceof shortintervaldatato study
andmonitorthunderstormactivity.
Usingalapseratevaryingfrom7.8km-l at260K,to 8.6Kkm-1at240K,to
8.0Kkm-1at 215KtheverticalvelocitywascalculatedusingEquation(1). The
maximumcalculatedwis7.8ms-l atabout9kin.
5. INTERPRETATIONFCALCULATEDVERTICALVELOCITIESINTERMS
OFMAXIMUMUPDRAFT
Theverticalvelocitiespresentedin theprevioussectionsof thispaperaremean
velocitiesoveranareaequivalentto thesatelliteinstantaneousfieldof view(IFOV),
whichin thiscaseisapproximately100kin2. In thetemperaturerange235-240K(~8.7kin)the19observedw'sbasedonthesatellitedatarangedfrom1.2to7.8
ms-l, withameanof 3.Sins-1. Althoughtheseareverylargevalueswhencom-
paredto typicalsynoptic-scalew's,theyaresm_dlwhencomparedto maximum
thunderstormupdraftmagnitudes.Thunderstormupdraftscanreachmagnitudes
of 10ms-l veryeasilyandaretypically30ms-1 insupercellthunderstorms(Brown-
ing,1977;Davies-Jones,1974).These large updraft values are probably representa-
tive of an area approximately 1 km 2. Thus there are two orders of magnitude dit:
ference in the area covered by the estimated w's obtained from the satellite data
in this study and the area covered by the peak updraft velocity.
Assuming axial symmetry and a knowledge of the shape and size of the radial
profile of vertical velocity, one can make an estimate of the maximum updraft mag-
nitude. The formula chosen in this study, based on Kyle et al., (1976) and Schlicht-
ing (1978) is
w = w o e-a(r/R) 2, (3)
where w o is the peak w, r is the radial distance, R is the radius of the updraft, and
the constant a = 2.3.
10
IntegratingEquation(3)overacircularareaofradiusrl, anddividingthere-
sultbytheareaof theintegrationproducesanexpressionfor themeanwoverthe
area,i.e.,
_/= Wo /-_-1/2
-- [1 -e-a(rl/R)2].
a
(4)
The size of thunderstorm updrafts is highly variable (Browning, 1977). Based
on the discussion of updraft sizes by Browning (1977) and an examination of cross-
sections by Kropfli and Miller (1976) and Ray (1976) of thunderstorm vertical mo-
tions deduced from Doppler radar data, an updraft radius of 3km is reasonable.
For an area of 100km 2 (approximately equal to the IFOV), the equivalent
radius of integration is 5.6km. Thus with R = 3km and r I = 5.6km,
= 0.12 w o. (5)
Thus, with all the assumptions as to profile shape and updraft size, Equation (5)
indicates that the mean _ of 3.5ms -1 is equivalent to a w o of 29ms -l and the 7.8
ms -1 value from the Neosho storm (Section 4) is equivalent to a w o of 65ms -1.
For an R of 3.5km, instead of 3km, the 65ms -1 value in the largest paragraph
would drop to 46ms -1. It is obvious that the calculated wo is sensitive to the size
of the updraft.
Despite the variability and sensitivity of the w o calculations, it is evident that
the satellite observations on a scale of 10km are producing _ of up to approxi-
mately 8ms -1, and this can be interpreted as being roughly equivalent to a maxi-
mum updraft of 50ms -1 in intense thunderstorms.
6. SUMMARY
Rapid-scan (5 minute interval) SMS/GOES IR data have been used to estimate
thunderstorm top ascent rates for severe and non-severe thunderstorms on two case
study days. On both days examined (May 6 and April 24, 1975) the thunderstorm
elements with associated severe weather reports have larger average w's. The severe
and non-severe elements had mean w's of 4.6 and 2.5ms -1. Intensity of convection
appears to be correlated with the occurrence of severe weather, and the satellite
data appear to be capable of quantifying the convection intensity.
The calculated vertical velocities are representative of an area (100 km 2) roughly
equivalent to the satellite instantaneous field of view (IFOV). Mass flux estimates
of approximately 2 x 1011gs -1 are calculated, which are reasonable in comparison
with other estimates.
Calculations were performed to estimate the peak updraft velocity from the
satellite based values (averages over 100 km 2 areas). With a reasonable value of R
(3-3.5km), the _ of 7.8ms -1 for the Neosho storm produces an estimate of approx-
imately 50ms -1 for w o.
REFERENCES
Adler, R. F. and D. D. Fenn, 1976: Thunderstorm Monitoring from a geosynchron-
ous satellite. In Preprints of 7th Conference on Aerospace and Aeronautical
Meteorology, 307-311.
11
Adler,R.F.,andD.D.Fenn,1978:"Satellite-basedThunderstormIntensityPar-
ameters,"NASATM78094(alsosubmittedto J. Appl. Met.; Preliminary ver-
sion of paper in Tenth Conference on Severe Local Storms, October 1977),
42 p.
Auer, A. H. and J. D. Marwitz, 1968: Estimates of air and moisture fllux into hail-
storms on the high plains. J. Appl. Met., 7, 196-198.
Billingsley, J. B., 1976: Interactive image processing for meteorological applications
at NASA/Goddard Space Flight Center. In Preprints of 7th Conference on
Aerospace and Aeronautical Meteorology and Symposium on Remote Sensing
from Satellites, 268-275.
Browning, K. A., 1977: "The Structure and Mechanisms of Hailstorms," In Hail:
A Review of Hail Science and Hail Suppression, A.M.S., Meteorological Mono-
graphs, 16, No. 38, 1-43.
Cox, S. K., 1977: Satellite derived cloud cluster cloud-top heights, l lth Technical
Conference on Hurricanes and Tropical Meteorology, Miami Beach, Florida,
355-356.
Davies-Jones, R. P., 1974: Discussion of measurements inside high-speed thunder-
storm updrafts. J. Appl. Met., 13, 710-717.
Hunt, G. E., 1973: Radiative properties of terrestrial clouds at visible and infrared
thermal window wavelengths. Quart. J. R. Met. Soc., 99, 346-369.
Kropfli, R. A. and L. J. Miller, 1976: Kinematic structure and flux quantities in a
convective storm from dual-Doppler radar observations. J. Atmos. Sci., 33,
520-529.
Kyle, T. G., W. R. Sand, and D. J. Musil, 1976: Fitting measurements of thunder-
storm updraft profiles to model profiles. Mon. Wea. Rev., 104, 611-617.
Negri, A. J., D. W. Reynolds, and R. A. Maddox, 1976: Measurements of cumulo-
nimbus clouds using quantitative satellite and radar data. In Preprint Volume
of Seventh Conference on Aerospace and Aeronautical Meteorology, 119-124.
Ray, P. S., 1976: Vorticity and divergence fields within tornadic storms from dual-
Doppler observations. J. Appl. Met., 15, 879-890.
Schlichting, H., 1968: Boundary Layer Theory. McGraw-Hill, Chap. 24.
12
215_ I I
11 x.11_' "
14)_
(5)_'
(6) /
!
2_
16)_
2, /
131M
2_ I I I
I I I I I
MAY 6, 1975
MEAN FOR SEVERE ELEMENTS
MEAN FOR ALL CASES
MEAN FOR NON-SEVERE
ELEMENTS
,(4)
4)
(4)
I I I I
2 3 4 5 S 7
VERTICAL VELOCITY. w (ms -I )
Fig. l-Composite vertical velocity
profiles for May 6, 1975. Numbers in
parentheses are the number of cases.
,7,
:C
210 t I I I I [ I _112
/215 I_ APRIL 24. 1975
2 (5) _ MEAN FOR SEVERE _ 11
!x--x MEAN FOR NON.SEVERE220 ELEMENTS
12J X (5) 0,- --e MEAN FOR WEAK ELEMENTS
225 10
( -
23s s _l /--
245 141 141
250
255
260 I I I I I I I e
1 2 3 4 5 6 7
w(ms -1 )
Fig. 2-Composite vertical velocity
profiles for April 24, 1975.
0 i 2 3 _ 6
_rELLLTt eASEO tSTI_ATt OF WI_ 1)
I
V//_
v///
V/l, '
7 8
Fig. 3-Frequency distributions of
estimated vertical velocities at 8.7km
for clouds on April 24 and May 6,
1975. Hatched portion of histogram
indicates thunderstorms with accom-
panying severe weather reports.
221
' [ I I i I i [ f I ' I
CLOUD18
(36=48'N,85' 09'Wl ,T
APRIL24, 1975
2220 Z_ ZJ Z_ _ lira
Fig. 4-Minimum equivalent blackbody
temperature (TBB) as a function of
time for cloud 18 on April 24, 1975.
13


Thunderstorm vertical velocities and mass flux estimated from satellite data

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