Interest in the possibility of developing useful estimates of convective rainfall with Area-Time Integral (ATI) methods is increasing. The basis of the ATI technique is the observed strong correlation between rainfall volumes and ATI values. This means that rainfall can be estimated by just determining the ATI values, if previous knowledge of the relationship to rain volume is available to calibrate the technique. Examples are provided of the application of the ATI approach to gage, radar, and satellite measurements. For radar data, the degree of transferability in time and among geographical areas is examined. Recent results on transferability of the satellite ATI calculations are presented

Johnson, L. Ronald

Smith, Paul L.

English

NASA Technical Reports Server

ATTACHMENT B
ESTIMATION OF CONVECTIVE RAIN VOLUMES UTILIZING THE AREA-TIME-INTEGRAL TECHNIQUE
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L. Ronald Johnson and Paul L. Smith
Institute of Atmospheric Sciences
South Dakota School of Mines and Technology
501 East St. Joseph Street
Rapid City, South Dakota 57701-3995
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I. INTRODUCTION
Interest in the possibility of developing
useful estimates of convective rainfall with
Area-Time Integral (ATI) methods is increasing
(Smith et al., 1990; Atlas et al., 1990). In
,_ practice, the rainfall volume V from a convective
system over a time interval can be identified as:
V : _ _. Ai ati • (I)
1
Here Ai represents the area over which some
measured quantity exceeds a specified threshold
during the (centered) time interval ati between
observations. The measured quantity can be gage
'q rainfall rate, but radar reflectivity factor or
L_ satellite infrared temperature can also be used.
_; The summation extends over the duration T = _at i
of the rainfall event of interest. The quantity
o _ represents the average rainfall rate over the
._ identified area for the case under study. The
summation in (1) is identified as the ATI.
L_ The basis of the ATI technique is the
observed strong correlation between rainfall
volumes and ATI values. This means that rainfall
can be estimated by just determining the ATI
values, if previous knowledge of the relationship
to rain volume is available to calibrate the tech-
nique. The ATl's can be de_ermined from rain gage
data, if the gage density and time resolution are
sufficient (Doneaud et al., 1979, 1981); from
radar data (Doneaud et al., 1981, 1984; Lopez et
at., 1989); or from satellite infrared observa-
tions (Doneaud et al., 1987; Smith et al., 1990).
The respective thresholds involve the minimum
measurable amount of rainfall, a minimum radar
reflectivity factor, or a maximum IR brightness
temperature. Correlations found between ATI
values determined from any of these sources and
rainfall amounts determined either from gages or
radar data have been 0.9 or greater in every case
studied thus far. For radar ATI's in particular,
the correlation is typically 0.98.
This paper provides examples of the
application of the ATI approach to gage, radar,
and satellite measurements. For radar data, the
degree of transferability in time and among geo-
graphical areas is examined. Recent results on
transferability of the satellite ATI calculations
will be presented at the conference.
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2. APPLICATION TO RAIN GAGE DATA
With a dense network of recording gages,
ATI values can be calculated from (I) by con-
sidering each gage that receives a threshold
amount of rain during the specified time interval.
The area A i can be established using a method
such as Thlessen polygons. A rough estimate of
the ATI can be obtained by assuming each gage to
represent an equal area, if the network is not too
far from uniform.
Such an analysis was made for McKenzie
County, North Dakota, in the summer of 1972
(Doneaud et al., 1979). There were 22 recording
gages distributed over an area of 7374 km2, and
the readings were reduced to hourly data which
were used to obtain the gage ATI values. The
results were compared with estimates of 12-hr
rainfall over the area obtained from a separate
network of 65 non-recording gages (read twice
daily) over the same area. Figure I shows the
results of this comparison for the 18 rain days
having at least 3 gage-hours of recorded data.
(The synoptic classification in the figure is
not of concern here.)
The slope on this log-log plot is about
1.16. It was recognized that even 65 gages might
not give a good estimate of the areal rainfall,
especially for the smaller events, so a similar
analysis was done using radar to estimate the area
rainfall. That analysis yielded a slope of about
1.03 (agreeing better with those in Table I below).
To place an absolute scale on the abscissa,
note that I% of the possible gage-hour rain events
(x = 0.0 in Fig. 1) would correspond to an ATI of
about 885 km2.hr. On the ordinate in the figure,
y = 0.0 corresponds to a rain volume of 103 kt =
103 km2.nTn. The regression lines for the gage and
the radar estimates of the area rainfall would
intersect at about x = 1.0 (AT[ = 8850 km2.hr),
y = 1.5 (rain volume = 3.16 x 10W km2-mm); at that
point, the average rainfall rate over the rainy
area would be 3.6 mm hr-z. This compares favor-
ably with the average rates obtained using a
reflectivity threshold of 25 dBz to calculate the
ATI from radar data. This fact suggested that we
were on the right track, even though much concern
has recently been expressed about the selection
of the proper threshold (Atlas et al., 1990).
https://ntrs.nasa.gov/search.jsp?R=19900017133 2020-03-19T22:25:38+00:00Z
. , i J m I , J J I I I i * m
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LOGARITHMOF PERCENTAG_OFPOSSIBLEGAGERAINEVENTS
: Log-log plot of gage-estimated daily rain
for McKenzie County, North Dakota vs. the
percentage of possible gage-hours which actually
had rain. The abscissa can be converted into an
AT] as indicated in the text.
3. APPLICATION TO RADAR DATA
The most extensive uses of the ATI concept
to date have involved radar observations. For
example, during the Cooperative Convective Precipi-
tation Experiment (CCOPE) that occurred in 1981 in
southeastern Montana, radar volume-scan data were
recorded continually during declared "go" days by
a C-band radar system with 1° beamwidth. An
extensive study of the CCOPE radar echo clusters
was accomplished (Johnson and Hjelmfelt, 1990).
Since the life history oP each cluster was known,
calculation of the Area-Time Integrals for these
clusters was straightforward. Calculation of
rainfall amounts using a Z-R relationship
developed for the region (Z = 155 R 1.8, Smith
et al., 1975) was accomplished at the same time.
Figure 2 compares the resultant radar-
estimated rainfall to the Area-Time Integral for
865 clusters for which time histories are avail-
able. The log-log plot indicates extremely good
correlation over a range that exceeds five orders
of magnitude in rainfall. Regression analysis
demonstrates a correlation coefficient of 0.988,
with y-intercept of 0.326 log (km2 mm) and slope
of 1.088. The root-mean-square logarithmic error
of 0.145 translates to a factor 1.4. Given any
radar ATI that is computed using the same reflec-
tivity threshold of 25 dBz, a straightforward
rainfall estimate can be produced using Fig. 2.
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CCOPE 1981
o
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Slope = 1.988
)be° Intercept = 0.326
rms log error = 0.145
10 1 100 10' 1 = 10 s 104 10 s lOS
AREA TIME INTEGRAL (km 2 hr)
: Log-log scatter plot of AT] vs. radar
ed rain volume for echo clusters from
CCOPE. Solid line shows the regression result.
Such comparison of area-time integral
values to radar-estimated rain volumes using an
appropriate Z-R relationship has been accomplished
for several projects; the results are presented in
Table I. Each regression relationship like that
established in Fig. 2 results in a power-law
relation of the form
V = K x ATI b , (2)
where V is rain volume; K and b are constants
determined by regression. Specifically, b is
the slope and K is the antilog of the intercept.
TABLE 1
ATI-Radar Rainfall Parameters Determined
by Regression for Several Projects
and Different Radars
...................................................
PROJECT (YEAR) K b
NDPP (1972) 2.62 1.09
NDCMP (1980) 3.68 1.01
NDCMP (1981) 3.07 1.08
NDCMP (1982) 3.74 1.02
NDCMP (1984) 3.57 1.03
CCOPE (1981) 2.12 1.09
FACE (78, 79, 80) 3.40* I.DO
COHMEX (1986) 6.01 1.05
*18-dBz threshold used for ATI.
RADAR
_ype, Bean)width)
S-band 2°
C-band 2 °
C-band 2°
C-band 2°
C-band 2°
C-band 1°
S-band 2°
S-band 2°
The first six entries of the table are for
data from the western portion of North Dakota and
eastern Montana, which represent similar geographic
locations. For those six entries, the b parameter
varies only from 1.01 to 1.09, while the K param-
eter varies from a low of 2.12 for CCOPE to a
maximum of 3.74. Thus, we see small year-to-year
variations as well as some differences (especially
in K between Montana and North Dakota in the same
year, 1981) that may be partly due to differences
in radar characteristics.
The COHMEX data from the southeastern U.S.
have a similar b parameter but the K parameter is
substantially larger. This increase may be a
climatological difference or only an artifact of
the data. The WSR-57 RADAP data for COHMEX were
recorded out to ranges of 250 km versus only
150 km for the ND/MT data. At ranges >150 km,
with a 2° beamwidth, the sampling volume becomes
rather large. Using the criterion that the
reflectivity factor for the sampling volume has
to exceed 25 dBz requires that a significant storm
event must be taking place at the larger ranges
before its inclusion in this study. Therefore,
the larger coefficient may simply reflect greater
rain amounts from these more mature events.
on the other hand, a similar radar was
used in southern Florida during the FACE project
for 1978, 1979, and 1980. Lopez et aT. (1989)
presented a composite figure for the three years
comparing integrated radar echo area to radar-
estimated rain volume. Their figure is similar
to Fig. 2 except that linear scales were used.
Scatter was evident about a line of slope I
(which would have the same slope on a log-log
plot); parameter K for 1-hr integration steps
at a threshold of only 18 dBz is the reported
average rain rate of 3.4 mm hr-l. This value
NOATH DAKOTA 1984
"Z
...f...o.o0 0 D_o
0 0 0 O
I
0" 100 101 102 103 104 105
RADAR ESTIMATED RAINFALL (krn 2 ram)
: Log-log scatter plot of rain volumes
ined from the radar ATI using the CCOPE
relationship (Fig. 2) for echo clusters from
North Dakota 1984 vs. their direct radar-estimated
rain volumes. The ideal 1:1 comparison line is
shown.
compares rather well with the K values from the
High Plains observations with 2° beamwidths, but
raising the threshold to 25 dBz would yield a
higher value. The instrumented region of the
project was within 170 km range of the radar.
Transferability of these relationships can
be tested by using one relationship (like Fig. 2)
to estimate rainfall amounts for other data sets.
For example, during the 1984 North Dakota Cloud
Modification Project, echo clusters were deter-
mined as in the CCOPE study. For each cluster,
the same Z-R relationship was used to produce an
estimate of rainfall. In Fig. 3, these estimates
are compared to rainfall amounts estimated by
using the observed ATI values with the CCOPE
relationship presented in Fig. 2. Here we are
comparing 1984 radar data to an ATI-rain volume
relationship determined from 1981 data obtained
with a different radar beamwidth. Yet, Fig. 3
demonstrates that the two different estimation
schemes are similar. The ATI-estimated rainfall
amounts do tend to be lower than those obtained
from the Z-R relationship. This is consistent
with the lower K parameter for the CCOPE
relationship, as indicated in Table I.
In another attempt to determine
geographical transferability of the ATI relation-
ships, the data secured by the RADAP system at
Nashville, Tennessee, during the COHMEX project
were similarly analyzed. The results are
demonstrated in Fig. 4. Again, the ATl-estimated
amounts tend to be lower than those obtained using
a Z-R relationship developed specifically for the
project (Peterson et aT., 1990). The scatter is
larger than that seen for North Dakota in the
previous figure, and the degree of underestimate
is a little greater. That is also consistent with
the differences in the K values in Table I.
_) COHMEX 1986
;I"" Y
_ _ oO
'- o De°_°
0 o , *
"-10 ° 10' 102 103 104 10s 106
RADAR ESTIMATED RAINFALL (krn 2 ram)
: Log-log scatter plot of rain volumes
ined from the radar AT! using the CCOPE
relationship (Fig. 2) for echo clusters from
OHMEX 1986 vs. their direct radar-estimated
ain volumes. The solid line shows the ideal
1:1 correspondence .....
Wecannot resolve the transferability
question, with the data analyzed thus far. Using
the same radar in the same location gives repeat-
able results (e.g., Doneaud et al., 1984). All
our geographical comparisons also involve other
differences, in wavelength, beamwidth, or range
coverage. Thus we are not yet certain which are
the more important factors, or whether they
outweigh geographic differences.
4. APPLICATION TO SATELLITE INFRARED DATA
A special study with the major goal of
establishing a satellite ATI method that could be
used to estimate rain volumes is in progress. The
initial analysis used radar data from the CCOPE
and North Dakota-81 field projects as ground truth
for comparison to satellite infrared rapidscan
data. By optimization, it was determined that the
ATI calculated using the area enclosed by the -23%
isotherm was most closely correlated to the radar-
estimated rainfall. The results are presented in
Fig. 5 and are discussed in Smith et al. (1990).
This satellite-identified ATI is
significantly different from the ATI determined by
radar or rain gages. The satellite ATI does not
represent just the rainy portion of the storm,
but, in fact, is many times greater. The slope in
Fig. 5 is substantially less than unity, indi-
cating that the satellite ATI grows more rapidly
than the corresponding rain volume. Yet the opti-
mization shows the area enclosed by the -23°C
isotherm to be most closely related to the rain
volume. Thus we expect to obtain good estimates
of storm rain volumes, although accurate posi-
tioning of the rainfall on the surface will not
be possible.
5. CONCLUSIONS
Application of the Area-Time Integral
technique to estimate rain volume is very
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17 CASES FROM 1981 DATA
CORR. COEFF. ,, 0.93
8LOPE " 0.688 aS
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SATELLITE ATI FOR -23.2°C THRESHOLD (km 2m h_
: Scatter plot and linear regression of
luster rain volume (estimated by radar)
vs. satellite ATI, for the optimized infrared
threshold temperature of -23°C.
successful with comparable radar data. The same
correlations appear in gage data where the gage
network is sufficiently dense. The technique also
appears promising using satellite infrared data.
Still, many questions need to be answered.
It is obvious that a radar-determined relationship
for the northern Great Plains may not be appli-
cable to the more moist environments of the south-
eastern United States. Signs of such differences
appear in our results, but other equipment or
analysis variations muddy the picture at this
time. We need more direct comparisons with
similar radars in different geographic areas
to resolve the transferability issue.
Using satellite data requires better
identification of rain-producing events before
application of the ATI method. The satellite ATI
calculation does not insure a raining event, but
can reasonably estimate the amount of rainfall
given that rain is occurring. We need more exten-
sive testing of the method with satellite data to
determine how to circumvent this concern as well
as to investigate geographic transferability.
Acknowledgments. This research was
sponsored by the North Dakota Atmospheric Research
Board under Contract No. ARB-IAS-89-2 and the
National Aeronautics and Space Administration
under Grant No. NAG 5-386.
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Estimation of convective rain volumes utilizing the are-time-integral technique

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