An empirical method was employed to delineate synoptic scale rainfall over land utilizing Nimbus-6 ESMR measurements

Chang, A. T. C.

Rodgers, E. B.

Siddalingaiah, H.

Wilheit, T. T.

English

At 37 GHz, the frequency at which the Nimbus 6 Electrically Scanning Microwave Radiometer (ESMR 6) measures upwelling radiance, it was shown theoretically that the atmospheric scattering and the relative independence on electromagnetic polarization of the radiances emerging from hydrometers make it possible to monitor remotely active rainfall over land. In order to verify experimentally these theoretical findings and to develop an algorithm to monitor rainfall over land, the digitized ESMR 6 measurements were examined statistically. Horizontally and vertically polarized brightness temperature pairs (TH, TV) from ESMR 6 were sampled for areas of rainfall over land as determined from the rain recording stations and the WSR 57 radar, and areas of wet and dry ground (whose thermodynamic temperatures were greater than 5 C) over the Southeastern United States. These three categories of brightness temperatures were found to be significantly different in the sense that the chances that the mean vectors of any two populations coincided were less than 1 in 100

Rodgers, E.

NASA Technical Reports Server

A statistical technique for determining rainfall over land employing Nimbus-6 ESMR measurements

PaperNo.18
A STATISTICAL TECHNIQUE FOR DETERMINING RAINFALL OVER
LAND EMPLOYING NIMBUS-6 ESMR MEASUREMENTS
E. Rodgers, Goddard Space Flight Center, H. Siddalingaiah, Computer Sciences
Corporation, Silver Spring, Maryland20910, A. T. C. Chang and T. Wilheit,
Goddard Space Flight Center, Greenbelt, Maryland.
ABSTRACT
An empirical method has been employed to deliniate synoptic scale
rainfall over land utilizing Nimbus-6 ESMR measurements.
INTRODUCTION
Savage et al. (1976) demonstrated theoretically that at 37.0GHz, the frequency
at which the Nimbus-6 ESMR (ESMR-6) sensor measures upwelling radiance, the
scattering by hydrometeors is strong enough to render a qualitative interpretation
of rain over land. Furthermore, Weinman and Guetter (1977) demonstrated from
theoretical considerations that the upwelling radiation at 37.0GHz emerging from
hydrometeors is essentially unpolarized. This in contrast to wet land surface whose
reduced emissivity (due to surface moisture) becomes highly polarized when viewed
obliquely. Thus, it is reasonable to conclude from these theoretical considerations
that rain over dry land surfaces can be at least qualitatively monitored employing
37.0GHz radiometer measurements from ESMR-6.
It is the purpose of this study to substantiate the above conclusions and to
arrive at aJq-algorithm which detects rain over land by statistically analyzing ESMR-6
data. This statistical analysis will be performed by first sampling three categories of
ESMR-6 brightness temperatures (T B's) (representing rain over land, wet land surfaces
without rain, and dry land surfaces), then testing these populations for uniqueness,
and finally developing a classification algorithm to delineate rain over land.
THE ESMR-6 SYSTEM
The ESMR-6 system flown aboard Nimbus-6 (Wilheit, 1975) receives the
thermal radiation upwelling from the earth's surface and atmosphere in a 250MHz
band centered at 37.0GHz. The antenna beam scans electrically in 71 steps an arc
of 70 ° ahead of the spacecraft along a conical surface with a constant incidence
angle of 50 ° to the earth's surface every 5.3 seconds with a nominal resolution of
20km crosstrack and 45km down track. The instrument measures both horizontal
and vertical polarization components by using two separate radiometric channels.
The data are calibrated using warm (instrument ambient) and cold (cosmic back-
ground) inputs to the radiometer. The T B as observed from the satellite are de-
pendent upon the emission from the earth's surface modified by the intervening
103
https://ntrs.nasa.gov/search.jsp?R=19790012480 2020-03-20T18:26:52+00:00Z
atmosphere.Theemissivity,beingafunctionof thedielectriconstant,isvariable
overlandsurfaces(dependingonvegetation,surfaceroughness,andsoilmoisture)
andgenerallylarge(ca,.9).In arainingatmosphere,threeconstituentscontribute
to theabsorption:molecularoxygen,watervapor,andliquiddroplets.Water
dropletsaretheonlysourceof scatteringatthisfrequency.Icecrystalsareessen-
tiallytransparent.
DATASAMPLING
InordertodevelopanalgorithmwhichclassifiesagivenESMR-6instantaneous
fieldofview(IFOV)asrainoverland,drylandsurface,orwetlandsurface,simulta-
neousgroundstationsandradarmeasurementsofrainandESMR-6TBwereneeded.EightdaytimesynopticscalerainfallcasesovertheSoutheasternU itedStateswere
usedwheresurfacerainratedatatakenfromstationsreportinghourlyrainfall
a_mountsandfromtheWSR-57radarcoincidedwiththeNimbus-6overpasstowith-
in5minutes.Thesurfacet mperaturein achofthesecaseswasnotlessthan5°C.Rain
areasweresampledwithinareasdelineatedasrainbytheWSR-57radar(rainrates/>
2.5mmhr-1)and/orthestationreportinghourlyrainfallamounts.Wetlandsurfaces
weresampledinareaswhererainhadfallenwithin3hoursandupstreamandadjacent
totheraincellsobservedontheWSR-57radar.Drylandsurfacesweresampledover
areaswhererainhadnotfallenwithina24hr.periodpreviousto theNimbus-6pass.
STATISTICALANALYSIS
Figure1presentshescatterplotof thesampleddata.TheC'srepresentthe
meanpointsof thepopulations.Eachof thefrequencyconcentrationellipsesen-
compasses68percent(onestandarddeviation)of thedatafromtherespective
populations.Thesellipsesrevealtheextentof scatteringof thedatafromeach
population,thecorrelationbetweenthevariablesTH andTv ineachpopulation(thehigherthecorrelationthelargertheeccentricityof theellipse),andtheex-
tentof overlapamongthepopulations.It canbeseenthatthelargestoverlapis
betweenthepopulationsrepresentingrainareasandwetlandsurfaces.Thisam-
biguitymaybeattributedto thefactthatanESMR-6IFOV(pixel)partiallyfilled
withmoderateo heavyrainorcompletelyfilledwithverylightrainis influenced
bythewetsurfacebackgroundandconsequentlyproducesasignaturesomewhat
similarto thatof wetlandsurfaces.
Thethreeconcurrentlinesdrawnin thisfigurearetheFisherdiscriminant
lines.Theselinesseparatewo-by-twotheensembleof pointsrepresentingrain
overland,drylandsurfaces,andwetlandsurfaces.
Table1showstheelementarystatisticsof thesampleddata.It canbeseen
fromFigure1andTable1,thattheTBrepresentingrainoverlandarecolderthan
thoserepresentingdrylandsurfaces.However,thiswillnotalwaysbethecase.
Sincethesurfacemissionisgivenby eT s (e is the surface emissivity and T s is the
surface thermodynamic temperature), there is an influence of T s on ESMR-6 meas-
ured dry land surface T B. A decrease in T s results in a decreased ESMR-6 T B of
dry land surfaces and consequently in the reduced T B contrast between dry land
surfaces and rain over land.
It can also be seen from this table that the difference in the means of the
horizontal and vertical polarized T B (6.5°K) representing rain over land is much
smaller when compared to the corresponding mean difference (16.1 °K) represent-
ing wet land surfaces. This in accordance with the theoretical findings that hydro-
meteors are not polarized (Weinman and Guetter, 1977) whereas wet land surfaces
are highly polarized.
104
Table 1
Rain Over Land
Rain Area Dry Ground Wet Soil
Sample Size: N 216 189
Mean: p
Standard Deviation: d
Sample Correlation Coefficient
Between T H And T v: O
THR TVR
254.53 260.98
7.21 5.81
THD
271.46
6.18
TVD THW
278.18 252.05
7.2 9.41
0.55 0.37
66
Tvw
268.86
7.64
0.82
Prior to employing these data for the development of classification algorithms,
an examination was made to verify whether the three populations were statistically
distinguishable from one another. To accomplish this, tests were carried out first
to determine the significance of the differences between the means of any two
classes and second to estimate the simultaneous confidence intervals for the differ-
ences of the means of any two populations. It was found that the differences be-
tween the means of any two classes were highly significant and that the probability
that the mean vectors of any two populations coincide was less than 1 in 100. The
simultaneous confidence intervals computed according to Scheffe's procedure
showed that none of the intervals contained zero except the one for the differ-
ences between the means of horizontal polarized TB's for wet land surfaces and
rain over land. However, the three populations are distinguishable from one another
when the dual polarization information is taken into account simultaneously. It
should be noted that the lower bounds for the differences of the means of the TB's
for rain over land and wet land surfaces are very small when compared to those of
the other two pairs of the populations. Hence, it will be more difficult to detect
rainfall over land from wet land surfaces. Since the populations were found to be
statistically distinguishable and satisfied the Gaussian frequency distribution, the
Bayesian pattern recognition technique was employed to develop a classification
algorithm to detect and delineate active rainfall areas from wet and dry land sur-
faces. (Rodgers, et al., 1978.)
ERROR ANALYSIS
An error estimate was made in order to evaluate the performance of the class-
ification algorithm. The error rates were computed according to the asymptotic
formulas given by Okamoto (1963). The results are seen in Table 2 which shows
that the chances of incorrectly classifying wet or dry land surfaces as rain over
land is nearly 23 percent. But when a given ESMR-6 pixel is classified as rain
over land and each of the eight contiguous pixels clustered around it is also classi-
fied as rainfall over land, then the chance of misclassification of that central pixel
is reduced to 7.7 x 10 -6 percent assuming each pixel is independently classified. Table
3 displays the actual probabilities that the classification algorithm classifies the sampled
data into various populations as indicated. The average accuracy is computed by taking
the mean of the diagonal elements of the corresponding error matrices. The apparent
average accuracy compares well with the estimated average.
105
Table 2
Probabilities of Misclassification: Theoretical Computation
Classified
Known _.._.,
Rain
Dry
Wet
Rain
77.15
6.67
16.28
Dry
6.66
82.08
11.29
Wet
16.19
11.25
72.43
Average Accuracy: 77.22 Percent
Table 3
Bayesian Classification Error Matrix
Classified
Known _...,. Rain Dry Wet
Rain
Dry
Wet
89.35
7.41
27.27
6.02
91.53
15.15
Average Accuracy: 79.49 Percent
4.63
1.06
57.58
ALGORITHM EVALUATION
A case not previously used was tested to verify qualitatively the performance
of the Bayesian Classification algorithm. This case consisted of a synoptic scale rain
pattern over the Southeastern United States (14 September, 1976) which was ob-
served by the ESMR-6 sensor (surface thermodynamic temperature _> 15°C). Rain-
fall as delineated by tile WSR-57 radar and stations reporting hourly rainfall amounts
is seen in Figure 2. The approximate time of the radar PPI images was 1630 GMT
(within 5 minutes of the Nimbus-6 pass). The reportin/_ times of the stations report-
ing rain amounts were 1500, 1600, and 1700 GMT. The shaded areas within the WSR-
57 radar PPI range (46 km) are rain rates greater than 2.5 mm hr -l . The radars were
located at Waycross and Macon, Georgia; Charleston, South Carolina; and Wil-
mington and Cape Hatteras, North Carolina. Surface station data were taken at
1800GMT. Dots, together with the hourly amounts of rain (see model in figure)
if any, denote hourly rainfall reporting stations.
The Bayesian classification map is seen in Figure 3. Areas of clouds deline-
ated by the Nimbus-6 Temperature Humidity Infrared Radiometer (THIR) 11.5t_m
channel (equivalent blackbody temperatures (TBB) _< 270°K) are shown on the map.
Rain areas in the absence of clouds or in areas of low clouds are misclassifications.
Only regions covered by clusters of contiguous pixels classified into a single indi-
vidual class are shown, since the probability of misclassifying clusters is much less
than that of a single pixel.
A comparison of Figure 2 with Figure 3 shows good agreement between areal
distribution of ESMR-6 derived rain over land and observed rain (no attempt was
made to verify wet surfaces areas). However, the classified area of rainfall over
North Carolina and Southwestern Georgia is contrary to ground observations. The
106
rainfall indicated by ESMR-6 over North Carolina may be suspended liquid water
in the clouds ahead of the rain area (the area of rain was moving NE towards North
Carolina). On the other hand, the ESMR-6 delineated rain over Southwestern Geor-
gia, which was upstream from the rain area, may be due to wet land surfaces pro-
duced by the rain that fell a few hours prior to the Nimbus-6 pass.
The Bayesian classification algorithm was applied to another case (1645GMT
August 27,1976, surface thermodynamic temperatures >/ 15°C) over the same geo-
graphical area as the previous case in order to determine whether the surface char-
acteristics (vegetation, soil moisture, and surface roughness) had influenced the
classification algorithm performance in the previous case. During this period, the
area in question was under the influence of a Bermuda high and there was only
convective rainfall in the area, particularly along the Gulf States. Results showed
that the only areas classified as rain over land were along the Gulf Coast. The re-
gions in the previous case where the algorithm showed rainfall were classified as
dry land surfaces. Hence, there was no influence of extraneous surface character-
istics on the outcome of the previous case study.
However, contradicting results occurred when the Bayesian classification al-
gorithm was applied to a night time Nimbus-6 pass over the same geographical area
(0525GMT, September 13, 1976, surface thermodynamic temperature/> 15°C)
where there was no synoptic scale rainfall reported. Almost all pixels were classi-
fied by the algorithm as rain over land. Examining the ESMR-6 T B showed that
the temperatures were below 0°C. This anomaly may be attributed to the change
in the surface emissivity caused by the presence of dew on the vegetation. There-
fore, the pattern classification algorithm trained by data sampled from Nimbus-6
daytime passes can be employed only when dew is absent.
CONCLUSIONS
Statistical analyses were performed on the sampled ESMR-6 data for the pur-
pose of detecting rainfall areas over land from dry and wet land surfaces. It was
found from these studies that synoptic scale rainfall over land, where surface ther-
modynamic temperatures were greater than 5°C and the vegetation was bereft of dew,
could indeed be delineated despite the large ESMR-6 IFOV. However, there was
some ambiguity in distinguishing between rainfall areas and wet land surfaces.
REFERENCES
Duda, R. O. and P. E. Hart, 1973: Pattern Classification and Seen Analysis, pp.
10-36, John Wiley and Sons, New York, NY.
Okamoto, M., 1973: An Asymptotic Expansion of the Distribution of the Linear
Discriminant Function. Ann. Math. Statist., 34, 1286-1301.
Rodgers, E. B., H. Siddalingaiah, A. T. C. Chang, and T. Wilheit, 1978: A Statis-
tical Technique for Determining Rainfall Over Land Employing Nimbus-6
ESMR Measurements, NASA TM 79631, pp. 33.
Savage, R. C., P. J. Guetter, and J. A. Weinman, 1976: The Observation of Rain
Clouds over Land in Nimbus-6 Electrically Scanned Microwave Radiometer
(ESMR-6) Data. Preprint Vol. 7th Conf. on Aerospace and Aeronautical
Meteorology and Symposium on Remote Sensing from Satellite, 131-136.
Weinman, J. A. and P. J. Guetter, 1977: Determination of Rainfall Distribution
from Microwave Radiation Measured by the Nimbus-6 ESMR. J. Appl. Meteor.,
16, 437-442.
107
Wilheit, T. T., 1975: The Electrically Scanning Microwave Radiometer (ESMR)
Experiment. Nimbus-6 User's Guide NASA Goddard Space Flight Center,
87-108.
NIMBUS O ESMR _ vs TH
Fig. 1-Vertical polarized vs. horizontal
polarized ESMR-6 T B
' . - _ ','. .... _ !'. , ._"'< i_L_,, ,
• _:_._ :.,,:-_,_,
. . ' . _, , . ._ ,,o_-_ "_, .-,
..... ,. .+. . i( "_ ._
_, ,_ • \
Ssptembe, 14, 1976 _l_e" , ,,_,
M
Fig. 2-Rainfall over the Southeast
United States is delineated by the WSR-
57 radar and hourly rainfall reporting
station. Time of data is approximately
1630 GMT September 14, 1976. Shaded
areas represent WSR-57 observed rain
(rain rates ) 2.5 mm hr.). Dots repre-
sent hourly rainfall reporting stations.
Nimbus 6 Orbit Date and Time
September 14, 1976 1630 GMT
THIR 11.Sktn_ Tee • 27_K
(_ ESMR.6 der_ed rain whccae
THiR 11.Sb¢m Tss -_ 27OAK
ESMR-6 derived wet ground
Fig. 3-ESMR-6 derived rainfall dis-
tribution using the Bayesian classifier.
Dark curve depicts equivalent blackbody
temperatures (Taa) of 270 ° K as mea-
sured by the Nimbus--6 THIR 11.5 chan-
nel. Areas that have Taa _< 270°K repre-
sent cloud cover. Time of Nimbus--6 pass
1630 GMT September 14, 1976.
108


A statistical technique for determining rainfall over land employing Nimbus-6 ESMR measurements

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