..ailA 9o943

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESIS

A STUDY OF
USING VISUAL

PRECIPITATION
AND INFRARED

OCCURRENCE
SATELLITE DATA

by

Linda Sue Pau

1

December 19 83

The:

sis Adv:

Lsor :

C. H. Wash

Approved for public release; distribution unlimited

1Z15A67

UMCLASSIFIFn

SECURITY CLASSIFICATION OP THIS PACE (Wttun Dmtm Bntwrtd)

REPORT DOCUMENTATION PAGE

READ INSTRUCTIONS
BEFORE COMPLETING FORM

1. REPORT NUMBER

2. GOVT ACCESSION NO.

3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and SuhtUlt)

A Study of Precipitation Occurrence
using Visual and Infrared Satellite Data

5. TYPE OF REPORT & PERIOD COVERED

Master's Thesis

6. PERFORMING ORG. REPORT NUMBER

7. AUTHORCa;

Linda Sue Paul

8. CONTRACT OR GRANT NUMBERr*;

9. RERFORMING ORGANIZATION NAME ANO ADDRESS

Naval Postgraduate School
Monterey, California 939^3

10. PROGRAM ELEMENT, PROJECT, TASK
AREA « WORK UNIT NUMBERS

11. CONTROLLING OFFICE NAME ANO ADDRESS

12. REPORT DATE

December 1Q83

13. NUMBER OF PAGES

114

14. MONITORING AGENCY NAME « ADDRESSC^/ (M//«ran( /rom Controtllnt OlUct)

15. SECURITY CLASS, (oi thiu report)

IS«. DECLASSIFICATION/ DOWNGRADING
SCHEDULE

IS. OlSTRItUTION STATEMENT (ol thi* Report)

Approved for public release; distribution unlimited

17. OISTRISUTION STATEMENT (et tli* mbttrmcl wtlMd In Block 30, II dlU»ttnt from Ruport)

It. SUR)*LCMeNTARV NOTES

It- KEY WORDS (Conllnuo on lovtao mido II nocoooarr and Idantlty by block numbor)

Satellite Precipitation Specification
Satellite Meteorology
Bi-spectral Satellite Threshold
Objective Forecasting

20. AMTRACT (Conllnua on rovoraa aid* II naeoaaarr and Idantlty by block numbar)

Bi-spectral satellite thresholds for precipitation speci-
fication are explored with visual and infrared satellite data
collocated with Service-A hourly observations for 137 surface
stations in the southeastern United States. The data span the
month of August 1979 and total 70,623 observations, including
538 daylight precipitation observations.

The distributional and statistical differences of four
I satellite resolution .gizp.q r^ng-ing from 484 to POPS nmi^ ^re. \

DO , ;S"7, 1473

EDITION OF 1 NOV «S IS OBSOLETE
S/N 0102- LF- 014- 6601

mr,] ASSTFTFD

SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Bntarma'

UMCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (Whmn Dmtm Entaradf)

(20. ABSTRACT continue)

explored and determined to be significant in the representation
of weather conditions. Precipitation and no-precipitation data
can be statistically differentiated with the visual and infrared
mean and standard deviation values.

For overcast ceiling reports, a simple linear bi-spectral
threshold based on a 50% probability of precipitation is defined
as extending from albedo 1.00 to 0.60 with associated cloud top
temperatures 290K and 210K, respectively. For overcast and bro-
ken ceiling reports, an albedo greater than 0.80 specifies a 50%
probability of precipitation.

S'N 0102- LF- 014-6601

IINrT.ASSTFTFD

SECURITY CLASSIFICATION OF THIS PAGE(TWi«n Datm Bnfrmd)

Approved for public release; distribation unlimitsd

A Study of Precipitation Occurrence
using Visual and Infrared Sazellite Data

by

Linda Sue Paul

Lieutenant, United States Navy

B. S., University Df Minnesota, 1977

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
December 1983

'^•'^ :UATE SCHOOL

ABSTRACT mo' .l.....,x . uij^iFORHiA 93943

Bi-spectral satellite thresholds for precipitation spec-
ification are explored with visual and infrared satellite
data collocated with Service-A hourly observations for 137
surface stations in the southeastern tJnited States. The
data span the month of August 1979 and total 70,623 observa-
tions, including 538 daylight precipitation observations.

The distributional and statistical differences of four
satellite resolution sizes ranging from 48U to 2025 nmis are
explored and deteriined to be significant in the representa-
tion of weather conditions. Precipitation and no-precipita-
tion data can be statistically differentiated with the
visual and infrared mean and standard deviation values.

For overcast ceiling reports, a simpls linear bi-spec-
tral threshold based on a 50% probability of precipitation
is defined as extending from albedo 1.00 to 0.60 with asso-
ciated cloud top temperatures 290K and 210K, respectively.
For overcast and broken ceiling reports, an albedo greater
than 0.80 specifies a 50% probability of precipitation.

TABLE OF CONTENTS

I. INTECDUCTICN 13

II. PRECIPITATION SPECIFICATION 18

A. INTRODUCTION 18

B. BI-SFECTRAL AND INFRARED THRESHOLD 18

• C. LIFE HISTORY 34

III. DATA PROCESSING H2

A. INTRODUCTION 42

B. CATA SORT 44

C. STATISTICAL TREATMENT 49

IV. RESULTS 51

A. INTBCDUCnON 51

B. RESOLUTION . , . , 51

1. Precipitaticn Data 52

a. Mean Statistics 52

t. Standard Deviation Statistics 52

c. Distribution Discussion 54

d. Summary 59

2. No-precipitation Overcast Data 61

a. Mean Statistics 61

b. Standard Deviation Statistics 62

c. Distribution Discussion 63

d. Summary 63

5

3. Precipitation and No-precipitation

Comparison 66

C, FRECIFITATION SPECIFICATION ' . 68

1. Overcast Ceilings 69

a. Mean of the Means 69

b. Mean of the Standard Deviations .... 70

c. Standard Deviation of the Means .... 71

d. Standard Deviation of the Standard
Deviations 71

e- Distribution Discussion 72

f. Precipitation Probabilities 74

g. Summary 78

2. Overcast and Broken Ceilings 80

a. Mean of the Means 80

b. Mean of the Standard Deviations .... 81

c. Standard Deviations of the Means ... 82

d. Standard Deviation of the Standard
Deviations 82

e. Distribution Discussion ...;.... 83

f. Precipitation Probabilities 85

g. Summmary 36

D. CONVECTIVE VERSUS CONTINUOUS PRECIPITATION . . 88
1. Mean Statistics 88

2. Standard DeviatiDn Statistics 91

3. Distribution Discussion 91

4. Summary 92

E. INTENSITY 95

1. Statistical Discussion 95

2. Distribution Discussion 96

3. Summary 100

V. SUMMARY AND CONCLUSIONS 101

A. DATA PROCESSING SUMMARY 101

B. STATISTICS SUMMARY 102

C. PRECIPITATION PFCBABILITY SUMMARY 104

D. DATA DISTRIBUTION SUMMARY 104

E. CONCLUSIONS 105

F. SUGGESTED FURTHER STUDY 105

APPENDIX A 107

LIST OF REFERENCES Ill

INITIAL DISTRIBUTION LIST 113

LIST OF FIGURES

Figure 1. One- hour Rainfall 21

Figure 2. Probability of One-hour Rainfall 21

Figure 3. Probability of One-hour Rainfall 22

Figure 4. Two Dimension Decision Space for Typing

Clouds 23

Figure 5. Precipitation Intensity Classification ... 26

Figure 6. Frequency Plot of Rain Distribution 28

Figure 7. Frequency Plot of No-rain Distribution ... 28

Figure 8. Geographical Locations of Service-A

Station Report Data 43

Figure 9. Flow Chart of Cata Processing 45

Figure 10. Precipitation Data for 10 x 10 Array size . . 54

Figure 11. Precipitation Data for 8x8 Array Size ... 55

Figure 12. Precipitation Data for 6x6 Array Size ... 55

Figure 13. Precipitation Data for 4x4 Array Size ... 56

Figure 14. Precipitation Array Size Distributions

Along Diagonal Line 58

Figure 15. Nc-Precipitation Overcast Data for 10 x

10 Array Size 64

Figure 16. No-Precipitation Overcast Data for 8x8

Array Size 64

Figure 17. No-Precipitation Overcast Data for 6x6

Array Size 65

Figure 18. No-Precipitation Overcast Data for 4x4

Array Size 65

Figure 19. Precipitation Overcast Data for the 10 x

10 Array Size 73

Figure 20. Precipitation Overcast Data for 4x4

Array Size 73

Figure 21. Precipitation Overcast Data Probability

10 X 10 Array Size 75

Figure 22. Precipitation Overcast Data Probability 4

X 4 Array Size 75

Figure 23. Precipitation Overcast and Broken Data

for 10 X 10 Array 83

Figure 24. No-Precipitaticn Overcast and Broken for

10 X 10 Array 84

Figure 25. Precipitation Overcast and Broken Data

for 4x4 Array 84

Figure 26. No-Precipitation Overcast and Broken for

4x4 Array 85

Figure 27. Precipitation Data Probability 10 x 10

Array Size 87

Figure 28. Precipitation Data Probability 4x4

Array Size . 87

Figure 29. Convective Precipitation Data for 10 x 10

Array Size 92

Figure 30. Continuous Precipitation Data for 10 x 10

Array Size 93

Figure 31. Convective Precipitation Data for 4x4

Array Size 93

Figure 32. Continuous Precipitation Data for 4x4

Array Size 94

Figure 33. Light Precipitation Data for 10 x 10

Array Size 97

Figure 34. Moderate/Heavy Precipitation Data for 10

X 10 Array Size 98

Figure 35. Light Precipitation Data for 4x4 Array

size 98

Figure 36. Mcderate/Hea vy Precipitation Daxa for H x

4 Array Size 9 9

Figure 37. Normalized Cloud Reflectivity 110

10

LIST OF TABLES

TABLE I. Summary of Bi-spectral and Infrared

Threshold Values 19

TABLE II. Cloud Classification to be used with

Fig. 1 2H

TABLE III. Threshold Values Describing

Precipitation Intensity Levels 25

TABLE IV. Statistical Comparison of Rain Area

Mapping Techniques 31

TABLE V. Statistical Comparison of the Accuracy

of Fain Areas 31

TABLE VI. Correlation Coefficients for

Determination of Precipitation 35

TABLE VII. Summary of Life History Threshold Values . . 36

TABLE VIII. Classification of No-Precipitation Data

Groups U7

TABLE IX. Classification of Precipitation Data

Groups 48

TABLE X. Precipitation Data Statistics for Four

Array Sizes 53

TABLE XI. No-Precipitation Data Statistics for

Four Array Sizes 62

TABLE XII. Precipitation Specification Overcast

Ceilings 70

TABLE XIII. Precipitation Specification Overcast and

Broken Ceilings 81

TABLE XIV. Continuous versus Convective

Precipitation Specification 89

TABLE XV. Light versus Moderate/Heavy

Precipitation Specification 96

TABLE XVI. List of Symbols 108

11

TABLE XVII. Basic Geometric Satellite-Earth

Relationships * 109

TABLE XVIII. Muench and Keegan Normalization

Equations * 109

12

I- INTROpaCTION

The determination of precipitation occurrence and
amounts is an important factor in scientific, commercial,
and operational endeavors. Scientific uses are concentrated
in the fields cf meteorology, hydrology, and oceanography,
where precipitation is essential in analysis, diagnosis,
prediction, and verification. Within meteorology, precipi-
tation serves as both a forcing and response element in the
study of daily weather and climatology. Indeed, precipita-
tion is a critical input for climate research and into gen-
eral circulation aodels which promise to extend the time
frame of skillful weather forecasts. Commercial uses encom-
pass agriculi-ure, forestry, transportation, communications,
wa^er resource management, and many othars.

Despite the importance of precipitation data to a vari-
ety of fields, there are serious shortcomings in current
precipitation determination. These shortcomings are due to
areal and economic limitations imposed upon the land-based
rainfall monitoring systems. k possible solution is embod-
ied in precipitation information extracted from satellite
data. With the advent cf high resolution, multi-spectral
channel satellites in the late 1970's, satellite derived

13

precipitation data are being studied as a viable method -o
complement and supplement conventional rainfall data.

The satellite image interpreter does a subjective analy-
sis based on the gray shade variations, representing a range
of digital counts, that appear in the satellite image. How-
ever, satellite data contain more information within the
digital values than can be resolved by the human eye in pho-
tographic images. The satellite digital counts input into a
computer allow use of the full range of the digital values.

Until recently, computer processing of satellite data
has been confined largely to research uses. Acquisition,
storage, and processing of the huge volumes of digital sat-
ellite data could not be handled operationally in real time.
However, with the recent advent of more capable mini-com-
puter systems, such as the United States Navy's Satellite
Data Processing And Display System (SPADS) developed by the
Naval Environmental Prediction Research Facility (NEPRF)
Monterey, California, real time quantitative use of digital
satellite data has become a reality. With the operational
availability of such systems as the SPADS unit, there is a
need for numerical schemes to aid in the objective
specification of current weather conditions.

ia

This thesis concentrates on the specification of visual
and infrared satellite data thresholds in determining pre-
cipitaxion occurrence and qualitative precipitation rates in
a mid-latitude coastal environment. The data set used con-
sists of collocated Geostationary Operational Environmental
Satellite--East (GOES-E) satellite data and hourly surface
observations at East Coast and Gulf Coast Uni-ed States sta-
tions, south of UO^'N, for the month of August 1979.

The use of satellite data for precipitation specifica-
tion is not new. There is the recognized limitation thar
infrared and visual satellite sensors are measuring proper-
ties associated with small cloud particles and not precipi-
tation sized particles. Nonetheless, Muench and Keegan
(1979) specified quantitative precipitation rates, Liijas
(1981a, 1981b) specified qualitative precipitation rates,
and Love joy and Austin (1979) delineated rain versus no-rain
cases using visual and infrared satellite data. Del Beato
(198 1) used cloud top temperatures within a restricted cloud
case classificatiDn to derive qualitative precipitation
rates.

The currently available precipitation study results are
based on data sets with region, season, and size

15

limitations. This research effort will use data from

stations covering more than 42 0,000 sgaare nautical miles
(nmi2) in the eastern and central United States with a total
of 70,623 observations (538 precipitation observations) . In
comparison, the relatively comprehensive precipitation study
of Muench and Keegan (1979) was based on 552 cases (300
rainfall cases) from five stations in the northeastern
United States for April through November 1977. The signifi-
cantly larger size of the present sampls will allow better
statistical determination of appropriate distributions and
threshold value significance.

The primary objective of this thesis is to investigate
specification of precipitation versus no-precipitation from
satellite visible and infrared digital counts. Addition-
ally, in precipitation cases, the feasibility of qualitative
specification cf light versus moderate/heavy precipitation
and quantiative specification of convsctive versus continu-
ous precipitation are investigated.

The thesis is organized into five chapters. Chapter II
reviews the satellite data based precipitation studies.
Chapter III describes the data set, tha data processing and
the testing program. Chapter IV describes the results.

16

Chapter V states the conclusions and suggests furthe:
research.

17

II. PRECIPITATION SPECIFICATION

A. INTRODUCTION

The specification of precipitation and tha estimation of
rainfall rates using satellite imagery have bean studied
using a variety of methods over a wide spectrum of time
scales. This review will concentrata on those methods

developed for synoptic scale and mesoscale analysis of pre-
cipitation on a diurnal or shorter time scale. The methods
reviewed include bi-spectral and infrared threshold (Muench
and Keagan, 1979; Liljas, 1981a, 1981b; Lovejoy and Aus-
tin, 1979; Del Beato, 1981; Wylie, 1982) and lifa history
(Scofiald, 1981; Griffith et al. , 1978; Stout et al. ,
1979; Wylie, 1979; Negri and Adler, 1981).

B. BI-SPECTRAL AND INFRARED THRESHOLD

The bi-spectral threshold method, in which infrared and
visual satellite data are used, involves mapping the extent
and distribution of precipitation. Combining the visual and
infrared data provides information on tha cloud temperatures
(infrared data) and on the cloud thiclcnass (visual data) .
Thus, while use of the visual or infrared data alone may

18

have limitations ia specifying precipitation, the combina-
tion of both may sacceed at specifying precipitation. The
multi-spectral satellite channels introdaced on satellites
in the late 1970»s yielded the possibility of bi-spectral
thresholds. Threshold values and study condition parameters
of selected bi-spectral studies are summarized in Table I.

TABLE I
Summary of Bi-spectral and Infrared Threshold Values

STUDY

LOCATION

CASES

TIME OF
YEAR

THRESHOLD
INFRARED

VALUE
VISUAL

Huench and
Keegan
(1979)

Northeastern
United States

552

obser-
vations

April-
November
1977

-12°C

0.60

Uljas
(1981)

Scandinavia

-

May 1979

August

1979

-12°C to
-15<=C

-

Love joy and
Austin
(1979)

Montreal

17 days

June 1977

-21°C.
-26°C.
-41°C

.80, .88

* Visual threshold based on normalized scale from 0-1

Muench and Keegan (1979) studied precipitation specifi-
cation using GOES visual and infrared satellite data and
hourly rainfall cli ma to logical data for five stations in the
northeastern United States for the period April through
November 1977. Their data set consisted of 552

19

observations, comprised of 300 rainfall observations and 252
cases of either nonprecipitating cloady or fair weather
observations. The visual (1 km resolution) and infrared (7
km resolution) satellite data were area averaged over 7x7
square kilometers (km2) and 14 x 14 km^, respectively. A 65
point visual data array (8x8 plus the center point) and a
17 point infrared data array (4x4 plus the center point)
were centered ever each station. The GOES visual data were
normalized using reflection values from Liou (1976) with the
modification of lower absorption and higher transmission to
compensate for Liou's treatment of the complete solar spec-
trum. The anisotropic radiation of clouds was corrected
with functions calculated by Mue nch and Keegan (1979) from
ground-based radiometers and satellite measurements. From
these data, they determined probabilities for precipitation
greater than .01 and .10 inches in one hour and the amount
of precipitation for the hour following the satellite
observation (see Figs. 1, 2, and 3).

Muench and Keegan (1979) did not provide the standard
deviations for the data in these figures. However, they

stated there was "considerable uncertainty in the specifica-
tion of rainfall amount." As an example, they stated that

20

IR Cloud Ttmp«ralurt (0«gC)

Figure 1. One-hour Rainfall as a Function of Normalized

Cloud Raflectivity and Infrared Cloud Temperature
(from Muench and Keegan, 1979)

1.0

0.9 -

i 0.8

0.71-

0.6

0.5
-SO

1 1

1 1

1
.70

1

/

/"

/ /

y /

/ -

y

1 .30

•■

^

/

Probability 2 0.01 inch

1 1

'

)-

1

.40 -30 -20

IR Cloud Temptrotur* (OtgC)

-10

Figure 2. Probability of One-hour Rainfall Greater than or
Equal to 0.01 inches as a Function of Cloud
Reflectivity and Infrared Cloud Temperature (from
Muench and Keegan, 1979)

21

1.0

0.9

I 0.8

0.7

0.6

0.5

Probobility > 0.10 inch
( Modtrot* or h«avy roin )

-SO -40 -30 -20

IR Cloud Tamptroturt (OtqC)

-10

Figure 3. Probability of One-hour Rainfall Greater than
0. 10 Inches as a Function of Cloud Reflectivit
and Infrared Cloud Temperaturs (from Muench an
Keegan, 1979)

using Fig. 3 "for a one-hcur rainfall spscif ication of 0.10,
two-thirds of the values would fall between 0.25 and 0-04."
Muench and Keegan stated that their figures emphasize the
requirement for both visual and infrarsd data to specify
precipitation amounts.

Liljas (1981a, 1981b) developed a bi-spectral cloud
classification based on visual and infrared data from the
polar orbiting TIR0S--6 satellite (see Fig. 4 and Table II).
The data set consisted of a limited number of daily observa-
tions, chosen for their synoptic characteristics, in May and

22

VISUAL

Figure 4.

Two Dimension Decision Space for Typing Clouds
frcm Visual and Infrared Digital Counts (Table II
defines the symbols for the clouds) (from Liljas,
1981a)

August 1979 over a region encompassing Norway, Sweden, Fin-
land, and the Baltic Sea with weather charts providing the
ground truth. Based upon the precipitation threshold
rasults of Muench and Keegan (1979), Liljas chose a cloud

23

TABLE II
Cloud Classification to be used with Fig. 4

(from Liljas, 1981a)

Mala and Cloud Typei
X, Cuauloalabus

2. Blaboscracufl

3* Cirroscracus

4« Cumtilus conges cus

3» Scracoctsnulus

6. Haze/Scracus

7. Land

•l

b

b.

8. Vacer

.'4
I

•2

'2
h

I

1

s
1
J

k

SeoTB cloud with high cop

Squall cloud vich scaccered showers

Large vertical thickness
Sacher low topside

Dense clrrostratus

Cirrus

Thin cirrus over water

Dense altostracus

Thla alcostratus over water

Thin altostratus

Dense altocumulus
Large piled up cumulus
Rather small and flat caiulus

Dense stratocumulus

Ordinary

Slightly piled up cumulus
with clear areas in between
Very dense haze/stratus
Dense haze/stratus

Ordinary haze/stratus
Cumulis humllls

Hare over water

Planting season spring or autumn

Warm green season

Cold

Vara

2H

top temperature threshold of -.120C to -IS^'C to classify
cumulonimbus and nimbostratus clouds. Starting with this
cloud classification and the assumprion that the highest and
densest clouds produce the maximum precipitation amount,
Liljas suggested a qualitative precipitation intensity scale
based on the sum of the visual and infrared satellite digi-
tal counts (see Table III). These sums represent the areas
of the Liljas nimbostratus and cumuloniibus cloud types in
his bi-spectral cloud classification (sae Fig. 5).

TABLE III
Threshold Values Describing Precipitation Intensity Levels

as Applied in Fig. 5 (from Liljas, 1981a)

Ik^ Sum of . Digital Le yels

Ch 1 + Ch 4 391-310 light rain

31 1-330
331-350
351-370
371-390

390 very strong rain

Lcvejoy and Austin (1979) studied rain mapping of cloud
areas based on GOES visual and infrared satellite data over

25

Q

a
en
<
on

z

H

Figure 5

VISUAL

Precipitation Intensity Classification from
Visual and Infrared Digital Counts. The
Precipitation Area is Represented with the Dark
Diaqonal Lines. (See Table III for the
mathematical description of the intensity areas.)
(from Liljas, 1981a)

Montreal, Canada, and the tropical Atlantic (Global Atmos-
pheric Research Program Atlantic Tropical Experiment, GATE,
data) with radar data providing the ground truth. The Mont-
real data set consisted of 17 observations over three days

26

during June 1977. Working with 4 x 4 Icm resolution satel-
lite image. Love joy and Austin plotted two dimensional fre-
quency grids for the radar-determined rain and no-rain
points on a 25 X 25 array (see Figs. 6 and 7). The visual
data were normalized by selecting the "brightest" and "dim-
mest" values in each image and linearly interpolating the
radiances between 0 and 1.

Lovejoy and Austin (1979) state, with reference to the
cumulus rain data distribution of Fig. 6 rhat, "The distri-
bution was to a good approximation a two-dimensional Gaus-
sian." They do not describe or provide the statistics to
support, this assertion. The no-fain cumulus cases (Fig. 7)
were described as a bimodal distribution with one peak near
the low visual and low infrared values and the other peak
near the rain peak but shifted slightly toward lower values.
In most cases, the separation of the cumulus rain and no-
rain cases was statistically significant with the probabil-
ity ranging from ^Q% to 50% that rhe rain and no-rain
samples came from the same population.

The Lovejoy and Austin (1979) two dimensional frequency
plots for non-cumulus storms were limited to one case. The
significant differences between the cumulus and non-cumulus

27

a

Pi

D
Eh
<
Pi
U

s

w

Eh

000000000
OOOOOtiOO
10 1 I 0 C 0 0 0
I 10)02000
? 1 J » » > 0 1 I
il>'12**l

> ; « I 0 * « ! (

I ] 2 ; 0 4 4 « 1
I 1 2 ; I I « » !

0 I • I 0 ) ) I •
?7?)00l««

1 ♦ » » J 1 • * r

10 0 13 7 1*3
00?3«4*4*

1 1 > • t > • I? 22

2 ♦ 3 I 17 t2 20 22 21
0 0 I «1I2II2I220
9 0 0 I 1 4 It 2* )1
0000004311

oooocooos

000000000
900000000
000000000

2t 44 31 2)

«a >» M 42

■4 140 144 124

«0 4) 10) 104

\9 24 41 I oa

BRIGHTNESS

Figure 6. Frequency Plot of Rain Distribution for GATE day
248, 1300 GMT (from Lovejoy and Austin, 1979)

Qi
Eh

W

a

Eh

l» 17 10

^» ?o i» i;

10 1^ 14

1* ?1 10 IS

1 11

6 «

10

^ IT

11

1*

n

?<

<«

1 >

c

c

0

0

0

0

0

>4 It 20

4 2) II 14
10 10 H 1«

BRIGHTNESS

Figure 7, Frequency Plot of No-rain Distribution for GATE
day 248, 1300 GMT (from Lovejoy and Austin, 1979)

28

data sets were that the non-cumulus no-rain plot lost its
bimodal character, relative to the cumulus no-rain plot, and
appeared as a broad two dimensional Gaussian distribution.
The non-cumulus rain plot points fell within the no-rain
distribution, but were shifted slightly higher in the vis-
ual. The separation of the non-cumulus rain and no-rain
cases was not statistically significant, with greater than a
50% probability of the rain and no-rain samples coming from
the same population.

Love joy and Austin ( 1 S79) attempted to further classify
the cumulus rain and no-rain cases into no-rain, light rain,
and heavy rain. Rainfall rates greater than 2 mm-h-i, as
determined by radar, were defined as heavy rain. As

expected, the mean of the heavy rain cases was shifted
slightly towards higher visual and infrared values than the
mean of the light rain cases. However, the shift was so
small that there was at least an 80% probability of the
light rain and heavy rain cases coming from the same popula-
tion. Lovejoy and Austin (1979) concluded that "little if
any rainfall-rate information is contained in a single (vis-
ual and infrared) satellite image."

29

Lovejcy and Austin (1979) tested a spectral threshold
technique for rain area mapping. Each satellite image of
400 X 400 km was divided into one hundred 40 x 40 km boxes.
The 100 sutareas were each checked with radar to determine
the total number zf rain areas. An equal total number of
satellite subareas were classified as rain areas. The sat-
ellite subareas with the highest visual and highest (cold)
infrared values were classified as rain areas, until the
total number of satellite rain areas equaled the total num-
ber of radar determined rain areas. This spectral threshold
technique was applied to three days accumulation of data and
is shown in Tables IV and V. When compared with the success
of the two dimensional frequency plot method, the visible
and infrared thresholds averaged 45% and 58% worse, respec-
tively. The accuracy of the visual threshold is limited by
the extent of low, thick clouds and the infrared threshold
is limited by the extent of the cirrus clouds in the satel-
lite image. Lovejoy and Austin (1979) concluded that "the
errors involved in using a 'best threshold' are very large
indeed. "

Del Beato (1981) studied correlations between cloud top
temperatures (based on NOAA-5 satellite data) and rainfall

30

TABLE IV
Staxistical Comparison of Rain Area Happing Techniques

(R /R X 100 indicates "percentage of correct satellite rain")
(from Lovejoy and Austin, 1979)

Op(. 2-D BoiindwT

IR Optimum ThrcshoM
IK(K) {H,/lf) X 100

VMble Optimwn ThreshoM

Area Rain
CovcraceCO

ToUlNo.
of Potnu.

Dajr

(ScbI«: O-I)

(«W*)«

100

GATE

242. 24J. 24«
247. 249, 231
252. 261

Monirtal
132

in

I3J

63

36

5«

33

<232

<232
<247
<254

33

20
S3
32

>0.69

>0.M

>0.|I0
>O.SI

64

31
4S
4*

IS.I

».7

24.0
13.9

47706

.40361
337JI
2233«

TABLE V
Statistical Comparison of the Accuracy of Rain Areas

(from Lcvejcy and Austin, 19 79)

Number of Images

Error

Technique

Region

or Sequences

Bias

Factor

£km»

2-D Paltern

Montreal

17

1.13

1.26

0.22

Matching

2-D Pattern

Montreal

3

1.08

1.19

0.18

Matching

Optimum IR

Montreal

3

1.38

1.74

0.71

Threshold

Optimum Visible

Montreal

3

1.54

1.59

0.58

Threshold

2-D Pattern

GATE

8

1.21

1.41

0.25

Matching

totals for 30- and 60-min intervals over eastern Australia.
The sa-ellite data had a 60 km2 maximum resolurion at subsa-
tellite point and cloud top temperatures were area averaged
for a resolution of 200 km2. The 21 data sets were first
classified according to synoptic situation in a rough

31

attempt to group the data by cloud typa, droplet spectra,
and air mass trajectory. The initial rasults suggested that
the cloud top temperature determined an upper limit on rain-
fall amount, with the maximum increasing as the cloud top
temperature decreases. A linear correlation analysis to

determine a quantitative relationship between rainfall
amount and cloud top temperature gave indefinite results.

Further study of surface and radiosonde observations
indicated that classification by proportion of cumuliform
cloud reports to all cloud reports and subcloud layer humid-
ity might be mere appropriate (Del Beato, 1981). This clas-
sification resulted in a correlation coefficient of 0.90,
excluding cases with cumuliform portions less than 50% and
dew-point depressions of greater than 6®C. Finally, a com-
posite frequency distribution was calculated based on three
cases, all southwesterly stream situations described as
"post-frontal cellular convection cases in cyclonically
curved flow." The fitted equation was;

f = 0.C57 - 0.004CTT - 0.054R (1)

where f is the rainfall frequency, R is the 30-min rain
total (mm) , and CTT is the cloud top temperature (^C) . The

32

equation was fitted to 41 independent f values. This equa-
tion is associated with a correlation coefficient of 0.79 at
the 99% confidence level. Equation (1) indicates no rain
from clouds warmer than ■••130C and a maximum 30-min rainfall
of 2.5 mm for a cloud top temperature of -20<'C.

In summary, Del Beato (1981) found that cloud top temp-
eratures and 30- and 60-min rainfall totals indicated sta-
tistically significant relationships for cloud systems with
a high proportion of cumulus clouds and high subcloud humid-
ity. Additionally, as cloud top temperatures decrease to at
least -35°C, rainfall totals increase.

Wylie (1982) attempted to correlate rainfall occurrence
with radiosonde soundings, hourly Service-A observations,
and visual and infrared satellite data. His data sample was
restricted to "large-scale cloud cover" areas with wide-
spread precipitation (rain gauge reports varied less than
20%) for the Great Plains States region for the period 27
February 1981 through 4 January 1982. From thirteen parame-
ters derived from the three data sources (see Table VI) , the
best linear regression equation for estimating rainfall
ra te s wa s :

6-hour rain (in) = 1.0242 ♦ 0.380Pw - 0,0304Qc

- 0.0047Ct (2)

33

where Pw is the vertically integrated precipitable water
vapor (in) , Qc is the moisture convergence (g/kg/day) , and
Ct is the cloud top temperature (Kelvins} . Equation (2) has
a linear correlation coefficient of 0.60. Linear regression
equations were also determined for the three parameters
alone and for a combination of Pw and Qc to be used when not
all three data types were available. The cloud temperature
regression equation was:

6 hour rain (in) = 2.10 - O.OOSCt (3)

The correlation coefficient was -0.35. Wylie (1982) stated
that the synoptic scale data base measurements were best
suited for estimating broad changes in rainfall rates asso-
ciated with changes in air masses and not suited for esti-
mating rainfall rates associated with small scale dynamic
processes.

C. LIFE HISTOEY

The life history methods are empirically derived precip-
itation estimation schemes based upon two assumptions,
first, that significant rainfall comes from convective
clouds, and second, that convective clouds can be identified
and measured in satellite images. These methods involve
manual analyses of convective cloud areas in a sequence of

34

TABLE VI
Correlation Coefficients for Determination of Precipitation

Based on the Three Data Types (from Wylie, 1982)

CORRELATION
MEASURED WITH 6 HOUR NUMBER

PARAMETER PRECIP. REPORT OF CASES F

Vertically integrated 0.48 196 58*

precipitacle water vapor

Cloud top brightness

Cloud top height

Moisture convergence

Cloud top temperature

Bubble model predicted cond.

500 mb vorticity advection

Parcel lifted index

700 mb temperature advection

Sfc temperature advection

850 mb temperature advection

Wind convergence (sfc)

Vertical wind shear

* Significant correlation at the 99% level.

visual, infrared, or both visual and infrared satellite
images. Threshold values and study condition parameters

-0.44

184

44*

-0.40

190

36*

0.38

184

31*

-0.35

199

27*

0.27

115

9

-0.21

173

8*

-0.20

200

8*

0.20

173

7*

0.19

156

6

0.17

189

6

0.09

167

1

0.03

156

0

35

associated with pablished life history studies are summa-
rized in Table VII.

TABLE VII
Summary of Life History Threshold Values

STUDY

LOCATION

CASES

TIME OF
YEAR

THRESHOLD
INFRARED

VALUE
VISUAL

Griffith.
et al.,
(1978)

Florida,

Venezuela,

Honduras,

and hurricanes

impacting East

Coast United

States

34 days

summers
1969-1976

-20°C

80 counts*

Stout,
et al.,
(1979)

tropical North
Atlantic

57 obser-
vations

September
1974

-26°C

0.45 albedo
(sun over-
head)

Wylie
(1979)

Montreal

6 days

June 1977

September

1977

-16°C

-

Negri and
Adler
(1981)

Oklahoma ,
Arkansas,
Missouri

1 day

(15 thunder-
storms)

April 24,
■ 1975

-27°C

-

• ATS-3 satellite

The Scofield/Oliver (Scofield, 1981) analysis follows a

decision tree procedure to estimate half-hourly rainfall for

deep convective systems within tropical air masses, Osing

enhanced infrared and high resolution visual satellite

36

images, the technique involves first identifying the active
convective portion of the cloud, or cluster, from two con-
secutive satellite images. Once the ac-ive portion is iden-
tified, the half-hourly rainfall estimation is computed
based on such factors as cloud top temperature, cloud
growth, and departure of precipitable warer from a summer-
time normal.

The Grif fith/Woodley (Griffith et al. , 1978) technique
is designed to estimate rainfall in the tropics, over large
space and time scales, using geosynchronous visual or infra-
red satellite imagery. This time-dependent technique was
empirically derived as a relationship between cloud area,
echo area, and rain rate for two areas in south Florida,
with raingage-radar providing the ground truth, and was then
tested in other tropical areas. This scheme was subse-
quently tested further in extratropical areas (Griffith et
al., 1980), with modifications to the rainfall amount
predicted.

The determination of a cloud area-rainfall relationship
first required the specification of both a visual and an
infrared threshold to define the cloud area. The visual

brightness threshold, normalized for radiation geometry, was

37

80 counts for the third Application Technology Satellite
(ATS-3) and the infrared threshold was 253K (-200C) . The
Thresholds were based on a comparison of the clouds with a
given maximum digital count and the radar echoes associated
with these clouds.

The empirical cloud area -rainfall relationship was
derived as a two step process. First, a relationship

between the cloud area and the radar echo area, normalized
for the maximum area achieved by the cloud or cluster, was
established for the visible and infrared satellite data.
Second, the relationship between the echo area and rain vol-
ume was determined and was of the form:

Bv = I Ae - (5)

where Rv is rain volume per hour (m^-h-i) , I is rain in units
of (m3-km"'2-h-*) , and Ae is the echo area (kmS) defined by
the 1 mm-h-i rain rate. Thus, given a zime sequence of con-
vective clouds (or cluster areas) measured from visible or
infrared satellite images, volumetric rain rate can be
estimated.

Stout €t al. (19 79) modified the Grif fith/Woodley tech-
nique (Griffith et al., 1978) to estimate volumetric rain

38

rate directly from a cumulonimbas cloud area and area change
according to the equation:

E = a^A + a, dA/dt (6)

where R is the volumetric rainfall of the cloud (m^-s-i), A
is the cloud area (m2) , dA/dr is the change of cloud area
over time (m2-s~i), and a^ and a, are constants with dimen-
sions m-s-* and m, respectively. The two constants were
calculated by a least squares fit of cloud area-rain rate
pairs based on visible and infrared geosynchronous satellite
data and 5.3 cm ship radar rain data collected during GATE.
The cloud area and its change are defined by the threshold
value. The visible threshold for cloud area calculations
was 60 digital counxs on the ATS-3 (corresponding to an
albedo of 0.45 with the sun overhead), or equivalently 172
digital counts on the first Geosynchronous Meteorological
Satellite (SMS 1). The infrared threshold was 160 digital
counts (-260C). The standard error between the estimated

rainfall and the mean radar rainfall was 62% and 76% for the
visual and infrared equations respectively.

Wylie (1979) attempted to use the tropical convective
rainfall techniques of Griffith et al. , (1978) and stout et

39

al.r (1979) for estimating precipitation in Montreal, Can-
ada. Osing visual satellite data, corrected for the chang-
ing sun angle (Mcsher, 1975), infrared satellite data, and
10.0 cm radar meaured rainfall rates, Wylie studied six days
of precipitation, three days each in June and September
1977. Wylie concluded that because of air mass differences
between Montreal and the tropics, the Griffith and Stout
estimation techniques did poorly in Montreal, Canada. The
singlemost important limitation with these two schemes was
the difficulty of measuring cumulonimbus cloud area when the
"anvils were often merged into large cloud masses and the
extensive stratus cloud cover often obscured the pictures."
Wylie also noted that the Griffith el. al. (1978) threshold
of -260C had to be changed to -16°C for the summertime Mont-
real, Canada, area. With the warmer cloud top temperatures
the cloud areas were a larger, more appropriate size for
tracking.

Wylie (1979) then attempted to combine sounding data
input into a one- dimensional model (Simpson and Wiggert,
1969) and satellite cloud cover measurements to estimate
rainfall for Montreal. With the GATE measurements for rain
rates associated with satellite- derived cloud areas and the

UO

model output, raiafall rates were estimated by multiplying
the two values. The most accurate estimations were for the
cumulus clouds in the warm air masses occurring in June, the
cases the model was designed to handle. Wylie concluded

that in order to estimate rainfall in all geographical areas
and seasons a more sophisticated model would be needed.

Negri and Adler (198 1) did one case study of fifteen
thunderstorms in the Oklahcma, Arkansas, and Missouri area
on 24 April 1975. They used radar data for ground truth and
had special 5 minute GOES-E satellite passes over the area
of interest. They were able to determine zhat the precipi-
tation began falling, as indicated by radar data, for cloud
rop temperatures ranging from 229K to 260K (-44oc to -13oc).
The mean cloud tcp temperature value was 2U7K (-26<^C) .

41

III. CATA PROCESSING

A. INTRODUCTICN

The data set assembled for this study consists of collo-
cated GOES-E satellite data and Service-A hourly surface
observations for the southeastern United States during
August 1979. The GOES-E data consists of 10 x 10 pixel

matrices of visual and infrared satellite data centered over
each of 137 surface stations (Fig. 8) all south of HO^m,

The satellite data are measured with the Visual Infrared
Spin Scanned Radiometer (VISSR) which have subsatellite
point spatial resolutions of 1 and 7 km for the visual and
infrared channels, respectively. The GOES-E navigation was
completed by Man-computer Interactive Data Access System
(McIEAS) at the University of Wisconsin using the full reso-
lution visual data, with an accuracy of 1-2 pixels (1-2 km).
The full resolution visual data were averaged to a 7 km res-
olution, to equal the infrared data resolution. The visual
and infrared digital counts range from values of 0-255. The
10 X 10 pixel GOES-E visual and infrared satellite data each
cover an area 45 nmi x 45 nmi at SO^'N (50 nmi x 60 nmi at

42

U20N). The Service-A hourly repDrts total 70,623

observations. No Service-A specials or record-specials are
included.

Figure 8. Geographical Locations of Service-A Station
Report Data

The data are divided into two no-precipi-ation catego-
ries (Table VIII) and seven precipitation categories (Table

43

IX) to investigate precipitation specification, convective
versus continuous precipitation specification, and qualita-
tive specification of light versus moderate/heavy precipita-
tion. The pixel array size is also varied from the 10 x 10
array size to an 8 x 8, a 6 x 6, and a 4 x 4 array size to
investigate the differences in the data resulting from vari-
ous resolution sizes within a particular weather condition
classification.

B. CATA SORT

For the combined visual and infrared threshold specifi-
cation of precipitation, satellite data for 1200-2000 GMT,
corresponding to 0800-1600 EDT, were sorted into precipita-
tion and no-precipitation groups (Fig. 9). The 0800-1600
EDT interval was chosen to avoid distortion of the visual
satellite data due to a low solar elevation angle. The vis-
ual data were normalized and converted to albedos based on
the work done by Muench and Keegan (1979). This scheme cor-
rects for the varying zenith angle as well as adjusting the
visual satellite data for anisotropic scattering as related
to the zenith angle. (See Appendix A for further specific
information concerning the Muench and Keegan normalization
scheme.)

44

SURFACE DATA

East Coast and Gulf Coast United
States. August 1979. Service - A

HOURLY observations (/O. 623)

COLLOCATED SATELLITE DATA

Visual 10 x 10
pixel size

DAYLIGHT TIME CHECK
(avoid low solar angle for

VISUAL satellite DATA)

Include 1200-2000 GMT
(0800-1600 EDT) reports

Isolate Applicable Weather

AND Cloud Cases for Study

(see Tables VIII and IX)

Delete reports with any
zero values in satellite
visual and infrared data

Normalize Visual Data

CONVERT visual DIGITAL
counts to ALBEDOS
(MUENCH AND KEEGAN. 1979)

Compute means and standard
deviations of the albedos
and cloud top temperatures

FOR EACH 10 X 10. 8 X 8. 6 X 6.
AND ^ X 4 PIXEL ARRAY SIZE

Calculate mean and standard
deviation of the means and
standard deviations for each
weather/cloud classification
and pixel array size

Infrared 10 x 10

PIXEL SIZE

Figure 9. Flew Chart of Data Processing

45

While altedo values camiot exceed 1.00, the Muench and
Kaegan (1979) scheme allows the values to overshoot 1.00, up
to a value of 1.20. Therefore, the visual satellite values
are not true albedos, but estimated albedos. The extended
visual normalized data scale was used to facilitate compari-
son of the results in this effort to the most extensive bi-
spectral threshold precipitation specification of Muench and
Keegan (1979). The Muench and Keegan (1979) normalization
scheme specifies that any computed albedo greater than 1.20
be set equal to 1.20 to limit the unreasonably large values.
Similiarly, the scheme specifies computed albedos less than
0.15 be interpreted as the ground or water surface reflec-
tance and the value 0.00 be assigned. The infrared data
were processed in digital coun-s and converted to cloud top
temperatures prior to statistical computations and graphical
displays.

The no-precipitation data (Table VIII) are comprised of
the digital visual and infrared 10 x 10 pixel arrays of
those Service-A station reports not showing any "R" in the
current weather group. Thus, the no-precipitation group
includes stations reporting drizzle (weather codes L-, L,
and L-«-) .

46

TABLE VIII

Classification of Nc-Prscipitatioa Data Groups

Servics- A
Current Weather/
Category Name Cloud Grou^ Reports

no "R'V
2A No-Precipitation, Cloud Groups 1976

Overcast Ceiling 300, 030, 003,

130, 230, 013,
023, 103, 203,
113, 123, 213,
223

no "R"/
2B No-Precipitation, Cloud Groups 7358

Overcast and Broken (above groups)

and 200^ 020,
120, 220, 002,
102, 202, 112,
122, 212, 222

The no-precipitation data are divided into two catego-
ries, overcast ceiling (category 2A) and overcast and broken
ceiling (category 2B) . Cloud cover is based on the three

digit cloud group in the Service-A surface observation. The
first digit indicates the amount of low clouds, where 0 is
defined as clear, 1 is scattered (one-eighth to four-
eighths cloud cover), 2 is broken (five-eighths to seven-
eighths cloud cover) , and 3 is overcast (eight-eighths cloud
cover) . The second and third digit indicate the amount of
middle and high clouds, respectively. The same 0-3 values
defined for the low clouds are used for middle and high
cloud amount.

47

Ih9 precipitation data (Table IX) are comprised of the
visual and infrared 10 x 10 pixel arrays of those Service-A
station reports showing any '• R" in the current weather
group. Two precipitation observations were excluded from
the data set because each report also indicated clear skies.

TABLE IX
Classification of Precipitation Data Groups

Service- A
Category Name Current Weather Reports

1 Precipitation any "R" 538

1A Precipitation any "R" and overcast 329

- ^ -._.,..__ ceiling (as defined in

Table vlll category 2A)

IB Precipitation any "R" and overcast 534

Overcast and and broken ceiling (as

Broken Ceiling defined in Table VIiI

category 2B)

1C Continuous R-, a, R+ 112

Precipitation

IB Convective RW-, RW, RW+,TRW-, 426

Precipitation TRW, TRW+, TR-, TR, TR

IE Light R-, RW-, TRW-, TR- 464
Precipitation

IF Moderate/Heavy R, R + , RW, RM-f, TRW, 74

Precipitation TRW+, TR, TR

The general precipitation data (category 1) are divided
into six groups: precipitation overcast ceiling (category

48

1A) , precipitation overcast and broksn ceiling (category
IB), continuous (category 1 C) , convective (category ID),
light (category IE), and moderate/heavy (category 1F) pre-
cipitation. These seven precipitation groups ar9 used to
investigate precipitation specification, convective versus
continuous precipitation specification, and qualitative
specification of light versus moderate/heavy precipitation.

C. STATISTICAL TREATMENT

The means and standard deviations of albedos and cloud
top temperatures of each 10 x 10 pixel array for the weather
types listed in Tables VIII and IX wera calculated. Means
and standard deviations of albedos and cloud top tempera-
tures were also calculated for the 8x8, 6x6, and 4x4
pixel arrays centered over the surface station. The 8x8,
6x6, and 4x4 pixel arrays are equal to 36 nmi x 36 nmi,
27 nmi x 27 nmi, and 22 nmi x 22 nmi at 30°N respectively.
Variation of the digital satellite areal coverage is used to
investigate the differences in the statistics due to the
chosen resolution size.

The data sets in Tables VIII and IX are represented,
first, by the mean and standard deviation of the resolution
cell means and standard deviations. Second, these data sets

(

49

are represented by the distributions of the mean cloud top
temperatures and albedos where the mean cloud top tempera-
tures are sorted into ten Kelvin (K) intervals and the mean
albedos are sorted into 0.10 intervals. These representa-
tive statisxics and distributions are calculated for the
four pixel array sizes.

The statistical and distribution results for differing
resolution sizes, bi-spectral threshold specification of
precipitation, and separation of light from moderate/heavy
precipitation are discussed in Chapter IV.

50

I V . RESDLTS

A. INTRODOCTION

The figures presented in this chapter display the dis-
tributions of the grand means of the resolution cell means
of albedos and cloud top temperatures for the data sets
listed in Tables VIII and IX for the four array sizes. The
mean values are sorted into ten Kelvin intervals and 0.10
estimated albedo intervals.

B. EESOLaTICN

The effect of satellite resolution in representing gen-
eral precipitation (category 1) and no-precipitation over-
cast (category 2A) data are explored for four resolution
sizes. The four sizes are 10 x 10, 8x8,6x6, and 4x4
and are approximately equal to areas of 2025 nmis, 1296
nmi2, 729 nmi2, and 484 nai^ at SO^N respectively.

The general precipitation (category 1) and no-precipita-
tion overcast (category 2A) data were chosen for study
because, while they represent two different weather condi-
tions, their albedo and cloud top temperature distributions
have the largest amount of overlap when compared to any

51

other pair of prscipitation versus no-pracipitation data
sets. The possibility arises that statistical differences
in the four resolution sizes might be sufficient or comple-
ment other information in delineating these two weather
conditions,

'^' Precipitation Data

The general precipitation (category 1) data are com-
prised of 329 overcast ceiling reporrs (61%), 205 broken
ceiling reports (38%), and 4 scattered ceiling reports (1%).

a. Mean Statistics

The precipitation data (category 1) differences
between the means of the cell means visual and infrared 10 x
10 and U X 4 array sizes are 0.035 and 2.2K, respectively
(Table X) . The trend of the mean of the means is toward

higher albedo values and colder cloud top temperatures with
the decreasing area or array size. The standard deviations
of the means similiarly show an increase in the albedo,
0.016, and cloud top temperature, 1.0K, from -he 10 x 10
array size to the 4x4 array size.

b. Standard Deviation Statistics

The standard deviation statistics display the
opposite trend with decreasing area as the mean statistics.

52

TABLE X

Precipitation Data Statistics for Four Array Sizes

Overcast, Broken, and Scattered Ceilings

Mean of (VIS)
Means

(IR)

Standard (VIS)

Deviations

of Means (IR)

10. X 10

. 579

253. OK
(-20OC)

. 211
20. 7K

8x8

. 591

252. 2K
(-2 10C)

. 214
21. OK

6x6

603

.219
21 .3K

U X U

.614

251. 4K 250. 8K

(-220C) (-220C)

.227
21. 7K

Mean of (VIS)
Standard
Deviations (IR)

Standard
Deviation (VIS)
of the
Standard
Deviations (IR)

. 173

. 161

. 144

. 124

10. 4K

9. IK

7.6K

5.6K

.078

. 078

.075

.072

7. OK

6.7K

6. OK

4.9K

The means and standard deviations of the standard deviations
decrease in the visual and infrared values with decreasing
area (Table X). The differences between the 10 x 10 and 4 x
4 array sizes visual and infrared means of the standard
deviations are 0.049 and 4.8K, respectively, and the stan-
dard deviations of the standard deviations are 0.006 and
2. IK, respectively.

53

c. Distribution Discussion

Th€ distributions of the precipitation data are
shown in Figs. 10, 11, 12, and 13. There is a discernible
shift toward higher albedos and colder cloud top tempera-
tures of the 2% and 3% frequency isopleth with decreasing
array size. This upward shift is also reflected in the mean
of the means (Table X). The appearance of the 5% frequency
isopleth in the 6x6 and 4 x 4 array sizes at high albedos
and cold cloud top temperatures highlights the shift.

1.20 •

0

0

0

0

0

0

0

0

0

0

0

1.10 ■

/ 1

0

0

0

0

I

I

1

1

0

0

/

1.

1.00 •

/

/

0

0

0

0

0

t*

0

3

5

/6

/

0

0.9 ■

^""^

v\

0

0

0

6

1

4

1

Azj

""^^^

1)9

0

0.8 ■

^-2%.

/^

//

0

0

c

2

ax

-^3

12

A25.

/6

0

0.7 ■

0

0

2

V

^

s45^»

23

C^

4

2

0

0.6 -

0

0

3

/

J'V

©y

<r

y(Q

9

0

0

0.5 •

0

0

'(<

3^

^21.

i>

^

3

0

0

0

0.4-

^^

•y——

0

2

10

s

9

3

0

0

0

0

0.3 •

<^2%-*-^

c

5

/i/T/

iv/

7

^

1

0

0

0

0

0.2 •

/

\

y

0

/

2^

^i^

5

1

0

1

1

0

0

0

y

/

0.1 ■

/

\0y

1

1

I

1

0

0

1

0

0

0

0.0

-+■

H 1

1

\

■» ^

-H

H

H

-H

1 —

310 300 290 280 270 260 250 240 230 220 210 200
CLOUD TOP TEMPERATURE (K)

Figure 10. Precipitation Data for 10 x 10 Array Size (The
mean, .579 and 253. OK, interval is boxed. The
2% and 3% frequencies are for 11 and 16
occurrences, respectively.)

54

Figure 11.

300 290

250 240 230 220
CLOUD TOP TEMPERATURE (K)

Precipitation Data for 8x8 Array Size (The
mean, .591 and 252. 2K, interval is boxed. The
2% and 3% frequencies are for 11 and 16
occurrences, respectively.)

Figure 12.

1.20 •

0

0

0

0

o'

0

0

0

0

0

0

1.10 ■

y\

0

0

0

0

1

1

1

1

0

1

/

i'

1.00 •

/

y

0

0

0

2

1

4

1

6

-^

/

0

0.9 •

^

"^^^^s

y^

^

0.8 ■

0

0

0

5

0 4

^^2%

3 >

S

S^5%

>>

)

0

0

0

0

4

/ih

13

X^

^7

f^

0

0.7 •

/

^•fc"

/ /

/

/^

0.6 ■

0

0

3

/

"(

|18J

/22/ 20

^

1

0

0

0

4

/16

11 \

C^L/

•-n^*

14^

/ 3

0

0

0.5 ■

/

y

0

0

y

15

/H/

^>

?« 5

4

3

0

0

0.4-

/

^^*"

\ '^ >

X

0

2

iJ^

^V

I \iy

5

3

2

0

0

0

0.3 ■

/

//

X

0

<t

/lO/

i(l.

/ k

5

0

0

0

0

0

0.2 ■

/

/

0

/

V 9

2

2

0

1

0

1

0

0

0.1 •

1 _

x

0.0

'5-

— +

1

1

—i

2

-i

1

— « 1

1
1

0

— »

1

^

0

— t 1

0

-+■

0

1 —

310 300 290 280 270 260 250 240 230 220

CLOUD TOP TEMPERATURE (K)

210 200

Precipitation Data for 6x5 Array Size (The
mean« .603 and 251. 4K, interval is boxed. The
2%, 3%, and 5% frequencies are for 11, 16, and
27 occurrences, respectively.)

55

Figure 13.

1.20 •

0

0

0

0

0

0

0

0

0

0

0

1.10 ■

0

0

0

1

0

3

1

1

0

1/

X

1

1.00 •

0

0

0

1

1

2

0

7 ^

^

.2*

13

y 0

0.9 •

0

0

0

4

2

8

6

^

€

'V

/

2

0.8 ■

0
0

0
0

1

2

9

Xl9 .

2

/

2

0.7 ■

14

"TT

15^

y
/ 24

0
0

0.6 -

0

0

6

A3

GX

Is

Nl4

A

0

0

0.5 ■

0

1

^c

>..

9

X
10

8

2

0

0

0.4 ■
0.3 •

0

1

10

9

7

3

2

0

0

0

0

3

/

e

/ 5

a

4

1

0

0

0

0

0.2 "

/

X

0 /

2

/

9

2

3

0

2

0

1

0

0

0.1 ■

■/

X

0.0

J^

1

5

2
H ¥

1

^

1

0

— t

0
-*

1

t

— t-

0

-+

0

1 —

310 300 290 280 270 260 250 240 230 220 210 200

CLOUD TOP TEMPERATURE (K)

Precipitation Data for 4x4 Array Size (The

mean. .614 and 250. 8K, interval is boxed. The

2%., 6%, and 5^ frequencies are for 11, 16, and
27 occurrences, respectively.)

The distributions of the 10 x 10 and 3x8 array
sizes (Figs. 10 and 11) are unimodal while the 6x6 and 4 x
4 array sizes (Figs. 12 and 13) appear to be more bimodal.
The four array sizes were tested for a Gaussian distribution
with the Chi-sguare test and all failed az any confidence
level. • Therefore, differences in the four resolutions can-
not be adequately tested by well defined statistical methods
based on an assumed normal distribution.

The similiarities between ths 10 x 10 and 8x8
array sizes (Figs- 10 and 11) and the 6x6 and 4x4 array

56

sizes (Figs. 12 and 13) are further illustrated in Fig. 14.
A diagonal cut is plotted for each of the four array sizes
where the lines plotted are shown as a dashed boxed area in
Figs. 10-13. The diagonal cut reveals the close agreement
between the 6x6 and 4x4 array sizes along the line. The
10 X 10 and 8x8 array size lines follow the same general
trend but do not coincide as closely as the 6x6 and 4x4
array size lines.

The chosen diagonal line results in the 8 x 8
array size distribution appearing more smoothed than the 10
X 10 (Fig. 14), as there is no relative minima at the 4.0
interval for the 8x8 array size. The 10 x 10 array size,
with the greater areal extent and therefore more averaging
of differing clouds and clear areas, is expected to possess
the "smoothest" appearance, the lowest number of relative
maxima and nicima of the four array sizes. However, the 8 x
8 array size actually displays the fewest relative maxima
and minima along the chosen diagonal line. The smoother 8 x
8 array size cannot be explained in terms of significant
differences in the number of cases of different ceiling
types or different precipitation types occurring in interval
4.0 between the four array sizes. Quite simply, the

57

smoother 8x8 array size apparently rssults from ths sort-
ing intervals chosen for the distributions.

CLOUD TOP TEMPERATURE/ RLBEDO INTERVALS

Figure 14.

Precipitation Array Size Distributions Along
Diagonal Line (The line rep;:esent3 the 10 x 10,
dotted line the 8x8, dashed line the 6x6,
and dash dot line the U x 4 array size.)

The elongated shape of all four precipitation
distribution array sizes (Figs. 10, 11, 12, and 13) reveal
the variation in the areal amount of cloudiness and precipi-
tation. The distributions range from high albedos and cold
cloud top temperatures (indicative of satellite fields of

58

view filled with precipitating clouds) to low albedos and
warm cloud top temperatures (indicative of satellite fields
of view partially filled with precipitating clouds). The
visual and infrared satellite data distributions in Figs.
10 r llf 12, and 13 agree with the elongated shapes of Piatt
(1981) for his cloud classifications of cumulus, frontal,
and Jetstream cirrus clcuds and agree with Coakley and
Bretherton (1S82) for their general clouds present in a 1000
km2 Pacific Ocean area,
d. Summary

A sarellite field of view filled with a precipi-
tating cloud is expected to have highsr albedo and colder
cloud top temperature values than a partially filled field
of view. Additionally, the filled field of view would have
a more uniform texture, as reflected in variance or standard
deviation values, than a partially filled field of view.
The statistics discussed in this study confirm these expec-
tations for this data set. As the array size or field of
view is decreased, the mean statistics increase while the
standard deviation statistics decrease (Table X).

Fcr the precipitation data (category 1) , there
are significant differences between the four resolution

59

sizes. These differences are reflected in the upward trend
in albedos and colder cloud top temperatures of the mean and
the standard deviation of the means with decreasing area or
array size (Table X) . The reverse trend is found in the
mean and standard deviation of the standard deviations.

The distributions have significant differences
also. The relatively coarse resolution 10 x 10 and 8x8
array sizes have a unimodal distribution while the rela-
tively fine resolution 6x6 and 4x4 have a bimodal
distribution.

The four array sizes discussed vary in their
statistics and distributions in representing the precipita-
tion (category 1) data. The choice of satellite resolution
for representation of the precipitation data will influence
comparison of these data with other data. Therefore, for
the remainder of this study the precipitation data for all
classifications will be discussed using both the 10 x 10 and
4x4 array size. ,

One additional topic to explore is that a number
of cases with albedos less than 0.40 appear in the precipi-
tation data (category 1) in all four size distributions
(Figs. 10, 11, 12, and 13). These low albedo values suggest

60

the possibility that there might be a consistent low bias in
the normalization scheme. But a closer look at the

individual reports with albedos less than 0.40 show no
pattern involved with either the GMT hour or the longitude
or latitude of these staticn reports. Further analysis of
these low albedo precipitation reports are discussed in the
light precipitation section (IV. E.).
2- No -precipitation Overcast Data
a. Mean Statistics

For the no-precipitation overcast cases (cat-
egory 2A) , differences between the means of the means visual
and infrared 10 x 10 and 4x4 array sizes are 0.011 and 0.3
K, respectively (Table XI). The 0.3K infrared difference is
within the 0.5K noise level of the VIS3R infrared sensor.
The trend of the visual mean of the means is upward with the
decreasing array size. The standard deviations of the means
show an increase in the albedo, 0.014, and cloud top temper-
ature, 0.8K, from the 10 x 10 to 4 x 4 array sizes. Once
again, both mean statistics have an upward trend with
decreasing array size.

61

TABLE XI
Nc-Precipitation Data Statistics for Four Array Sizes

Overcast Ceiling

20x20 8x8 6x6 ixU

Mean of (VIS) .101 .411 .415 .418

Means

272. 6K
(-I^C)

272. 5K
(-10C)

272. 4K
(-10C)

272. 3K
(-10C)

. 205

. 208

.213

.219

17. 8 K

18. IK

18. 3K

18. 6K

(IR)

Standard (VIS)

Deviations

of Means (IR)

Mean of (VIS) .122 .113 .102 .087

Standard

Deviations (IR) 5.4K 4.7K 3.9K 2.9K

Standard

Deviation (VIS) .056 .054 .052 .049

of the

Standard

Deviations (IR) 4.8K 4.4K 3.9K 3. IK

b. Standard Deviation Statistics

Conversely, the standard deviation statistics
have a downward trend with decreasing area size. The dif-
ferences between the 10 x 10 and 4x4 array visual and
infrared means of the standard deviations are 0.035 and
2.5K, respectively. The differences in the standard devia-
tions of the standard deviations are 0.007 in the visual and
1.7K in the infrared values.

62

c. Distribution Discussion

The distributions of the no-pracipitation over-
cast data are shown in Figs. 15, 16, 17, and 18. These dis-
tributions are quite different from the precipitation
distributions (Figs. 10, 11, 12, and 13). As expected, the
no-precipitaticn overcast data are clustered at the low
albedo and warm cloud top temperature values. The 5% fre-
quency isopleths in Figs. 15, 16, and 17 show a grouping of
the data at albedos ranging from 0.30 to 0.50 and cloud top
temperatures from 280K to 290K. A bimodal distribution

appears in the finer resolution 8x8, 6x6, and 4x4
array sizes (Figs. 16, 17, and 18). This shifting of the
no-precipitaticn overcast data into two relative maxima for
the three smallest array sizes is the sole significant dif-
ference in the four distributions.

d. Summary

The no-precipitation overcasr data display an
upward trend in the two mean statistics with decreasing
array size, although the 0. 3K mean of the means infrared
difference is not significant. Conversely the two standard
deviation statistics decrease with decreasing array size.
These trends are consistent with the expected statistical

63

Figure 15.

Figure 16.

290 280

i-
240

230

270 260 250 240 230 220 210
CLOUD TOP TEMPERATURE (K)

Nc-Precipitation Overcast Data for 10 x 10 Array
Size (The mean, .407 and 272. 6K, interval is
boxed. The 2^, 3%, 5% and 7% frequencies are
for UO, 5 9. 99, and 138 occurrences,
respectively. )

300 290

270 260 250 240 230 220
CLOUD TOP TEMPERATURE (K)

No-Precipitation Overcast Data for 8x8 Array
Size (The mean, .411 and 272. 5K, interval is
boxed. The 2%, 3%, 5% and 7% frequencies are
for 40, 59, 99, and 138 occurrences,
respectively. )

64

Figure 17.

Figure 18.

310

-i 1

300 290 280 270

260 250 240 230 220 210 200
CLOUD TOP TEMPERATURE (K)

No-Precipitation Overcast D--=; for 6x5 Array
Size (The mean, .UIS and 272. 4K, interval is
boxed. The 29?, 3%, and 5% frequencies are for
40, 59, and 99 occurrences, respectively.)

310 300

270 260 250 240 230 220
CLOUD TOP TEMPERATURE (K)

210 200

65

trends discussed in the precipitation section (IV.B.I.)*
However, in these data, there is a greater similiarity in
the statistics for the four sizes because the ceilings are
all overcast reports.

The distributions (Figs. 15, 16, 17, and 18)
provide visual conf irmaticn of the similiarities between
each of the four array sizes. With the exception of the

second relative maxima at albedos of 0.30 zo 0.40 and cloud
top temperatures of 260K tc 270K appearing in the 8x8, 6 x
6, and 4x4 array sizes (Figs. 16, 17, and 18), the four
distributions are nearly identical. Because there are sta-
tistical differences and distributional differences in the
four array sizes, the 10 x 10 and 4x4 arrays sizes will be
used to represent the two no-precipitation data categories.
3» Precipitation and No- precipitation Comparison

The possibility arises that statistical differences
in the four resolution sizes might be sufficient, or at
least complement other information, in delineating the pre-
cipitation frcm the nc- precipitation weather condition. The
question then becomes, is there a sta-is-cic associated with
variation of the array size within Tables X and XI which
differentiates the precipitation reports from the no-precip-
itation overcast reports?

66

If the satellite data procassor can vary the
resolution size, as was dene in this study by simply averag-
ing different pixel array sizes, a trend in the visual and
infrared data might be used to differentiate these two
weather conditions. The most significant trend difference
in the precipitation data (Table X) and no-precipitation
overcast data (Table XI) occurs in the mean of the means.
Recall that the mean of the means precipitation visual dif-
ference between the 10 x 10 and 4x4 array sizes was 0.035
while the no-precipitation overcast visual difference was
0.011. Similiarly the infrared differences were 2.2K and
0.3K for the precipitation and no-precipitation overcast,
respectively. The precipitation data show a greater upward
trend toward higher albedos and colder cloud top tempera-
tures than the no-precipitation overcast with the finer sat-
ellite resolution.

Differentiation between these two data sets based on
a compai^iscn of the trend in the mean of the means are sug-
gested by Tables X and XI. It musx be emphasized that these
tables are based on many reports and therefore reflect the
most rypical values. Individual reports within a given

interval should he studied to provide conclusive evidence as

67

to whether these statistics can be used on a few reports to
differentiate precipitaticn from no-precipitation overcast
reports.

C. PRECIPITATICN SPECIFICATION

An essential difference between this specification study
and most of those in the literature is that the distribu-
tions of the precipitation and no-precipitation data sets
are examined in detail to extract information about the
probability of correct classifications. Only Lovejoy and
Austin (1979) present their data distributions. The bi-

spectral and life history method thresholds (Tables I and
VII) refer to the typical or most common threshold values
for precipitation, which is assumed to be equivalent to the
mean of the means in this study. Therefore, the mean of the
means can be coipared to the threshold values in Tables I
and VII. Additionally, a bi -spectral threshold can be pro-
posed based on the distributions and with these distribu-
tions the amount of overlap, or the percentage of correctly
classified precipitation or no-precipitation cases, can be
calculated.

68

''• OUISlIl Ceilings

Are the precipitation overcast (category 1A) and
no-precipitation overcast (category 2A) data sets suffi-
ciently separated to allow differentiation of the two popu-
lations? If so, how much overlap is there between the two
data sets?

a. Mean of the Means

The mean of the means statistics for the precip-
itation overcast versus no-precipitation overcast data.
Table XII, show there is a .2U2 and 24. 4K difference between
the two populations for the 10 x 10 array size and a .254
and 25. 9K difference for the 4x4 array size. The respec-
tive differences are greater than one standard deviation of
the means of either of the two populations.

If the two precipitation overcast array sizes
are compared to the no- precipitation overcast array sizes,
the stronger trend in the mean of the means (Table XII) is
seen in the precipitation overcast data. While the precipi-
tation visual and infrared values vary by 0.023 and 1.8K
between the 10 x 10 and 4x4 array sizes, the no- precipita-
tion visual and infrared values vary by 0.011 and 0.3K.
Both the mean cf the means and their trends can be used to

69

TABLE XII
Precipitation Specification Overcast Ceilings

Mean of (VIS)
Means

(IR)

Standard (VIS)

Deviations

of Means (IR)

Precipi- No-Preci- Precipi- No-Preci-
tation pitation tation pitation

10 X 10 10 X 10

.64 9

. 407

4x4

.672

4x4

.418

248. 2K
(-250C)

272. 6K
(-10C)

246. 4K
(-270C)

272. 3K
(-10C)

. 186

.205

.201

.219

18. 9K

17. 8K

19. 8K

18. 6K

Mean of (VIS)
Standard
Deviations (IR)

Standard
Deviation (VIS)
of the
Standard
Deviations (IR)

. 152

. 122

.108

.087

8.9K

5.4K

4.4K

2.9K

.078

.056

.069

.049

6.3K

4.8K

4. OK

3. IK

differentiate precipitation from no-pcecipiration for a
large numter of reports in a region similiar to this summer-
time convective shower dominated area.

b. Mean of the Standard Deviations

The visual and infrared means of the standard
deviations vary by 0.030 and 3.5K for -che 10 x 10 array size
and by 0.021 and 1.5K for the 4x4 array size. In the

infrared values, the no -precipi tat ion mean of the standard
deviations have a magnitude 60% of the precipitation values

70

and produce relatively large differences. In the visual
values, the no-precip itaticn mean of the standard deviations
have a magnitude 80% of the precipitation values. The rela-
tively large differences (only the mean of the means have a
larger difference) suggest the use of this statistic to dif-
ferentiate precipitation overcast from no-precipitation
overcast.

c. Standard Deviation of the Means

The differences in the standard deviations of
the means (Table XII) are nearly equal when comparing the
two 10 X 10 array sizes and the two U x U array sizes. The
visual differences are 0.019 for the 10 x 10 and 0.018 for
the 4x4 array size. Similiarly, the infrared differences
are 1.1K for the 10 x 10 and 1 . 2K for the 4x4 array size.
The differences in the 4x4 array size (0.018 and 1.2K) are
comparable to the relatively significant differences in the
means of the standard deviations (.021 and 1 . 5K) . However,
the differences are not comparable in the 10 x 10 array
size .

d. Standard Deviation of the Standard Deviations
The differences in the standard deviations of

the standard deviations (Table XII) for the two array sizes

71

are approximately equal also. The visaal differences are
0.022 for the 10 x 10 and 0.020 for the 4x4 array size.
The infrared differences are 1.5K for the 10 x 10 and 0.9K
for the 4x4 array size. Once again the differences in the
4x4 array size (0.020 and 0.9K) are approximately equal to
the differences in the means of the standard deviations
(0.021 and 1.5K), particularly in the visual value,
e. Distribution Discussion

The distributions for the 10 x 10 array size
precipitation overcast (Fig. 19) and no-precipitation over-
cast (Fig. 15) and the 4x4 array size precipitation over-
cast (Fig. 20) and no-precipitation overcasx ((Fig. 18)
allow visual confirmation of the degree of separation of
these two populations. These figures verify the separation
between the the occurrence maxima of rhe -cwo populations
while showing that there is overlap of some of the values in
the two populations.

The appearance of a bimodal distribution in the
relatively fine resolution 4x4 array size precipitation
overcast (ca-cegory 1A) and no-precipitation overcast (cat-
egory 2A) in Figs. 20 and 18 cannot be explained in terms of
the precipitation categories (Table IX) or ceiling cover.

72

Figure 19

Figure 20.

H 1-

300 290

-t
280

270 260 250 240 230 220
CLOUD TOP TEMPERATURE (K)

210 200

Precipitation Overcast Data for the 10 x 10
Array Size (The mean, .649 and 248. 2K, interv
is boxed. The 2%, 3%, and 5% frequencies are
for 7, 10, and 16 occurrences, respectively.)

1.20 •■

i.io -•
1.00 ■■

0.9 •■
0.8 -■
0.7 ••
0.6 -■
0.5 ■■
0.4 -•

0.3 ••
0.2 -•
0.1 ••

0.0

■+■

■+■

310 300 290

— t 1—

240 230

-H—
220

■+■

-+-

210 200

280 270 260 250

CLOUD TOP TEMPERATURE (K)

Precipitation Overcast Data for 4x4 Array Size
(The mean, ,672 and 246. 4K, interval is boxed.
The 2^, 3^, 5% and 7% frequencies are for 7, 10,
16, ana 23 occurrences, respectively.)

73

An alternate explanation might be that these two maxima
reflect different synoptic signatures. Four weak frontal
systems impact this data set region during August 1979 and
cause a change in the cloudiness and precipitation pattern
which is normally produced by daytime heating. Recall that
the Lovejoy and Austin (1979) data set also showed bimodal

distributions for the cumulus no-rain reports. The bimodal
distributions in this study may not be due to a synoptic
signature. Nonetheless, this possibility should be

investigated.

f. Precipitation Probabilities

Precipitation probabilities (Figs. 21 and 22)
were computed from the precipitation overcast (category 1A)
and the no-precipitation overcast (category 2A) data for the
10 X 10 (Figs. 19 and 15) and the 4x4 (Figs. 20 and 18)
array sizes. Estimated albedos greater than 1.00 were not
included in rhese prcbabilities as they accounted for only
two and three no-precipitation overcast reports and four and
five precipitation overcast reports in the 10 x 10 size and
4x4 array size, respectively. The two probability figures
indicate that the 50% probability cf precipitation is not a
simple function of mean albedo and mean cloud top
temperature.

74

290 270 250 230
CLOUD TOP TEMPERATURE (K)

210

Figure 21. Precipitation Overcast Data Probability 10 x 10
Array Size

1.00 •

0.27"

''^^'*"8x^2

0.64

0.68

0.80 ■

0.0

0.07

0.2 8

N

<i^^2^

0 .36

o
a

0.60 -

■

pa

0.0

0. 06

0.13

0.25

0.31

•J

<

0.40 -•

•

0.20 •

0.0

0.02

0.0 7

0.02

0.0

0.0

0.03

0.07

0/^0^

1.00

1

1

_L

1

1

^^

1

T^

1

290

270 :

25C

) 230

210

CLOUD TOP TEMPERATURE (K)

Figure 22. Precipitation Overcast Data Probability 4 x a
Array Size ^

The 50% probability line (Fig. 21) shows the
precipitation at low cloud top temperatures (270K-290K)

75

occurs at high albedos (0.80-1. 00) and at cold cloud top
temperatures (210K-230K) occurs at relatively low albedos
(0.40-0.60). One exception occurs in the 0.60-0.80 albedo
and 210K-230K cloud top temperature interval and represents
26 precipitation reports of 64 total reports. The 100% pre-
cipitation probability at 0.00-0.20 albedo and 230K-250K
results from two precipitation reports. Two reports in a
0.20 albedo and 20K cloud top temperatura interval are not a
sufficient number of reports to be a significant indication
of a high probability of precipitation. The 50% precipita-
tion probability line (Fig. 22) in the 4x4 array size data
shows the same general trend of decreasing albedo with
decreasing cloud top temperatures. In this fine resolution
data (Fig. 22) , there is an upturning of the 50% probability
line at the coldest cloud top temperatures, 210K-230K.
There are 73 no-precipitaticn overcast and 80 precipitation
overcast reports in the 4x4 array size dara in the
210K-230K interval so the upturning is nor the result of
lack of data. The appearance, once again, of a greater than
50% probability of precipitation at low albedos, 0.00-0.20,
between 210K-250K results from a total of four reports (one
precipitation report of two total reports in the 230K-250K

76

interval and two precipitation reports of two reports in the
210K-230K) and is not a significant indication of high pre-
cipitation protability.

If a straight line is drawn to represent the 50%
probability line, the lines for the two array sizes are
nearly coincident until the 230 K cloud top temperature is
reached. For the purposes of this study, a simple linear
function bi-spectral precipitation threshold based on a 50%
probability of precipitation can be approximately defined as
extending from 1.00 albedo and 290K cloud top temperature to
0.60 albedo and 210K cloud top temperature.

Comparison of this linear bi-spectral threshold
with the Muench and Keegan (1979) threshold (Fig. 2), shows
•che proposed thrshold has an albedo approximately 0,10
smaller at corresponding cloud top temperatures. The 50%

probability asymptote at the warm cloud top temperatures
shown in the Muench and Keegan (1979) results (Fig. 2), are
not shown in Figs, 21 and 22 due to lack of reports in these
values. The lower albedo values for this linear bi-spectral
threshold may be associated with the dominance of convective
precipitation (426 of 5 38 reports) in the precipitation
data. The effect of convective precipitation reports on the
satellite albedo values is discussed in Section IV. D.

77

g. Summary

The two significant statistics for precipitation
specification of overcast ceiling reports for both array
sizes are the mean of the means and the mean of the standard
deviations (Table XII). The probabilitas in Figs. 21 and 22
make use of the mean of the means only. Inclusion of the

mean of the standard deviations in the precipiration and
no-precipitaticn distribution plots may more distinctly
define the two weather data types. The question is, how to
graphically display four variables (i.e. four dimensions) in
one plot?

One solution is to find a three-dimensional plot
that involves the four variables. The most straight forward
approach is tc define the 50% probability for the mean of
the means (Figs. 21 and 22) in terms of a surface. A plane
would be the simplest surface choice. The equation of a
line perpendicular to the 50% probability plane intersecting
its midpoint in the distribution planes shown would then be
calculated. All of the precipitation and no-precipitation
points would be projected onto the line and the line would
become the x-axis in a new plot. Thus this x-axis reflects
the visual and infrared mean of the means. The visual and

78

infrared m€an of the standard deviations would define the
y-axis and z-axis, respectively.

The defined plot for the precipitation and no-
precipitation data would show the relative dependence of the
data on the four variables. If the plots produced distinct
groups for the precipitation and no-precipitation data, new
precipitation probabilities would be calculated. The varia-
tion with satellite resolution size of the precipitation
probabilities would then have to be reconsidered with the
new data. The data processing described is beyond the scope
of this particular research effort and is recommmended for
future investigation.

Precipita-cion specification for overcast ceil-
ings can fce delineated by the values for the mean of the
means and the mean of the standard deviations for any array
size discussed in this study. The mean of the mean values
when used with Figs. 21 and 22 will indicate the probability
of precipitation, given a similiar time of year and climato-
logical area. A simple linear bi-spectral threshold, based
on a 50% probability of precipitation, is defined approxi-
mately as extending from a 1.00 albedo and a 290K cloud top
temperature to a 0.60 albedo and a 210K cloud top
temperature.

79

2. Overcast and Broken Ceilings

Once again the question arises, are the precipita-
tion overcast and broken (category 1B) and no-precipitation
overcast and troken (category 2B) data sets sufficiently
separated to allow differentiation of tha two populations?
If so, how much overlap is there between the two data sets?

a. Mean of the Means

The in^.n of the means statistics for the precip-
itation overcast and broken (category IB) versus no-precipi-
tation overcast and broken (category 2B) data. Table XIII,
show there is a .309 and 27. OK difference between the two
populations for the 10 x 10 pixel size and a .339 and 29. 1K
difference for the 4x4 pixel size. The respective differ-
ences are approximately equal to one and one-half standard
deviations of the means of either of tha two populations.

For these data, the differences in the trends of
the mean of the means between the 10 x 10 and 4x4 array
sizes for the precLpitaticn overcast and broken reports are
more dramatic than for the precipitation overcast reports.
There is a 0.036 visual and a 2.2K infrared difference in
the precipitation overcast and broken data and only a 0.006
visual and a O.IK in the no-precipitation overcast and

80

TABLE XIII
Precipitation Specification Overcast and Broken Ceilings

Precipi- No-Preci- Precipi- No-Preci-
tation pitation tation pitation

Mean of
Means

(VIS)
(IH)

.580

252. 8K
(-20OC)

Standard
De viations
of Means

(VIS)

(IR)

.210

20.5K

10 X 10 10 X 10

. 271

279. 8K
(1-70C)

. 189
16. 6K

U X 4

.616

.225
21. 5K

4 X a

.277

250. 6K 279. 7K

(-230C) (+70C)

.207
17. 8K

Mean of (VIS)
Standard
Deviations (IR)

Standard
Deviation (VIS)
of the
Standard
Deviations (IR)

. 173

. 128

.124

.094

10. UK

5.9K

5.6K

3.2K

.078

. 064

.072

.057

7. OK

5.7K

4 .9K

3.7K

broken data between the 10 x 10 and 4x4 array sizes.
Therefore, variation of the resolution size and the trend
for the mean of the means can be used, as well as the mean
of the means value itself, in delineating precipitation from
no-precipitation for these overcast and broken ceiling
reports.

b. Mean of the Standard Deviations

The values of the mean of the standard devia-
tions are important. The 0.045 albedo and 4.5K cloud top

81

temperature difference between the two data sets for the 10
X 10 array size are significant as well as the 0.030 and
2.4K difference for the U x U array size.

c. Standard Deviations of the Means

The differences in the standard deviations of
the means are nearly equal when comparing the two 10 x 10
array sizes and the two U x 4 array sizes. The visual dif-
ferences are 0.021 for the 10 x 10 and 0.018 for the 4x4
array size. Similiarly, the infrared differences are 3.9K
for the 10 x 10 and 3.7K for the 4x4 array size. The vis-
ual differences are 40% less than the statistically signifi-
cant visual mean of the standard deviation differences and
the infrared differences are comparable to the infrared mean
of the standard deviation differences.

d. Standard Deviation of the Standard Deviations
The differences in the standard deviations of

the standard deviations are approximately equal. The visual
differences are 0.014 for the 10 x 10 and 0.015 for the 4 x
4 array size. The infrared differences are 1.3K for the 10
X 10 and 1.2K for the 4x4 array size. Both the visual and
infrared differences are 50% less than the respective sig-
nificant differences in the mean of the standard deviations.

82

e. Distribution Discussion

The distributions for the 10 x 10 array size
precipitation overcast and broken (Fig. 23) and no-precipi-
taticn overcast and broken (Fig. 24) and the U x U array
size precipitation overcast and broken (Fig. 25) and no-pre-
cipitation overcast and broken (Fig. 26) allow visual con-
firmation of the relatively larger degree of separation
between these two populations compared to the overcast ceil-
ing data. These figures once again also show overlap
between the two populations.

310 300 290 280 270 260 250 240 230 220 210 200

CLOUD TOP TEMPERATURE (K)

Figure 23. Precipitation Overcast and Broken Data for 10 x
10 Array (The mean, .580 and 252. 8K, interval is
boxed. The 2% and 3% frequencies are for 11 and
16 occurrences, respectively.)

83

Figure 24 .

270 260 250 240 230
CLOUD TOP TEMPERATURE (K)

Nc-Precipitaticn Overcast and Broken for 10 x 10
Array (The mean, .27 1 and 279. 8K, interval is
boxed. The 2f, 3%, 5%, and 7% frequencies are
for 147, 221, 368, and 515 occurrences,
respectively. )

1.20 •

0

0

0

0

0

0

0

0

0

0

0

i.io ■

0

0

c

1

0

3

1

1

0

1

1

1.00 ■

— ^

0

0

0

1

1

2

0

7

/14

13>

) °

0.9 •

0

0

0

4

2

3

6

^

^

'/^

f

2

0.8 ■

*«* i^£

>eo

^^ ^^

/

/

0

0

1

9

^

12

i>

■^8

20A

/ 7

0

0.7 •

^

y

ziT

/r

Q

c

0

2

h

U

W\

24

19

/A

2

0

Q

0.6 •

.

^

.^—^,

7

CQ

0.5 '

0

0

e

/

j'<

a
\

VI

/^

Vii/

/ 3

0

0

0

4

13

3

9

10

8

2

0

0

0.4 ■

V

-a*-

^

0

10

li

s

7

3

2

0

0

0

0.3 ■

0

8

. 5

e

4

1

0

0

0

0

0.2 -

0

s

2

3

0

2

0

1

0

0

0.1 ■

0.0

3

0

4

2

1

1

0

0

1

0

0

0

300

290

280 270

260

250

240

1 \

230 220

210 200

CLOUD TOP TEMPERATURE (K)

Figure 25. Precipitation Overcast and Broken Data for 4x4

Array (The mean, .616 and 250. 6K, interval is

boxed. The 2%, 3%, and 5% frequencies are for
11, 16, and 27 occurrences, respectively.)

84

1
1

13

10 33 15

35 32 26 15 12 25 37
79 64 63 2a 36 39 30

27 1^ 93 77 <*'* <f^ 50 16

2%

95 ICt 65 62 34 7

93^125 102 70 22 2

111/132 75 26 2 1

7 68 16 3 3 0

19 31 5 10 1

i 1 1 1 1 1

16
9
1
0
0
0
0
0

■+■

■+■

-+-

Figure 26 .

310 300 290 280 270 260 250 240 230 220 210 200

CLOUD TOP TEMPERATURE (K)

No-Precipitat icn Overcast and Broken for 4x4
Array (The mean, .277 and 279. 7K, interval is
boxed. The 2%, 3%. 5%, 7%, and 12% frequencies
are for 147, 221, 368, 515, and 883 occurrences,
respectively. )

f. Precipitation Probabilities

Precipitation probabilities (Figs. 27 and 28)
were computed from the precipitation overcast and broken
(category IB) and the no-precipitation overcast and broken
(category 2B) cata for the 10 x 10 (Figs. 23 and 24) and the
4x4 (Figs. 25 and 26) array sizes. As in the overcast
ceiling reports, there is a greater than 50% probability of
precipitation at the low albedo values, 0.00-0.20. In Fig.
27, the 75% probability between 230K-250K interval results
from three precipitation reports of four total reports. The

85

overcast ceiling reports account for two of the
precipitation reports. Therefore, one precipitation and one
no-precipitaticn broken report have been added to the inter-
val. Similiarly in Fig. 28, the 67% probability in the
210K-230K interval results from two precipitation reports of
three total reports. The overcast ceiling reports account
for two of the precipitation reports. Thus, one no-precipi-
tation report has been added to the interval. A few reports
in these low albedo and cold cloud top temperature intervals
are producing misleadingly high precipitation probabilities.
The 50% probability line is nearly constant, at a 0.80
albedo, at all cloud top temperatures for the overcast and
broken ceiling data.

The same treatment for displaying the four vari-
ables in a three dimensional diagram suggested in the previ-
ous section (IV.C. 1.), is recommended for these data as
well. The new displays then could be used to calculate pre-
cipitation probabilities that might allow a more accurate
bi-spectral threshold specification of precipitation,
g. Summmary

As for the overcast ceilings, precipitation
specification of the overcast and broken ceilings can be

86

1.00 '

•

0.80 ■

•

Q^-^a

0.0

0.06

o

0.60 •

•

0.0

0.C7

0.40 •

-

0.01

0.03

0.20 •

-

0.00

0.01

0.56 0.63 0.63

0.3 5 0.42 0.30

0.19 0.15 0.38

0.06 0.05 0.0

290 270 250 230
CLOUD TOP TEMPERATURE (K)

210

Figure 27. Precipitation Data Probability 10 x 10 Array
Size (Overcast and Broken Ceilings)

1.00 ••

0.80 -•

§ 0.60 -•

OQ

< 0.40 '■

0.20 -•

0.0

0.02

0.00

0.00 0.02

0.60 O5,

0.29 0.40 0,28

0.07 0.13 0.18 0.17

0.02 0.06 0.05 0.0

0.04

0.22 ^0.67

290 270 250 230
CLOUD TOP TEMPERATURE (K)

210

Figure 28. Precipitation Data Probability 4x4 Array Size
(Overcast and Broken Ceilings)

delineated by the values for the mean of the means and the
mean of the standard deviations for any array size discussed

87

in this study. The mean of the means values when used with
Figs. 27 and 28 will indicate the probability of precipita-
tion, given a similiar time of year and climatological area.
A very simple threshold for these data is actually dependent
upon the visual data value being greater than 0.80.

D. CONVECTIVE VERSUS CONTINOOUS PRECIPITATION

The physical processes involved in convective precipita-
tion, or showers, are different from those processes usually
involved in continuous precipitation. The inherent differ-
ences in the processes might result in a statistical separa-
tion in the thresholds between the two -cypes of
precipitation. For this data set, 426 of the 538 cases are
classified as convective by the surface wea-her report.
With the data set consisting of southeastern United States
stations in August, the dominance of the precipitation cases
by convective reports is not surprising.
"•• M®3n Statistics

The statistics for the convective and continuous
precipitation {Table XI7) indicate differences in the means
of the cell means of .013 and 5.7K for the 10 x 10 array
size and differences of .015 and 6.8K for the 4x4 array
size. As mentioned in the life history methods, convective

88

precipitation is expected to be associated with relatively
higher albedos and colder cloud top temperatures. For these
data, the convective precipitation are associated with
colder cloud top temperatures resulting from the cumulonim-
bus clouds.

TABLE XIV
Continuous versus Convective Precipitation Specification

Contin- Convec- Contin- Convec-

uous tive uous tive

10x20 loxjo ix4 ± ^ a

Mean of (VIS) .589 .576 .602 .617
Means

(IE) 257.5K 251. 8K 256. 2K 2U9.4K

(-160C) (-210C) (-170C) (-2UOC)

Standard (VIS) .201 .21U- .221 .228

Deviations

of Means (IR) 19.4K 20. 8K 20. IK 21. 9K

Mean of (VIS)
Standard
Deviations (IR)

Standard

Deviation (VIS) .075 -078 .058 .075

of the

Standard

Deviations (IR) 5.3K 7.2K 3.2K 5.2K

The statistics for the convective and continuous
precipitation (Table XIV) suggest that for visual satellite
values, the mean of the standard deviations is the best sta-
tistic for differentiation of these two data types, while

147

. 180

.099

. 131

7. 6K

1 1.1K

3.8K

6. OK

89

for infrared values, the mean of the means is the best
statistic. The use of two different statistical types to
qualitatively specify continuous precipitation from convec-
tive precipitation is unique to this pair of convective ver-
sus continuous precipitation data comparison.

The infrared mean of the cell means show that the
convective precipitation has colder cloud top temperatures
due to the greater vertical development of the clouds. The
greater vertical variation of the convective precipitation
clouds is seen in the visual "texture" or visual mean of the
standard deviation statistics. This "texture" difference
also appears in the infrared values, but it is not as sig-
nificant as the differences in the infrared mean of the
means. The lack of a large difference in the visual mean of
the means between the convective and continuous precipita-
tion reflects the averaging of open areas and cumulus clouds
associated with convective precipitation. Note that for the
fine resolution 4x4 array size, the visual mean of the
means is larger for the convective than the continuous
precipitation.

The visual means of the standard deviations have a
difference of 0.033 for the 10 x 10 and 0.032 for the 4x4

90

array size. Contrast these difference to the visual mean of
the mean differences of 0.013 and 0.015 for the 10 x 10 and
4 X U array size, respectively. The infrared mean of the

means have a difference of 5. 7K for the 10 x 10 and 6.8K for
the 4x4 array size. These differences are larger than the
infrared mean of the standard deviations differences of 3.5K
for the 10 x 10 and 2.2K for the 4x4 array size.

2- Standard De y i at i o n Statistics

The standard deviation of the means and the standard
deviation of the standard deviations display quite similiar
and relatively insignificant differences. The visual stan-
dard deviation of the means vary by 0.013 in the 10 x 10 and
0.007 in the 4x4 with the infrared values varying by 1.4K
for the 10 x 10 and 1.8K for the 4x4 array sizes. The
visual and infrared 10 x 10 and 4x4 array size differences
in the standard deviations of the standard deviations are
0.003, 0.017, 1.9K, and 2. OK, respectively.

3- Distribution Discussion

The distributions of the convective and continuous
precipitation for the 10 x 10 array sizs (Figs. 29 and 30)
and for the 4x4 array size (Figs. 31 and 32) demonstrate
the similiarity of the distributions. This similiarity

91

disallows quantitative separation of the convective and con-
tinuous precipitation.

Figure 29

CLOUD TOP TEMPERATURE (K)

Convective Pr-ecipitation Data for 10 x 10 Array
Size (The mean, .576 and 251. 8K, interval is
boxed. The 2%, 3%, and 5% frequencies are for
9, 13, and 21 occurrences, respectively.)

4 • Summary

Defining the qualitative delineation of convective
versus continuous precipitation in terms of the shift toward
colder cloud top temperatures for the convective precipita-
tion cases is one available delimiter. The second qualita-
tive separation is in terms of the shift toward higher
albedo values of the mean of the standard deviations for the

92

Figure 30.

310 300 290 280

270 260 250 240 230 220 210
CLOUD TOP TEMPERATURE (K)

200

Continaous Precipitation Data for 10 x 10 Array
Size (The mean, .589 and 257. 5K, interval is
boxed. The 2%, 3%, and 5% frequencies are for
2, 3, and 6 occurrences, respectively.)

■+

300

290 280 270 260 250 240 230

CLOUD TOP TEMPERATURE (K)

i H

220 210

Figure 31. Convective Precipitation Data for 4x4 Array
Size (The mean, .617 and 249. 4K, interval is
boxed. The 2%, 3%, and 5% frequencies are for'
9, 13, and 21 occurrences, respectively.)

93

CLOUD TOP TEMPERATURE (K)

Figure 32. Ccntinuous Precipitation Data for 4x4 Array
Size (The mean, .602 and 256. 2K, interval is
boxed. The 2%, 3%, and 5% frequencies are for
2, 3, and 6 occurrences, respectively.)

convec-cive precipitation cases as compared to the continous
precipitation cases.

The convective precipitation cloud top temperature
mean of 251. 8K (-210C) ccmpares quite well with those asso-
ciated with life history methods (Table VII) . The continu-
ous precipitation cloud top temperature of 257. 5K (-le^C)
compares well with the -le^C threshold of Wylie (1979) (a
life history threshold for Montreal, Canada, in summertime)
and with the -12oc bi-spectral threshold of Muench and Kee-
gan (1979). These research efforts focused on mid-latitude
precipitation associated with fronts.

94

E. INTENSITY

As there is little statistical difference between the
convective and continuous precipitation data, the gualita-
tive analysis of precipitation can be based strictly on all
light or all moderate/heavy precipitation. The light pre-
cipitation cases are expected to have a lower mean albedo
and warmer cloud top temperature when compared ro the moder-
ate/heavy precipitation cases.

1 . Statistical Discussion

The statistics fcr the two precipitation intensi-
ties. Table XV, show 0.100 and 8.6K diffsrences for the 10 x
10 array size and .117 and 8. IK differences for t-he 4 x 4
array size in the means of the means. The differences are
approximately equal to one-half a standard deviation, an
insufficient separation for specification of these two pre-
cipitation classifications. The remaining three sets of
statistics (Table XV) show nearly identical values in the
light and moderate/heavy precipitation for the two array
sizes.

95

TABLE XV
Light versus Moderate/Heavy Precipitation Specification

Light Moderate/ Light Moderate/

Heavy Heavy

11 i iQ, 11 ^ 19. a ^ 1 a 1 a

Mean of (VIS) .565 -665 .598 .715

(IR) 25a. 2K 245. 6K 251. 9K 243. 8K

(-I90C) (-280C) (-210C) (-290C)

Standard (VIS) .210 .201 .226 .204

Deviations

of Means (IR) 20. 5K 20. 4K 21. 6K 21. 3K

Mean of (VIS) .172 .177 .124 .129

Standard

Deviations (IR) 10. 2K 11. 9K 5.5K 6. IK

Standard

Deviation (VIS) .078 .081 .072 .079

of the

Standard

Deviations (IR) 7. OK 7. OK 4.9K 5.2K

2« Distribution Discussion

The distributions of the light and moderate/heavy
precipitation for the 10 x 10 (Figs. 33 and 34) and the 4 x
4 array size (Figs. 35 and 36) allow visual confirmation of
the overlap between the two intensities. Basically with

only 74 cases cf moderate/heavy precipitation, the frequency
contours (Figs. 34 and 36) reflect a noisy distribution
created by a sorting of just two or three reports into a
given interval. Additional intensity data, specifically

96

moderate/heavy prscipitation cases, are needed before a
threshold delineating qualitative intensities can be
proposed.

Figure 33.

10 300 290 280 270 260 250 240 230 220 210 200
CLOUD TOP TEMPERATURE (K)

Light Precipitation Data for 10 x 10 Array Size
(Tee mean, .565 and 254. 2K, interval is boxed.
The 2%, 3%, and 5% frequencies are for 9, 14,
and 23 occurrences, respectively.)

For the 10 x 10 and 4x4 array sizes moderate/heavy
precipitation (Figs. 34 and 36), the area encompassed by the
7% frequency isopleth at the higher albedos and colder cloud
top temperatures gives an indication of a possible
separation between the twc intensities. However, the bimo-
dal nature of the 10 x 10 distribution (Fig. 34) and the

97

Figure 34.

300

-♦
290

270 260 250 240 230 220
CLOUD TOP TEMPERATURE (K)

210

200

Moderate/Heavy Precipitation Data for 10* x 10
Array Size (The mean, .665 and 245. 6K, interval
is boxed. The 3%, S%, and 7% frequencies are
for 2, 4, and 5 occurrences, respectively.)

Figure 35.

310 300 290 280

270 260 250 240

CLOUD TOP TEMPERATURE (K)

Liaht Precipitation Data for 4x4 Array Size
(THe mean. .598 and 251. 9K, interval is boxed.
The 2% and 3% frequencies are for 9 and 14
occurrences, respectively.)

98

310 300 290 280 270 260 250 240 230 220 210 200

CLOUD TOP TEMPERATURE (K)

Figure 36. Moderate/Heavy Precipitation Data for 4x4

rhree relative maxima of the 4x4 distribution (Fig. 36)
suggest that there will be a significant amount of overlap
between these two qualitative intensitias. Because the sta-
tistics fcr the two rainfall rates are nearly identical
(Table XV) , with the exception of the mean of "che means, the
method discussed in the precipitation specification section
(IV. C.) which involved the mean of the standard deviations
to aid in further differentiation of two data types cannot
be applied to these two intensities. The delineation will
have to be derived from the mean of the mean statistics and
their resultant distributions.

99

3 . Summary

There are slight manifestations of the expected
downward shift in the albedcs and the warmer cloud top temp-
eratures for the light precipitation relative to the moder-
ate/heavy precipitation- However, additional data are
required before a threshold can be proposed to delineate
light versus moderate/heavy precipitation. The
investigation of the additional data should begin with
consideration of the mean of the means and their
distributions.

During the cell resolution discussion of Section
IV.B.1., a significant number of low albedo values (less
than 0.40 albedo) were noted. A comparison of the light
precipitation data (Fig. 33) and precipitation data (Fig.
10) for the 10 x 10 array size reveals that 96% (105 of 109
reports) are classified as light precipitation. Further
analysis shows that 79% (86 of 109 cases) are classified as
light convective precipitation. (The decomposition of con-

vective and continuous precipitation data into light and
moderate/heavy are not shown.) These low albedo values are
not unreasonable for light convective precipitation which
can be produced by small, isolated cumulus congestus clouds.

100

V. SOMMAEY AND CONCLJSIQNS

A. DATA PROCESSING SOMMABY

The data were first filtered for the correct time,
12 00-2000 GMT, to ensure reliable visual satellite values.
The visual counts were converted to albados according to the
Muench and Keegan (1979) normalization scheme (see Appendix
A) . This scheme corrects for Lambertian scattering as well
as anisotropic cloud radiation. Sorting the data according
to the Service-A reports (current weather and cloud group)
provided seven precipitation groups: convecrive, continuous,
light, moderate/heavy, general, overcast ceiling, and over-
cast and broken ceiling precipitation and two no- precipita-
tion groups: no-precipitation overcast and no-precipitation
overcast and broken. In order to investigate the impact of
satellite resolution on precipitation specification, the
stated groups were subdivided into four sizes: 10 x 10 (U5 x
U5 nmi) , 8x8 (36 x 36 n mi) , 6x6 (27 x 27 nmi) , and 4x4
(2 2 X 22 nmi) pixel array sizes. The means of the albedos
and cloud top temperatures for each array size for each
weather or cloud group were calculated. The mean values

101

ware sorted into 10K cloud top temperature intervals and
0.10 estimated albedo intervals to provide a visual descrip-
tion of the distributions. The standard deviation of the
means and the mean and standard deviation of the standard
deviations for toth albedo and cloud top temperature were
also computed for each distribution.

B. STATISTICS SUMMARY

The computsd mean and standard deviation of the means
and the mean and standard deviation of the standard devia-
tions for both albedo and cloud top temperature were evalu-
ated for specification of precipitation, specification of
continuous versus convective precipitation, and specifica-
tion of light versus moderate/heavy precipitation.

For precipitation specification (Tables XII and XIII),
the visual and infrared mean of the means produced the larg-
est statistical differences between the precipitation and
no-precipition data sets for both the overcast and the over-
cast and broken ceiling reports. For the overcast ceiling
reports (Table XII), the separation in the visual and infra-
red means of the means were one standard deviation. For the
overcast and broken ceiling reports (Table XIII), the sepa-
ration in the visual and infrared means of the means were

102

one and one-half standard deviations. The mean of -he stan-
dard deviations and the trend of the mean of the means also
yielded a large difference between rhe precipitation and
no-precipita-cion data sets.

Fcr specification of continuous versus convective pre-
cipitation (Tatle XIV), the infrared mean of the means and
the visual mean of the standard deviations yielded the larg-
est statistical differences. The convective precipitation
infrared mean of the means was 6K-7K colder than the contin-
uous precipitation value and the convectiva visual mean of
the standard deviations was 20% greater than rhe continuous
precipitation valus. These two statis-ics, however, were
only indications of possible separation as the two data dis-
tributions displayed significant overlap.

For light versus moderate/heavy precipitation specifica-
tion (Table XV), the mean of the means yielded the largest
statistical differences. However, the relatively small
quantitative differences (one-half standard deviation) in
the visual and infrared values only provided an indication
of the upward shift in albedo and the downward shift in
cloud top temperature for the moderats/hea vy precipitation
relative to the light precipitation.

103

C. PRECIPITATION PROBABILITY SUMMARY

For the overcast ceiling reports, tha 10 x 10 array size
(Fig, 21) 50% probability line decreased linearly to lower
albedos with colder cloud top temperatures, while the 4 x f*
array size (Fig. 22) 50% probability line decreased linearly
to approximately 2U0K and then increased linearly at colder
cloud top temperatures. For the overcast and broken ceiling
reports, the 10 x 10 array size (Fig. 27) 50% probability
line was constant at 0.80 albedo while the 4x4 array size
(Fig. 28) 50% probability line gradually decreased linearly
to approximately 240K and then gradually increased linearly
at colder cloud top temperatures.

D. DATA DISTRIBUTION SUMMARY

The distributions of all seven precipitation classes and
both no-precipitation classes were non-Gaussian. This

result disagrees with the assertion of Lovejoy and Austin
(1979) that their cumulus rain, non-cumulus rain, and non-
cumulus no-rain data distributions were Gaussian. At the
relatively fine resolution 4x4 array size, all seven pre-
cipitation classes and the no-precipitation overcast data
displayed bimodal distributions while at the relatively
coarse 10 x 10 array size, all displayed an unimodal
distribution.

104

E. CONCLUSIONS

The conclusions from this study of precipitation speci-
fication are:

• Varying the satellite data resolution from 484 nmi2 (4
X 4 array size) to 2025 nmi2 (10 x 10 array size)
results in a statistically significant difference in
the representation of precipitation or no-precipitation
data. Variation in the distribution functions and the
characteristic means and standard deviations with
increasing cell size demonstrates systematic trends
which may, with further study, provide improved basis
for rain detection and/or quantification.

• For overcast ceiling reports, a simple linear bi-spec-
tral threshold based on a 5 0% probability of precipita-
tion is defined as extending from an albedo of 1.00 and
a cloud top temperature of 290K to an albedo of 0.60
and a cloud top temperature of 210K for overcast ceil-
ing reports. For overcast and broken ceiling reports,
a threshold based on the albedo being greater than 0.80
specifies a 50% probability of precipitation. However,
the precipitation probabilities varied with the satel-
lite resolution size.

• The precipitation and no-precipitation data sets can be
differentiated by the mean of the means, the mean of
the standard deviations, and the trend of the mean of
the means.

• Differentiation of convective precipitation from con-
tinuous precipitation shows promise through the differ-
ences in the infrared mean of the means and through the
visual mean of the standard deviations.

• Qualitative specification of light versus moderate/
heavy precipitation shows some promise through a
threshold based on the relative shift toward colder
cloud top temperatures and higher albedos of the moder-
ate/heavy precipitation relative to the light precipi-
tation.

F. SUGGESTED FURTHER STUDY

The recommendations for further study are:

• The proposed data processing that would display the
visual and infrared mean and standard deviation of the
means (IV.C.1. ) should be investigated for both the
overcast and the overcast and broken data to determine
if the precipitation and no-precipitation data can be
more distinctly separated.

105

The appearance of bimodal distributions at the fine
resolut:Lons (6x6 and 4x4 array sizes) in zhe seven
precipitation categories and in the no-precipitation
overcast category should be invesrigared as a possible
synoptic signature.

Formal discriminant analysis should be applied to the
relevant statistics to yield confidence levels of indi-
vidual visual and infrared satellite data pairs for
precipitation specification.

The data should be further investigated at the 2 x 2
array size to analyze this resolution in representing
the data.

106

AEPENDIX A

The Muench and Keegan (1979) normalization relates the nor-
malized reflectivity, r'^ , to the varying solar angle and
maximum digital counts through the reflectance term, r, and
the anisotropic scattering through the 'X term. Table XVI

defines the symbols. Table XVII lists the geometric identity
equations and Table XVIII list the normalization equations.
Fig. 37 gives an example of the normalization applied to the
stated location.

107

TABLE XVI
List of Symbols

Symbol
C

d
h

r
Y

C
A

A.
X

Description

GOES video count number (0-63)

GOES video count number for perfect
diffuse reflector and overhead sun

Greenwich meridian time

Distance of earth to sun

Mean distance of earth to sun

Julian date

Hour angle

Cloud reflectivity

Arc-length observer to subsatellite
point

Declination of the sun

Zenith angle of the sun

Longitude

Longitude of subsatellite point

Anisotropic scattering coefficient

Latitude

Azimuth of the sun

Azimuth of the satellite

Units
dimensionless
dimensionless

hours-minutes-
seconds

km

km

dimensionless

radians

dimensionless

radians

radians

radians

radians

radians

dimensionless

radians

radians

radians

108

TABLE XVII
Basic Geometric Satellite- Earth Relationships *

Declination :

5 = 0.408 sin [(d-81) * 2tt/365]
Solar distance ratio:

a/Rg = 1 - 0.167 cos [(d-14) • 2Tr/365]
Hour angle :

h = A + TT - G(hours) x it/12
Arc-length:

COSY = cosCA - A) cos*
Satellite azimuth:

sin ((})2 - tt) = sin (A^ - A)/sinY
Solar azimuth angle:

cos^ = sin* sin6 + cos* cos6 cosh
Solar azimuth;

siniji, = cos6 sinh/sinc

Angles in radians

TABLE XVIII
Muench and Keegan Normalization Equations *

C 2
r = (7^) * secJ

C^ = cos CC? - 50) * 1.8)

C^ = 0.7 cos C(C - 22,5) * 4) * (1 - cos? )

C^ = cos^ UH - 70) * 1.3)

X 5 1.0 + 0.05 * (1 + cos(2*^)) + 0.20 * (C^ + C^) * C3

r^ = [1.09 - 2*(1.09 - f * X *(R/R )^)/(l + cos^^^ ^^j

Angles in degrees

109

a

a

o
o

I I I I I 1 1 I I I

12.013.0 14.0 15. G 16.0 17.0 18.0 19.0 20.0 21. Q 22.0

TIME (GMT)

Figure 37.

as a Function of
or April 16 at 420N

Normalized Cloud Reflectivi

Video Count and Time of Day ^

and 74<5W, with Calibration Coum: (C.) equal to
60. (Example taken from Musnch and^Kesgan,
1979.)

110

LIST OF REFERENCES

Coakley, J. A. and F. P. Erethsrton, 1982: Cloud cover from
high-resoluticn scanner data: detecting and allowing for
partially filled fields of view. J. Geophys. Res., 87,
t^9 17-4932. " -■ ^

Del Eeato, R. , 1981: The relationship between extratrcpical
rainfall and satellite clcud-xop temperatures. Aust. Met.
Maa- r 29, 125-131.

Griffith, C. G., J- A. Augustine, and W. L. Soodlsy, 1980:
Satellite es-cimation in the U. S, high plains. J. Appl.
Mllecr., 20, 53-66. " "

Griffith, C. G., W. L. Wocdley, P. G. Grube, D. W. Martin,
J. Stout and D. N. Sidicun, 19/8: Rain estimation from
geosynchronous satellite imager- -visible and infrared
studies. Mon. Wea. Rev., JOb, 1153-1171.

Liljas, E. , 1981a: Analysis of cloud and precipitation
through an automated classification of AVHRR data. RMK 32,
SMHI (in Swedish) , 33 pp.

Liljas, E. , 1S81t: Automated techniques for satellite
imager analysis. Proc. lAMAPS Symposium, Hamburg, 25-28
Aug. 198 1, 331-3 397

Liou, K. N., 1976: On the absorption, reflection and

rr ansntissicn of solar radiation in cloudy atmospheres. J.

Atmos. Sci., 3J, 79 8-805.

Lovejoy, S. and G. L. Austin, 1979: The delineation of rain
areas from visible and IR satellite data for GATE and mid-
latitudes. Atmcs-Ocean, J7, 77-92.

Mosher, F., 1S75, Appendix to: D. W. Martin, J. Stout, and

D. N. Sikdar, 1975: GATE area rain estimation from

satellite images. Report, NOAA Grant 04-5-158-47, Space

Science and Engineering Center, University of Wisconsin-
Madison.

Muench, H. S. and T. J. Keegan, 1979: Development of
techniques to specify cloudiness and rainfall rate using
GOES imagery data. AFGL-TR-79-0 255, AD A084, 757 pp.

Negri, A. J. and R. F. Adler, 19 81: Relation of satellite-
based thunderstorm intensity to radar-estimated rainfall.
1' A££l- Miil2I- f 20, 28 9-300.

Piatt. C. H. R.. 1981: Twc dimensional histogram of GMS-1
satellite visitle albedo and infrared temperature for
selected cloud systems. Division of Atmospheric Physics
Tech. Paper No. 40, Commonwealth Scientific and Industrial
Research Organization, Australia.

1 11

Scofield, R. A., 1981: Visible and infrared technigues fo:
flash flood, hydrological, and a gricul-cural applica-ions.
In, D, A-las and 0. t« . Thiele (editors), £ -icibita^icn
Measurements frcni S^ace, Wcrksho p Repor-, H — '^
FISI7 Go'3^afd Space Center, GreenbeTt, ^d. ,

Hctober T9HT,
0145-0152.

Simpson, J. and V. Wiggert, 1969: Models of precipitating
cumulus towers. Mon. Wea. Rev., 89, 471-489.

Stout, J., 0. W. Martin and S. N. Sikdar, 1979: Estimating
GATE rainfall from geostationary satellite images. Mon.
lia- Ml, 107, 585-5 98.

Wylie, D. P., 1979: An application of a geostationary
satellite ram estimation technique to an extratrcpical
area. J. A££l. Meteor., 18, 1640-1648.

Wylie, D. P., 1982: Some statistics for combining
radiosonde soundings with satellite images for estimting
rainfall. Report, NOAA Contract NA-80-SAC-0072 1 , Space
Science and Engineering Center, University of Wisconsin-
Madison.

112

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Cenrer 2
Cameron Station

Alexandria, VA 22314

2. Library, Code 0142 2
Naval Postgraduate School

Monterey, CA 93943

3. Professor Robert J. Renard, Code 53Rd 1
Department of Meteorology

Naval Postgraduate School
Monterey, CA 93943

4. Professor Christopher N. K. Mooers, Code 68Mr 1
Department of Oceanography

Naval Postgraduate School
Monterey, CA 93943

5. Assistant Professor Carlyle H. Wash, Code 63Wy 9
Department of Meteorology

Naval Postgraduate School
Mon-erey, CA 93943

6. Assistant Professor James L. Mueller, Code 68My 1
Department of Oceanography

Naval Postgraduate School
Monterey, CA 93943

7. LT Linda S. Paul 3
U. S. Naval Oceanography Command Detachment

APO San Francisco, CA 95519

8. Director 1
Naval Oceanography Division

Naval Observatory

34th and Massachusetts Avenue NW

Washington, D.C. 20390

9. Commander 1
Naval Oceanography Command

NSTL Station

Bay St. Louis, MS 39522

10. Commanding Officer 1
Naval Oceanographic Office

NSTL Station

Bay St. Louis, MS 39522

11. Commanding Officer 1
Fleet Numerical Oceanography Center

Monterey, CA 93940

1 13

12. Commanding Officer

Naval Ocean Ks search and Development

Activity
NSTL Station
Bay ST. Louis, MS 39522

13. Commanding Officer

Naval Envircnmental Prediction Research
Facilit

)%

Monterey, CA 93940

14. Chairman, Oceanography Department
U.S. Naval Academy

Annapolis, MD 21402

15. Chief of Naval Research
800 N. Quincy Street
Arlington, VA 22217

16. Office of Naval Research (Code 480)
Naval Ocean Research and Development

Activity
NSTL Station
Bay ST. Louis, MS 39522

17. Dr. Donald Wylie
SSEC — U. W.

1225 West Dayton Street
Madiscn, WI 53706

18. CAPT A. Shaffer, Code 63
Department cf Meteorclogy
Naval Postgraduate School
Monterey, CA 93943

1 14

10 1

" ><

Paul

207^26

Thesis

P2713 Paul

c.i A study precipitation
occurrence using visual
and infrared satellite
data.