master of science · these factors have caused a saturation of the standard telecommunications...

Preliminary Processing and Evaluation of Radar Measurements In

Satellite-Path Propagation Research

by

Carcl Diane Friberg

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree si‘ Master of Sciencein

Electrical Engineering

APPROVED:

:/5< /2/(/,-E( /’

<;> ‘·C.W. Bastian, Chairman ·—

/

xÄT.

Pratt I.H. Eesieris

1Jane 1985

Blacksburg, Virginia

H

Preliminary Processing and Evaluation of Radar Measurements In

SateI|ite·Path Propagation Research

by

Carol Diane Friberg

C.W. Bostian, ChairmanA

Electrical Engineering

(ABSTRACT)

Rain and other precipitation cause attenuation and depolarization of high

frequency satellite signals. Some characteristics of rain can be measured

by dual-polarized radar. These characteristics can then be used to pre-

dict the effects of the rain on satellite·path propagation.

This thesis describes briefly the theory of radar and satellite linkA

measurements. Methods for calibrating the equipment and deriving actual

experimental values from measured power are presented in detail. A set

of computer programs to approximately predict radar and link values from

measured rain rate are developed. Predicted and measured values may then a

be compared by a researcher to evaluate system operation and assess the

importance of the event data. A discussion of the use of sampled data

and these comparisons concludes the report.

ACKNOWLEDGEMENTS

The author wishes to thank Dr. C. W. Bostian and Dr. T. Pratt for all their

help and encouragement, both in the preparation of this thesis and in the

entire course of graduate study. Thanks are also due to Dr. I. M.

Besieris for serving on my graduate committee, and to Dr. W. L. Stutzman

for help with the data processing information.

Acknowledgements iii

TABLE OF CONTENTS _

Chapter 1 Introduction ..................... 1

1.1 Purpose of Thesis ......................L 1

1.2 Description of the INTELSAT Experiment ........4 . . . 3

1.3 Overview of Thesis ..................... 7

Chapter 2 - Determining and Using Reflectivity ......... 9

2.1 Summary of Radar Theory ................... 9

2.2 Extracting Z from Received Power Measurements ......‘ . . 11

2.2.1 Antenna Calibrations ................... 12

2.2.2 Receiver Calibration ................... 16

2.2.3 Range Normalization .................... 18

2.2.4 Transmitter Power Calculations . „ ............ 19

2.3 Calculating Z from R .................... 20

2.4 Comparing Calculated Z with Radar Z ............. 23

Chapter 3 - Determining and Using Differential Reflectivity . . . 25

3.1 Definition of ZDR ...................... 25

3.2 Extracting ZDR from Received Power Measurements. ....... 26

3.3 Using the Distrometer to Verify ZDR ............. 32

3.3.1 Drop Size Distributions. .................. 32

3.3.2 The Distrometer .... L ................. 34

3.3.3 Distrometer Rain Rate ................... 36

3.3.4 Calculating Drop Size Distribution from ZDR ........ 38

Table of Contents iv

3.4 Calculating R from Z and ZDR. ................39

3.5 Further Calculations from Z and ZDR ............. 40

Chapter 4 — Determining and Using Satellite Link Data ......41

4.1 Definition of Attenuation and XPD .............. 41

4.2 Extracting A and XPD from Received Power Measurements ....42

4.2.1 Calibration of Receivers ................. 42

4.2.2 Clear Weather References ................. 44 '

4.3 Calculating A From R - the SAM Model ........... 44

4.4 Comparing Link A with Calculated A ............. 48

Chapter 5 - Presentation of results for operator - Verification of

equipment operation .......................49

A 5.1 Description ......................... 49

5.2 Sampling .......................... 49

5.3 Calculations and Presentation of Results .......... 51

5.4 Evaluation ......................... 55

Chapter 6 - Evaluation of Results For Further Data Analysis — As-

sessment of Event Data Quality .................58

Appendix A. Front End Program .................60

Appendix B. Preprocessing Program ...............68

Appendix C. 'Dummy Data' Generation Program ..........78

Table of Contents v

References ............................91

Vita ...............................93

Table of Contents vi

CHAPTER 1 INTRODUCTION

1.1 PURPOSE OF THESIS

The VPI&SU °Octopod° radar system is used, in conjunction with satellite

receivers and weather instrumentation, to collect data about rain. More

specifically it measures and records rain reflectivity as a two-byte bi-

nary number, from 125 Volumes in space, in eight different polarizations,

approximately every two seconds. This amounts to 3.6 million bytes per

hour of recorded radar data alone. Data from three satellite receivers _

and several weather instruments are recorded concurrently. This infor-

mation will eventually be processed to formulate relationships between

rain, as measured by radar, and satellite link attenuation. But before

such extensive and time-consuming processing can be done, the collected

data must be °preprocessed°, for two major purposes. This preprocessing

stage - its formulation, organization, realization, and evaluation - is

the topic of this thesis.

The first purpose of preprocessing is to convert all recorded values from

their raw form to useful experimental values. For example, radar data

are recorded as computer °counts°, proportional to the output Voltage of

the radar receiver. These must be converted, by means of calibration

equations and range normalization, to reflectivity Values in decibels. ·

Satellite receiver data and weather instrument data must also be converted

Chapter 1 Introduction 1

to link attenuation and isolation, and rain rates. This important step

allows for much easier processing later.

The second purpose of preprocessing is to perform a quick evaluation of

a rain event. This gives the researcher an indication of the validity

of the data and the relative interest of the event. For our purposes, a

°first-look' file is created, selecting maximum points from the data

during the conversion process. Approximate predictions are made from

these maximum points, and the consistency of the data is evaluated. Some

of the major tests for consistency are described below:

Reflectivity(Z)

•Are measured reflectivity values, Z, reasonable for observed rain-fall? ”

•Do maximum Z values correspond, in time, to maximum measured link

attenuation and rain rates?

•Does Z calculated from measured rain rate correspond to radar-

measured Z? r

• Does attenuation calculated from measured rain rate correspond to

measured link attenuation?

Chapter l Introduction 2

Differential Reflectivity(ZDR)

•Are measured ZDR values reasonable for observed rainfall?

•Does rain rate calculated from Z and ZDR correspond to measured rain

rate?

1.2 DESCRIPTION OF THE INTELSAT EXPERIMENT

Over the past several years, the use of satellite systems for many ap—

plications in communications has greatly multiplied. In addition, many

of the new systems use higher power and wider coverage. These factors

have caused a saturation of the standard telecommunications frequency

bands. The most promising direction for expansion is up, into the higher

frequency region, specifically frequencies above 10 GHz.

There are some unique problems, however, which affect the use of these

microwave frequencies, especially over long distances. An

electromagnetic signal can be seriously disturbed by objects in its path,

provided that the object and the wavelength of the signal are of the same

magnitude. Above 10 GHz, rain drops and other precipitation paticles meet

this condition, and consequently, precipitation of any kind along the link

path can adversely affect the signal. The degradation is of two types:

attenuation, which is a fading of signal strength, and depolarization,

which is a random shift of the signal orientation. Attenuation affects

all systems of these frequencies, and requires that a higher power margin


be allowed in the design process to maintain a reasonable reliability

during storms. Depolarization affects mainly those systems which use two

orthogonally polarized channels, at the same frequency and on the same

path, in order to double the information capacity of the system.

Depolarization lowers the isolation between these channels by mixing some

of one channel into the other.

The VPI&SU Satellite Communications Group, under contract to INTELSAT,

has undertaken an extensive experiment to systematically study weather

effects on the propagation of a dua1—polarized satellite system. [1] The

basic components of the experimental system are:

Three dua1·polarized satellite earth terminals

The °Octopod° weather radar

Rain gauges

A distrometer

Supporting data acquisition equipment

Supporting computer systems

Two of the satellite receivers are located at the main experimental site

and share an antenna and front end equipment. A third receiver is located

at a diversity site, 7.3 km from the main site. All three receivers are

dual—polarized, and receive a single, right-hand circularly polarized

beacon signal at 11.492 GHz from an INTELSAT V satellite. The signal

received as right-hand circularly polarized is defined as the co-

polarized signal, and that received as left-hand circular is called


cross-polarized. Since only the co·polarized signal is transmitted by

INTELSAT V, any received cross-polarized signal is the result of

depolarization along the path. It is expected to be much lower than the

co-polarized signal. The change in the co-polarized signal level from

clear-weather conditions to precipitation conditions is defined as the

attenuation.

The °Octopod° weather radar is an S-band (2.8 GHz) system adapted from a .

Verlort NASA tracking radar. It has been specially fitted with a feed

whose linear polarizer is mounted on an axially rotating joint. This

makes the polarization of the transmitted signal rotate at 1800 rpm. The

firing of the transmitter pulse is linked to this rotation of 30 revo-

lutions per second. The transmitter pulse repetition frequency (PRF) is

480 Hz, or 16 times the rotation rate of the polarizer. Thus, 16 pulses

are fired in each 660° rotation. Since linear polarizations l80° degrees

apart are identical, 8 distinct polarizations are sampled by the °Octopod°

radar. They are defined as follows, in degrees from vertical:

POL O = 22.5°

POL 1 = 45°

POL 2 = 67.5°

POL 3 = 90° l

POL 4 = 1l2.S°

POL 5 = l35°

POL 6 = 157.5°

POL 7 = 180° (1.2.1)


The radar receives power reflected by objects in its path, in this case

rain or other precipitation. This continuous return signal is sampled

by the data acquisition system (DAS) every 1.7 usec., corresponding to a

range distance of 255 m. For each polarization, reflected power is re-A

corded for 125 range 'binsl, 120 m long and 255 m apart.

The rain gauges used in the experiment are of the tipping-bucket variety.

Two gauges are used at both the main and diversity sites, one with a large

opening for accuracy at low rain rates, and one with a smaller opening

for effective use at high rain rates. The times of the rain gauge trips

are recorded and later converted to rain rate as a function of time. The

distrometer is an instrument for recording the size distribution of

raindrops over a period of time. Its principle of operation and data

format are discussed in Chapter 3.

The data acquisition system (DAS) handles all radar data in real-time,

controlling timing for collection, providing averaging capabilities,

converting from a logarithmic scale to a linear scale, and sends the data

for storage to the S-100 computer, described below. An IBM Personal

Computer (PC) controls data collection and transfer for the distrometer.

A microcomputer, the Ithaca 800 system manufactured by Ithaca Intersys—

tems, controls all data storage. It is based on a Zilog Z-80 micro- ·


processor, and controls an S·l00 standard bus. For this reason, it is

commonly referred to, in the remainder of this thesis, as the S-100 com-

puter. It is linked directly to the receivers and rain gauges, and re-

ceives data from the radar DAS and the IBM PC. All collected data are

stored on tape by the S-100 for further analysis.

A Harris 800 "superminicomputer" reads the data tape produced by the S-100

computer, and is used to perform all preprocessing and processing work

after collection of data for an event. All programs described in this

thesis are intended for use on the Harris system.

1.3 OVERVIEW OF THESIS

The remainder of this thesis is divided into two main sections. Chapters

2, 3, and 4 describe the theory and procedures necessary to extract radar,

satellite link, and weather data from the measured quantities. Prediction

equations, which approximately relate some of these extracted values are

also described. Chapters 5 and 6 describe how these procedures and re-

lationships are used to create a summary of a rain event in the form of

a 'first look' file. These chapters also provide guidelines for inter-

preting this file, both to evaluate the operation of the equipment and

to assess the data quality before further data analysis.

The author°s contributions to the project can be divided into three parts.

First, the appropriate calibration and prediction equations were re-

searched, compared, and adapted from a variety of such information


available in the literature. In the case of the prediction schemes, this

generally involved a choice of one approximation theory over several

others. Secondly, these equations were adapted for our specific exper-

imental situation, and developed into a set of algorithms for computer

calculations. Finally, guidelines for the evaluation of the first-look

file, based on the background theory, were suggested.


CHAPTER 2 - DETERMINING AND USING REFLECTIVITY

2.] SUMMARY OF RADAR THEORY

The most basic principle of radar is. that it transmits bursts of

electromagnetic energy and measures both the amount of energy reflected

back, and the time between energy transmission and reception. This allows

the calculation of the relative size of a target, as well as its location.

The radar equation [2], in its most general form, is

Pt 62 X2 6Pr = -—————————— (2.1.1)

(46>3r“

where

PI = received power

Pt = transmitted power

G = antenna gain

X = radar wavelength

0 = target radar-cross-section (RCS)

r = range (distance) to target.

Raindrops reflect electromagnetic energy at high frequencies. However, '

rain must be analyzed as a collection of independent scatterers within a

given volume of the radar beam, with statistical distributions of size

Chapter 2 · Determining and Using Reflectivity 9

and shape. The value Z, called the radar reflectivity factor, is al

measure of the amount of rain in the beam of the radar. For particles

of diameter D, reflectivity is defined as a summation over a unit volume

by ‘

_ 6Z — E Di (2.1.2)

Rayleigh scattering, which states that the echo area of very small spheres

is proportional to)-4

[3], is an extremely good approximation when the

diameter D < 0.2). Thus it is appropriate for rain in microwave fre-

quencies below 5 GHz, and we can apply the Rayleigh scattering law to a

single drop [2].

6. = (ns |k|2/)L) D3 (2.1.3)1 1

_ 2 2 2_ . .where |k|—|(n -1)/(n +1)|, n —complex dielectric constant of water. For

microwave frequencies, |k|2 is assumed to be 0.93 [4]. The total c for

a distribution of drops in a beam volume Vm is given by

6 = Vm 2 6i (2.1.4)

Vm is a function of range, pulse length I, and 3 dB beam width angles OB

and ¢B , in radians

Vm =(n/4) (r20B¢B/2(ln 2)) (ct/2) (2.1.5)

Chapter 2 - Determining and Using Reflectivity 10

where c is the speed of light. The u/4 factor accounts for the elliptic

shape of the beam area, and the 2(ln 2) represents reduction of equivalent

volume based on a Gaussian-shaped antenna pattern. For a Gaussian beam

shape, we may use G = nz/GB ¢B, and so (2.1.4) becomes

_ 3 2o — (n /16 ln 2) (r ct/G) E ci . (2.1.6) _

Equations (2.1.2), (2.1.3), and (2.1.6) may now be used in (2.1.1) to

obtain a relationship between average received power from a collection

of scatterers and reflectivity Z

6 P GPr =———————"

°T-

|k|2 z (2.1.7)1024 (ln 2) P2 12 _

This is the basis for the calculation of Z in this experiment.

2.2 EXTRACTING Z FROM RECEIVED POWER MEASUREMENTS

The radar Data Acquisition System (DAS) is a microprocessor-controlled

digital system designed specifically to control and organize radar data

collection [S]. A 10-bit number with the fictitious units of computer

"counts", proportional to the output Voltage of the receiver, is provided

for each of the 125 range bins in each of the eight polarizations. A

number of these samples are averaged over time to lower noise effects and

decrease the total amount of data transferred and stored. This average

is then transferred to the S-100 computer and stored on magnetic tape.

Chapter 2 - Determining and Using Reflectivity ll

The rather arbitrary units of "computer counts" must then be converted

to a Z value for each range-bin/polarization combination at each pointV

in time during the event. These calculations are made on the basis of

antenna and receiver calibrations, calculation of range, and simultaneous

transmitter power measurement.

2.2.1 ANTENNA CALIBRATIONS -

Two experimental procedures will be used to calibrate the antenna system.

Briefly, these are: received power measurements, from a known polarized

source, and reflected power measurements, from a spherical reflector.

Polarized source measurements

In this procedure, a rectangular horn, mounted on a rotating joint, is

driven by a synthesizer at the radar frequency. (See Figure 2.2.1.1)

Received power at the radar is measured, both at the input to the re-

ceiver, and by the DAS in computer counts, for each combination of

transmitter and receiver polarizations. That is, as the transmitter is

held fixed at each polarization given in (1.2.1), the receiver measures

power in all eight polarizations.

These measurements allow the calculation of cross—polarization effects

and make it possible to verify that the depolarizing effect of the antenna

is negligible. Furthermore, the differences in co-polar received power


II Pt

POWER

METER

MRADAR

SYNTHESIZERRECEIVER

DASDISPLAY:

‘ ‘ COUNTS

S—lOO

DISK:

COUNTS

Figure 2.2.1.1 Polarized source calibration arrangement.Block diagram.


as a function of polarization can be measured. These can then be ac-

counted for in the final calculation of Z by' the use of polarization

offset factors, a small number for each polarization to correct this

difference.

A second test with this equipment involves scanning the radar antenna past

the source antenna for each transmitted polarization. Again, the power

into the receiver and the computer counts from the DAS are recorded.A

These measurements are used to produce plots of the radar antenna pattern

in each polarization plane, and any significant beam shape distortions

can be corrected in data conversion.

Reflected power measurements

A second calibration test is necessary to determine the gain of the radar

antenna. ~This involves measuring the reflected power from a six-inch

metal sphere suspended from weather balloons approximately 1.5 km from

the radar, at a height of approximately 100 m. This gives an elevation

angle of between 3° and 4°, enough to reasonably clear the ground clutter.

(See Figure 2.2.1.2)

Since only 125 m of space are sampled in each 255 m range bin, it is im-

portant that the target sphere be inside this window to be measured. The

DAS controls the sample timing, providing a delay time before the first

range bin and spacing the subsequent range bins as specified. This ini-

Chapter 2 — Determining and Using Reflectivity 1A

I'

'1'RANSMITTER

POWERMETER:

” ° PI_(dBm) ·

DISK:

COUNTS S-100 DAS RECEIVER

Figure 2.2.1.2 Reflected power measurements. Block diagram andg€Om€C1'y.


tial delay corresponds to a distance, called the dead zone, before the

first range bin. A set of eight digital switches allows the dead zone

to be set dynamically by the radar operator for this calibration proce-

dure. The lowest-bit switch corresponds to a dead zone shift of 15 m,V

so the target may be accurately found and measured. The dead zone value

is recorded with data so that range normalization can be done correctly.

The basic radar equation (Eq. 2.1.1) is used to solve for gain G when all

other terms are known. At a radar wavelength X of 10.7 cm, the radar cross

section of a six inch diameter sphere is given approximately by

0 = uaz (2.2.1.1)

where a is the radius of the sphere [2]. PI and Pt are measured, and r

is calculated as discussed later. Gain G is then computed as

Pr r“(4 w)3 R

G. = 10 log — l- ———· I(2.2.1.2)MB) P P. ..2 A2 „

t

2.2.2 RECEIVER CALIBRATION

The radar receiver is calibrated by measuring the output response, in

volts, to an input power level, in dBm. The synthesizer is used as a

source at the radar frequency, injected into the waveguide at the input

to the receiver. As the power level is varied over the receiVer‘s dynamic

range, both the Voltage out of the receiver (at the input to the DAS) and

the computer count output of the DAS are recorded. (See Figure 2.2.2.1)


SYNTHESIZER

POWER

METER Pin

RECEIVER

VOLTV.

METERl“

DAS _

CRTDISK s-100 COUNTS

DISPLAY

Figure 2.2.2.1 Block diagram of receiver and Data AcquisitionSystem (DAS), showing measurement points forcalibration.


The relationship between input power and output Voltage is essentially

linear over most of the dynamic range, and a slope and intercept point

can be determined from the resulting curve. The relationship between

Voltage into the DAS and output computer counts is strictly linear, and .

a slope and offset can be calculated. The combination of these curves

gives a relationship between received power from the antenna and computer

counts from the DAS. This can be substituted into the equation for PI.

10 log PI = (COUNTS x RADAR SLOPE) + RADAR OFFSET (2.2.2.1)

2.2.3 RANGE NORMALIZATION

Each recorded measurement of received radar power is assigned a range bin

number 3 through 127. (Range bins 1 and 2 are saturated by transmitter

power and are therefore disregarded. Bin 0 is used as a measure of the

peak transmitted power). After the dead zone delay, set at 15 m except

for calibrations, all range bins are spaced 255 m apart. A window 125 m

in length, at the beginning of each range bin, is the actual sampled

space. For purposes of range normalization of a measured radar signal,

the center of this window is assumed to be the range. The calculation

‘ of range is then given by

‘r = DZ + (WINDOW/2) + (RBL x RBN) (2.2.3.1)

where


DZ = Dead zone length (usually 15 m)

WINDOW = Sampled length (125 m)

RBL = Range bin length (255 m)

RBN = Range bin number.

All received power measurements are weighted by 1/r2in the conversion

to reflectivity Z, as in equation (2.1.1).

2.2.4 TRANSMITTER POWER CALCULATIONS

" The peak transmitter power Pt is measured for each radar pulse. The

Voltage from the measurement system is converted to computer counts by

the DAS and recorded with the radar data. Calibration of the measurement

system gives a relationship between power and counts in terms of a slope

and intercept:

10 log Pt = (PWR COUNTS x PWR SLOPE) - PWR INTERCEPT (2.2.4.1)

This value of Pt is used in the calculation of Z.

The radar equation for rain (2.1.6) can be rewritten in decibel form

vrs c 110 log PI — 10 log ............ + Pt(dB) + G(dB)

1024 (ln 2)

- 20 log r + 10 log Z + 180 dBw (2.2.4.2)


I and X are constants for the radar system: I = 0.8us and X = 10.714 cm.

The factor of 180 arises from the conversion of equation (2.1.2), where

all lengths are in meters, to a system where D is in millimeters and r

is in meters.

Equation (2.2.4.2) can be rearranged, then as

DBZ = Pr(dB) - Pt(dB) ~ G(dB) + 20 log (r) - Kl (2.2.4.3)

where

DBZ = 10 log Z l ws c IKl = 10 log _i + 180 (a radar constant)

1024 (ln 2)

andPr(dB), Pt(dB), G(dB),

and r are given by equations (2.2.2.1),

(2.2.4.1), (2.2.1.2), and (2.2.3.1), respectively.

This is the algorithm for converting all measured power values to

reflectivity in decibels, DBZ, in the preprocessing routine.3

2.3 CALCULATING Z FROM R

The relationship between reflectivity Z and rain rate R

Z = aRb

(2.3.1)


has long been used to predict Z from measured rain rates. Battan [6] has

compiled a list of experimentally derived pairs of the constants a and b

in (2.3.1). These show a wide Variation, which is only partly accounted

for by temperature, storm size, and location. We desire to select two

equations of the form of (2.3.1) and use these to predict a range of

possible Z values from each of the largest measured rain rates.

The Various combinations of a and b have been plotted as a scatter plot

in Figure (2.3.1). The greatest density of these points occurs for 200

< a < 350 and 1.3 < b < 1.6. Somewhat arbitrarily, the pairs (230, 1.4)

and (220, 1.6) were chosen as extremes. These correspond to the equations

21 = 230Rl‘“

Z2 = 220Rl°6 (2.3.2)

Next, equi·Z curves were drawn through these two points of the graph for

a rain rate R = 25 mm/hr. That is, a curve was drawn through all points

(a,b) such that

230(25)l'& = zl = a (25)b (2.3.3)

and another curve through all points (a,b) such that

220(25)l'6 = Z2 = a(25)b (2.3.4)


Eääé§¤§F

F

,F====lIIII1.1

zw

This was repeated for a very high rain rate, R = 150 mm/hr. These curves

are also shown on Figure 2.3.1. .

It can be seen that a large number of the experimental points fall between

the two sets of curves. This indicates that, if equation (2.3.2) is used

to indicate a range of Z values for a given rain rate, all the Z values

predicted by those enclosed points will fall within the range.

Furthermore, equation (2.3.2) gives a reasonable range of Z values for

purposes of comparison, not so wide as to be useless, nor so narrow as

to be inaccurate. For R = 5 mm/hr,

AZ5 = Z2 - Z1 = 1.2 dB

and for R = 150 mm/hr,

‘AZISO = Z2 - Z1 = 4.2 dB

2.4 COMPARING CALCULATED Z WITH RADAR Z

As stated in the previous section, it is possible to predict a Z value

or a range of Z values from a rain rate. The major difficulty, however,

in comparing calculated and measured reflectivity is caused by a time

delay. The radar measures the reflectivity of the rain at a significant

height as it falls through the beam, while the rain gauge measures the


rain at ground level. The time it takes the rain to fall this distance

is highly variable, depending on rain rate, drop sizes, wind conditions

and other factors.

For this reason, automatic comparison of these values is not performed.

Instead, during the conversion process, the computer records a number of

the highest Z values for the event, and the corresponding times, and a

number of the highest rain rates during the event, with their corre-

sponding time. At the end of the conversion process, Z ranges are cal-

culated for the selected rain rates, and these can be compared by the

operator to the selected measured Z values. The operator looks for some

correlation in the time between measured rain and measured reflectivity,

and compares calculated reflectivity range to the measured reflectivity.


CHAPTER 3 · DETERMINING AND USING DIFFERENTIAL REFLECTIVITY

3.] DEFINITION OF ZDR .

The most valuable feature of the Octopod radar system is its ability to

measure reflectivity in eight different polarizations, as explained.in

Section 1.2. This provides considerably more information about the rain

parameters than a single polarization measurement and allows the use of

more exact models to predict rainfall rate and attenuation. The major

strength of this measurement scheme is the ability to calculate differ— j

ential reflectivity, ZDR.

Strictly speaking, ZDR is the ratio of reflectivity in the horizontal and

vertical polarizations. When expressed in decibels, the ratio becomes a

difference V

ZDR = ZH(dB) — ZV(dB) (3.1.1)

However, since we are measuring DBZ in eight polarizations, it is desir-

able to define four ZDR values, each describing a ratio of reflectivities

measured on orthogonal polarizations. These are

ZDR0= DBZ(3) - DBZ (7)

ZDRl= DBZ(4) - DBZ (0)

ZDR2= DBZ(5) · DBZ (1)

Chapter 3 - Determining and Using Differential Reflectivity 25

ZDR3= DBZ(6) — DBZ (2) (3.1.2)

where the values DBZ(O) through DBZ(7) are the reflectivities at the eight

angles POL O through POL 7 as defined in equation (1.2.1), respectively.

ZDR0 , then, is the horizontal minus the vertical reflectivity or the

standard definition of ZDR. As raindrops are assumed to be oblate

spheroids, with the long dimensions in the horizontal plane, ZDR0 should

be the largest of the four.

Once these four values of ZDR are calculated, we can fit a cosine curve

to them of the form

ZDRx= ZDRMAX Cos (ux/8 + ¢) (3.1.3)

and extract a ZDRMAX and a canting angle ¢[7].

3.2 EXTRACTING ZDR FROM RECEIVED POWER MEASUREMENTS.

Since ZDR is calculated directly from the calibrated Z measurements, no

further calibrations of measurements need be made. However, two factors

essential to accurate ZDR values must be considered during the previously

mentioned calibrations. (Section 2.2).

First, the position of the rotating polarizer must be known accurately.

The pulse repetition frequency (PRF) generator is controlled by this ro-


tation and subsequently controls the timing of the transmitter pulses.

Adjustments may be made in the DAS to delay the pulses, if necessary, to

insure that polarization 3 is indeed horizontal, etc. This process can

be tested by observing the polarizer with a strobe light synchronized to

the timing pulse. The polarizer should appear stationary at the appro-

priate angle. Alignment can also be tested by measuring in all eight

polarizations the power level from a known polarized source aligned with

the desired position. Maximum power is received when the two antennas

are co-polarized. The horn antenna used in Section (2.2.1) would be ap-

propriate for this purpose.A

A second, and more difficult consideration is the contribution of cross-

polarized signal components to the measured power level. The antenna

reflector depolarizes the signal slightly, both in transmission and re-

ception. The target (in this case rain drops) also causes some

depolarization. The basic results of each of these depolarizations are

a) that the magnitude.of the signal in the original polarization is de-

creased, and b) that a small cross-polarized component is introduced.

This introduces two problems. First, some of the transmitted signal is

reflected back from the target but not measured, having been depolarized

once and so received in the orthogonal polarization. This causes a de-

crease in the magnitude of the received signal. Secondly, a portion of

the transmitted signal is depolarized twice, and thus reappears in the

original polarization. However, this component represents the

reflectivity of the target in the orthogonal polarization. '


The first effect is accounted for by the antenna calibrations of reflected

power. This measurement gives us a ratio between transmitted and received

power. Thus the part of the signal lost due to antenna depolarization

is built into the calibration.

The second effect is more complicated to analyze. Let us represent the

transmitting antenna, target, and receiving antenna polarization effects

as matrix functions [T], [G], and [R], respectively:

RTll T12 G11 G12 ll R12 _

T2l T22 021 c22 R21 R22

In the transmitting antenna matrix,Tij

represents the ratio of input’

voltage in polarization j to the transmitted field in polarization i.

Similarly, [G] represents the transfer functions of incident to reflected

fields at the target, and [R] the transfer function of received field to

output voltage at the antenna. Polarizations l and 2 are two arbitrary

orthogonal polarizations.

Assuming that the medium is non-depolarizing but has attenuation a, it

can be represented as a matrix as well:

Chapter 3 — Determining and Using Differential Reflectivity 28

a 0

O a

Then the equation relating the transmitted Voltage and the received

_ Voltage is given by

VR TR R a O 0 0 a 0 T T V1 11 12 11 12 11 12 1

= (3.2.l)VR

R R O a 0 0 O a T TVT

2 21 22 21 22 21 22 2

Since we are transmitting in only one polarization, V; is zero. The power

lost to the orthogonal channel is vg and is given by(3.2.2)

VR= az VT

R 0 T + R 0 T + R 0 T + R 0 T2 1 21 11 11 22 22 21 21 12 21 22 21 11

As stated before, this is accounted for in the antenna calibration. Vä,

the signal actually measured by the receiver, is given by .

R 2 TV = a V R 0 T + R 0 T + R 0 T + R 0 T

1 1 11 11 11 11 12 21 12 22 21 12 21 11

This is proportional to reflectivity in decibels DBZ. (3.2.3)

The factor Rll0llTll is the desired response · transmitted, reflected,

and received in the same polarization. The other three terms account for

the cross-polarization error. For example, Rll0l2T21 represents the

cross—polar component depolarized at the transmitting antenna (Tzl) and

repolarized by the target (012).


The maximum error for a single Z value occurs when all the error terms

are in phase - that is, they don°t cancel each other out. The relative

error can be expressed as the error components divided by the desired

component.

I R11G12T2lI "’ I R12O22T2lI+ I Rl2G2lT11 IRelative error = (3·2·l*>

' I R11¤11T11 I

Furthermore, since the same antenna is used for both receiving and

transmitting, we can relate the antenna matrices by

R R T T-1

11 12 11 12

= (3.2.5)

R21 R22 T21 T22

Thus the relative error in DBZ becomes

T21G12 T12

021T21

T12 C22 3 2 6R_E_Z :I

____ ____|+I___ ____ +«_______ ____ ( • • )

T11 G11 T22 G11 T1lT22 U11

For ZDR, if errors all add up, the relative error of the difference be-

tween DBZ in polarization 1 and polarization 2 is


1 I2T21c12

2T12o21 T12T21 IR‘E'z1>R + + 11 + 22„ Io I- o T .T T T

11 22 11 22 11 22

(3.2.7)

While these errors cannot be eliminated, their maximum values can be found

by measuring the antenna parameters |T2l/T11] and|Tl2/T22|

and estimat-

~ ing the raindrop depolarization effects. The antenna characteristics can

be obtained simply from the calibration measurements described in Section

2.2.1 with a polarized source.

The raindrop depolarization effects are, at worst, proportional to the

average value of the differential reflectivity over the measured volume.

Even at high rain rates, this should not exceed 3 dB, and so is probablyI

negligible in comparison to the antenna effects.

We can further assume, for the sake of estimating the error, a constant ‘

depolarization value for all the measured polarizations. If we define

the quantity|T2l/Tlll = XA, the antenna depolarization averaged over the

beam width, in all polarizations, then the relative errors of Z and ZDR

can be described in terms of XA for a worst case (3 dB) target

depolarization:

_ 2· R.E.Z - 2 XA + 4 XA

_ _ 2R.E.ZDR — 3 XA + 24 XA (3.2.8)

where XA and R.E. are expressed as ratios, not in decibels.


Graphs of these relative errors are shown in Figure (3.2.1). This can

be used to find the expected relative error when the antenna

depolarization is measured.

3.3 USING THE DISTROMETER TO VERIFY ZDR

3.3.1 DROP SIZE DISTRIBUTIONS.

In a given volume of rain, there is a distribution of drop sizes, de-

pendent upon the rain intensity. Drop sizes are generally described by

an equi-volume diameter, that is, the diameter of a sphere with the same

volume as the drop. Attempts have been made to mathematically describe

the drop size distribution of rain at a particular rain rate. In general,

the number of drops of diameter D per unit volume per increment of drop

diameter is

N(D) = no Du e-AD(3.3.1.1)

where u is an integer and NO and A are constants of a particular dis-

tribution.

Marshall and Palmer [8] proposed a specific distribution, with n(D) inmm_lm_3,

D in mm, and rainfall rate R in mm/hr,mand


¤==¤gg¤¤==ggggggggg¤g¤¤g¤¤ggggggg¤g==ggggggggggggg=gggg¤ggggggggggggggEägggägääiääiiäääIéäggääägäEgggääälälliiliäääääEgggggggggäggggggggEggggägwglHIäiäggggggäilliääilägäIgigggggggääägggg0 lgääää“*“%EääL?äääEEEElmg"ä?ääEääE‘' , g

ääéääääl“

*hääääääülggguulmugl ll'lläääääm-Elääääägg

läääläaälläggäägglgäälgäääggääggggggägäggägg 5=ggggg=g 6.-„i rg gg, „

:a ‘~· a .‘~¤ ·gg·gg .ggggggägääägäiägggägl Iägggggiääääggggggä

gg ggggääääääägällgggg .. gg g gggggÖl 1*

M1 Ilääääggagggglegg Eäiäääälggäggg_„„ 1114 01 iäääläääälääg

-10 -15 -20 -25 -30 -35

Figure 3.2.1 Relative error inwtdünd ZDR as a function ofantenna depolarization XA.


u= 0

N0= 8000 (3.3.1.2)

A = 4.1 R°0•21„

This is also called an exponential distribution since n(D) is directly

proportional to e

_AD

.

Other distributions have been proposed with various integer values of u.

The gamma distribution, with u=2, is quite commonly used.

For the purpose of this experiment, we will be measuring a drop size

distribution, as described in the following sections, and predicting an

exponential distribution from measured differential reflectivity. _

3.3.2 THE DISTROMETER

The Distrometer used in this experiment is an electromechanical device.

which measures the sizes of individual rain drops. A cylindrical nylon

'head° is held in a metal tube, and is free to move slightly up and down.

The top of the head is slightly conical to allow raindrops to roll off.

The head rests on a piezoelectric crystal, whose electrical output is

proportional to the mechanical pressure on it.


When a raindrop strikes the top of the head, its force is transmitted by

the movement of the head to the piezoelectric crystal. The output Volt-

age, then, is a measure of the drop°s momentum, or mass times Velocity.

If a Velocity is assumed, and the density of water is known, then the

signal represents the drop°s Volume. Further calibration allows us to

interpret the Voltage as proportional to the equivolume diameter.

AThe distrometer and its related circuits, including its link to an IBM

PC, collect data from rain drops over a specified period of time. During

this time interval, in this case 30 seconds, the raindrop diameters are

sorted into 'bins° of data. Each bin represents a range of drop diam-

eters, and the set of bins covers the entire range of expected drop di-

ameters. A set of these numbers for a given period of time, then,

represent a discrete drop size distribution.

The output of the distrometer is therefore a set of numbers representing

the relative distribution. The actual drop sizes of the bins and the size

increments per bin are supplied by the calibration procedure.

The number of drops measured by the distrometer is proportional to, but

r not equal to, the actual number of drops in the drop size distribution.

The measured number is also proportional to the collecting area of the

distrometer head, the rain drop terminal Velocity, the drop size incre-

ment, and the length of the collection period. The actual distibution

is then given by


n(D) = nCOLL(D) /,TC V(D)AreaDiSt ADi (3.3.2.1)

where nC0LL(D) is the number measured by the distrometer

TC is the collection time, in seconds

AreaDiSt is the area of the distrometer head, in m2 I

ADi is the drop size interval, in mm

and v(D) is the terminal Velocity of drops of diameter D, in m/s.

The terminal Velocity formula used is that of Atlas [9],specifically,

VT(D) = 9.65 - 10.3 6°° GD (3.3.2.2)

where D is in mm

VT (D) is in m/s

3.3.3 DISTROMETER RAIN RATE

As explained above, the distrometer measures the number of drops in each

drop size bin over a short period of time. This makes it quite easy to

calculate a rain rate for that time period. The water content of the rain

can be calculated by numerically integrating the number of drops times

their average volume.


The volume of water in a cubic meter of space above the distrometer at

any moment in time is given by

V = E n/6D3

n(i) AD (3.3.3.1)W i i

where i = the index of the drop size bin ~

Di= mean diameter of drops in theith

bin, in mm

n(i) = number of drops in theith bin,

A Di= width of the bin

Vw hasunitsTo

obtain the rain rate, we multiply equation (3.3.3.1) by the terminal

velocity of rain drops, which is a function of their size. We also in-

troduce the factor 10-6 to eliminate the units mm3m_3 of Vw.

R = E V (D )10-9 (v/6 D

3n(i) AD ) (3.3.3.2)

T i i i

This, however, assumes VT and R have the same units. lt is more conven-

ient to express VT in m/s and R in mm/hr. Thus we introduce a final factor

of 3.6 x106.

Our rain rate equation becomes, then, ·

-4 3 . .R(mm/hr) = Z(6 x 10 )u

VT(Di)Di n(i) A Di (3.3.3.3)

where VT(Di)is in m/s


D., A D. are in mm1 1

R is in mm/hr

To use this formula in the preprocessing program in order to calculate a

rain rate from the distrometer data, it is more convenient to use the

number of measured drops, as described in the last section. Using

equation (3.3.2.1), the rain rate calculation becomes _

R(mm/hr) = Z(6 x 10-4)w D3

n (D)/(T Area ) (3 3 3 4)i COLL C Dist ° ' '

Each distrometer-calculated rain rate is compared with the simultaneous

measured rain rate from the co-located tipping-bucket rain gauge (diver-

sity site gauge). Over the course of the event, the average difference

and the maximum difference, at any one point, of these rain rates is re-

corded. This information is provided to the operator in the °first-look'

data file produced by the preprocessing programs. The operator can then

evaluate the operation of the distrometer.

3.3.4 CALCULATING DROP SIZE DISTRIBUTION FROM ZDR

For purposes of initial comparison of radar and distrometer data, a drop

size distribution (DSD) is calculated from ZDR for the five highest Z

values during the event. This method is not expected to be very accurate,

because the DSD is not a unique function of ZDR. A preferred approach

would be to fit a curve to the measured DSD, obtain values of NO, A, and


u and then predict a ZDR. Such calculations, however, are too lengthy

for the preprocessing and first-look stage, and will be done in later

analysis. We restrict ourselves therefore to prediction of a DSD.

From Atlas and Ulbrich [10], for u = 0,

A = 3.086 ZDR-O°6452

-3 7N = 1.389 x 10 Z A (3.3.4.1)0 H

These values are then used to calculate n(D) from equation (3.3.1.1) at

the same diameters as the distrometer measurements, and both DSDs, cal-

culated and measured, are available in the first—look file for evaluation

by the operator.

3.4 CALCULATING R FROM Z AND ZDR.

The measurement of Z gives an indication of the quantity of rain in the

radar path. As shown in the previous section, differential ZDR in addi-

tion allows a measurement of the average shape of the raindrops, since

it is a ratio of the horizontal to vertical dimensions. This in turn

allows an estimation of the average size of the drops, based on the

principle that larger drops experience more air resistance than small

drops and thus are more oblate. This enlarged description of the observed

drops provides for a more exact prediction of rain rate, based not only


on rain quantity, which is defined by Z, but also on rain drop sizes,

based on ZDR.

Seliga, Aydin, and Direskeneli [ll] propose the following relationship

based on an exponential (u=0) DSD:R

R/ZH = (1.93 x 10-3) ZDR-l'5 (3.4.1)

Here, ZH and ZDR are expressed as ratios, not in decibels, and R is in

mm/h. This equation is used in the preprocessing program, and the rain

rate thus computed is compared to the measured rain rate.

3.5 FURTHER CALCULATIONS FROM Z AND ZDR

Further calculations from Z and ZDR are being carried out by Cahit Ozbay,

a graduate student with the VPI&SU Satellite Communications Group. He

is using the Z and ZDR measurements produced by the programs described

in this thesis to predict the link attenuation and XPD, and the rain rate.

For given values of mean canting angle c, the fraction of drops that are

oblate FO, and the exponent u, as in equation (3.3.1.1), backscattering

theory gives the drop size distibution parameters NO and A, and the rain

rate R as unique functions of Z and ZDR. Forward scattering theory is

then used to calculate attenuation and XPD from the drop size distribution

values.


CHAPTER 4 - DETERMINING AND USING SATELLITE LINK DATA

4.°I DEFINITION OF ATTENUATION AND XPD

As described in Chapter 1, rain or other precipitation causes degradation

of radio signals above 10 GHZ. Attenuation is a decrease in the signal

magnitude due to absorption and/or scattering from the rain drops. [12]

It can be expressed as a ratio of the clear weather amplitude to the am-

plitude in rain, but is more often described in decibels as a difference

between the two levels

ARAIN(dB) = PCLEAR(dBm) - PRAIN(dBm) (4.1.1)

where PCLEAR = Signal level in clear weather (clear weather

reference)

PRAIN = Signal level at a particular time during a

rain event

Note that this is a measure only of the additional attenuation caused by

precipitation, not of any constant loss or absorption in the atmosphere.

For systems that use two signals at the same frequency but in orthogonal

polarizations, rain can depolarize both signals and cause interference

between the channels. The cross-polarization discrimination (XPD) is ae

Chapter 4 - Determining and Using Satellite Link Data 41

measure of this interference. It is defined as a ratio of received signal

in the channel co-polarized to the transmitter to the received signal in

the cross-polarized channel. Again this is most easily expressed as a

difference in signals expressed in decibels.

XPD(dB) = PCO(dBm) - Px(dBm) (4.1.2)

where PCO = Received co-polarized signal level

Px = Received cross-polarized signal level

XPD is particularly appropriate for a system, such as the one in this

experiment, where a signal is transmitted in only one polarization, and

the received levels are measured for both the co- and cross-polarizations.

4.2 EXTRACTING A AND XPD FROM RECEIVED POWER MEASUREMENTS

4.2.] CALIBRATION OF RECEIVERS ‘

The calibration of the satellite receivers consists of two procedures.

The first finds the relationship between the power into the IF receiver

and the computer counts produced by the S-100. This allows us to convert

these counts to relative signal level. The second procedure measures the

difference in gain between the co- and cross~polarized channels in the

receiver. «


In the first calibration, the antenna is pointed away from the satellite

path. Thus the only power from the front end receiver is due to noise.

A signal at the IF frequency, 1.05 GHz, is then injected immediately after

the front end. This produces an output voltage from the main receiver

and a computer count output from the S-100 computer for each channel. A

step attenuator is used to vary the input signal level over the dynamic

range of the system. For each signal level, the output voltage and com-

puter counts are recorded for both channels in each receiver. A graph

of these measurements gives a relationship between relative input signal

level and output computer counts, in terms of a slope and intercept of a

curve for each channel.

The second calibration step measures the channel gain difference (CGD)

of each receiver. The feed horn of the antenna is manually switched to

the linear mode, and the antenna is realigned with the satellite path.

The co- and cross- polarized receivers now receive in two orthogonal

linear polarizations. The satellite transmits a right-hand circularly—

polarized signal, which has equal components in any two orthogonal linear

polarizations. Thus the inputs to the two channels of the front end re-

ceiver are equal. The outputs of the two channels are measured in com-

puter counts and converted to relative power in decibels by means of the

previous calibration. The difference in these two levels, in decibels,

is the channel gain difference.

CGD(dB) = Px(dBm) — PCo(dBm) (#.2.1.1)

Chapter # - Determining and Using Satellite Link Data #3

Note that all the measurements are in terms of relative signal strength.

This is sufficient for the calculation of attenuation and XPD as described

in section 4.1.

4.2.2 CLEAR WEATHER REFERENCESl

Attenuation is calculated by the differenee in the co-polarized signal

levels, as given in equation (4.1.1). The only remaining value required

is the signal level in clear weather, or the clear weather reference.

As measured and recorded on a regular basis, this value experiences short

term variations due to system noise, and a longer daily Variation due to

temperature changes. It is also sensitive to changes in the satellite

position and antenna pointing. These variations make it difficult to

automatically provide a single value for the clear weather reference. A

far more accurate method is to plot the measurements of the co-polarized

signal level at 30 second intervals over a 24 hour period. A person then

estimates the average co-polar level from this plot, and enters this value

into the computer as the clear weather reference.

4.3 CALCULATING A FROM R · THE SAM MODEL

As a part of the preprocessing program we need to calculate attenuation

values from the highest measured rain rates and compare these with the

measured attenuations. This calculation should not be lengthy or time-

consuming, but should be accurate enough to provide a check on the con-

sistency of the data and the operation of the link. The Simple


Attenuation Model, or SAM, of Stutzman and Dishman [13] was chosen as

meeting these conditions. SAM is described fully in the paper referenced

above, so only a summary of the necessary equations is given here.

For a rain rate R, the total attenuation is given by

A(R) = aRb

L for R S 10 mm/h

bl — exp(—Yb ln(R/lO) L cos 6)

A(R) = a R for R > 10 mm/hYb ln (R/10) cos 6

(4.3.1)

where for frequency f in GHz

Ca= 4.21 x

10-S f2'A2 2.9 S f < 54 GHz

b = 1.41 f'°‘°779_ 8.5 s 25 GHz

X = 1/22

6 = elevation angle of path

Path length L in equation (4.3.1) is given by

L =°(H€- HO)/sin 6 (4-3-2)

where


H = H. R S 10 mm/he 1

He = Hi + log(R/10) R > 10 mm/h .

Ho = altitude of earth station above sea level

Hi = 4.8 |A| s 60°

Hi = 7.8 - 0.1|A| |A| > 30°

For our system, these constants apply

f = 11.492 GHz

6 = 18.5° (4.3.3)

HO = 0.640 km

A = 67.229°

These gives the following values

a = 1.55 x 10-2

b = 1.166 (4.3.4)

H. = 4.0771

L = (Hi — HO)/sin s = 10.832 R S 10 mm/h


L = (Hi + log(R/10) - HO)/sin 6 = 10.832 - 3.152 log(R/10) R > 10 mm/h

SAM can then be Simplified to

a) for R S 10 mm/h

bA(R) = a R L (4.3.5) -

where

L = 10.832

a = 1.55 x 10-2

b = 1.166

and

b) for R > 10 mm/h

b 1 — exp(—vb ln(R/10) L cos 6)A(R) = a R ·————————————————-——-—————-——— (4.3.6)

vb ln (R/10) cos 6

where L = 10.832 - 3.152 log(R/10)

a = 1.55 x10-2

b = 1.166

X = 1/22

Chapter 4 — Determining and Using Satellite Link Data 47

z = 16.s°

4.4 COMPARING LINK A WITH CALCULATED A

In comparing a measured link attenuation with an attenuation calculated

from a rain rate, simultaneous measurements do not describe the same

phenomena. This is because of the variable time delay described in sec-

tion (2.4). However, similar to the comparisons described in that sec-I

tion, the maximum attenuation values and the calculated attenuation from

the maximum rain rates can be compared. This comparison takes into ac-

count both the magnitudes of the values, and the times they occurred.

From this comparison, conclusions can be drawn concerning the operation

of the equipment and the correlation of the data.

Chapter 4 — Determining and Using Satellite Link Data 48

CHAPTER 5 - PRESENTATION OF RESULTS FOR OPERATOR -

VERIFICATION OF EQUIPMENT OPERATION

5.] DESCRIPTION

All of the theory discussed in the previous chapters is brought together

uin the preprocessing and first-look programs. (These programs, FNTEND,

which converts computer data in hex to counts and calculates the

distrometer rain rate, and PREPRO, which does the other conversions and

contains the first look calculations, are given in Appendices A and B,

respectively). The preprocessing stage converts all measurements to

useful values — Z, ZDR, A, etc., for further analysis. The first-look

program uses the approximate prediction equations, e.g. Z calculated from

rain rate, for selected data points during the event. This allows the

operator to verify the proper functioning of the equipment. This chapter

describes the process of data sampling, calculations, and presentation,

and provides guidelines for evaluating the first-look files.

&2 SAMPUNG

The preprocessing program provides the following output

•Rain rate from gauges, both local and diversity site

•Distrometer rain rate, as calculated from Equation (3.3.3.3)

Chapter 5 - Presentation of results for operator - Verification ofequipment operation 49

•Z in eight polarizations, 125 bins

•Link attenuation and XPD for three receivers:

"Fred", "Wilma" and "Diversity"

As these are converted in the preprocessing program, the maximum value

in each 4.5 minute segment is recorded for the following values: local

rain rate, diversity site rain rate, Z at local site, Z at diversity site,

and link attenuation for each receiver. The radar operates on a scanV

sequence of 4.5 minutes, hence the time base for sampling. This sequence

includes periods when the radar is stationary along the main path and over

the diversity site. Z at the local site is defined as the horizontal

reflectivity, Z(3), in the nearest range bin during the period when the

radar is stationary along the main path. Z at the diversity site is de-

fined as the horizontal reflectivity in range bin 28 during the period

when the radar is stationary over the diversity site. (Bin 28 corresponds

to the 7.3 km distance from the radar to the diversity site.) For each

maximum Z chosen, the corresponding ZDR0 is also saved. For the diversity

site Z values, the corresponding drop size distribution is also stored.

These sampled maximum values are the input to the first-look program.

In addition to this sampling the preprocessing program compares all si-

multaneous values of measured rain rate at the diversity site and

distrometer calculated rain rate. The average difference between the rain

rates and the maximum single difference are computed in the preprocessing

program and these values are passed along to the first-look program.

4Chapter 5 - Presentation of results for operator — Verification ofequipment operation 50

5.3 CALCULATIONS AND PRESENTATION OF RESULTS _

With the sampled maximum values and their corresponding information as

inputs, the first—1ook program performs the prediction calculations. An

example of the first-look data, both the input samples and the predicted

values, is given in Figure (5.3.1). Local rain rate is used to predict·

a range of reflectivity values, using Equation (2.3.2). Similarly, the

diversity site rain rate predicts a range of reflectivity values for the

diversity site. Attenuation for the two paths is calculated from these

rain rates by Equations (4.3.5) and (4.3.6). The output to the first—look

file, for the local site first and then for the diversity site, is a rain

rate, the corresponding time, the calculated Z range, and the calculated

A.4

All maximum attenuation values, and their corresponding times, are re-

corded in the first—look file for each receiver: Fred, Wilma, and di-

versity. No calculations are performed on these data.4

For each maximum Z value, both at the local site and at the diversity

site, a rain rate is calculated from Z and ZDR using Equation (3.4.1).

The Z values, the time, the corresponding ZDR, and the calculated rain

rate are recorded in the first·look file. For each diversity site maximum '

Z, a drop size distribution is calculated using Equation (3.3.4.1). This

is recorded in the first look file, along with the simultaneous measured”

drop size distribution.


The average and maximum differences between measured and distrometer-

calculated rain rate are also given in the first-look file.

A ‘dummy data' tape was produced to test this process. (The program

MAKETAPE, which produces this tape from a series of rain rates, is given

in Appendix C). Assuming a single, uniform rain rate for each 4.5 minute

segment, all the °measured° values were generated from the prediction and

calibration equations. For example, Equation (2.3.2) was used to find a

range of Z for the rain rate. The average Z in this range was then used

in Equation (2.2.4.2) to calculate the radar computer counts for each

range bin. Receiver data, distrometer data, and rain gauge trips were

similarly simulated. The preprocessing and first—look programs were then

tested on this tape. The output of the first·look file is shown in Figure

(5.3.1) The comparison of drop size distributions has not been completed

and so is not shown here. »


15 HIGHEST LINK ATTENUATICNS OURING EVENTAILMA RECEIVEPATTENUATIOV TIME

· 13.6 00:31:30:016.9 00:60:30:015.6 00:27:00:013.9 00:36:00:013.1 00:6::00:012.3 00:22:30:0

9.2 00:13:00:09.2 00:69:30:06.0 00:53:30:05.3 00:09:00:05.1 00:56:00:05.0 00:06:30:05.0 00:13:30:03.6 00:00:00:0

FRED RECEIVERATTENUATION TIME

18.6 00:31:30:016.9 00:60:30:015.6 00:27:00:013.9 00:35:00:013.1 00:6::90:012.3 00:22:30:09.2 00:13:00:0 .9.2 00:69:30:06.0 00:55:30:05.3 00:09:00:0:.1 00:56:00:05.0 00:06:30:05.0 00:13:30:03.6 00:00:00:0

DIVERSITY RECEIVERATTENUATION TIME

18.6 00:31:30:016.9 08:69:38:015.6 0 :2 :0 :013.9 00:35:00:013.1 00:65:00:0~ 12.5 00:22:30:09. 00: 3:00:09.2 00:69:30:06.0 00:53:30:0

· 5.3 00:09:00:05.1 00:56:00:0

- 5.0 00:06:30:0" · 5.0 00:13:30:0

3.6 00:00:00:0

- 15 HIGHEST RADAR Z VALUESMAIN SITE · LOCAL RATH BIN 3

-~ Z(3) TIME ZDRTO) PREDICTED RAIN RQTE56.5 00:33:62:0 5.0 155.655.8 00:62:62:0 6.8 162.655.1 00:29:12:0 6.7 125.956.3 00:32:12:0 6.5 111.6:3.9 00:67:12:0 6.6 106.653.6 00:26:62:0 6.3 96.1

·- 51.1 00:20:12:0 3.8 66.551.1 00:51:62:0 3.3 66.567.6 01:00:62:0 3.2 36.566.7 00:11:12:0 3.1 30.666.6 00:56:12:0 3.0 29.266.1 00:06:62:0 3.0 27.866.1 00:15:62:0 3.0 27.862.9 00:02:12:0 2.6 15.3

Figure 5.3.1 Sample 'First-Look' Output From Dummy Data


DIVERSITY SITE · EIN 23-Z‘§l-- --I£'£ä....

EE5‘°’22E2‘£I§2-*££! EEIE

56.1 00:31:30:0 5.0 140.755.4 00:40:30:0 4.8 127.154.7 00:27:00:0 4.6 114.453.9 00:36:00:0 4.4 101.2

sol? Sghäääoio slé 5;:450.7 00:49:30:0 3.9 59.447.2 00:58:30:0 · 3.3 32.6 .46.2 00:09:00:0 3.1 27.645.9 00:54:00:0 3.0 26.445.6 00:04:30:0 3.0 25.045.6 00:13:30:0 3.0 25.042.4 00:00:00:0 2.6 13.9

15 HIGHEST RAIN RATES _ IMAIN SITE

2££N_RAIä___-IEj§____ CELCEBATED Z PENGE CALCULATED ATN

152.4 00:49:24:0 54.2 T0 55.4 24.7114.3 00:31:35:0 52.4 TO 56.4 19.1

151% °5’?*‘¥5’1 §**1 15 1%% 1%%.!·• 2.. Z' . .. .

91.4 80:27:00:0 51.1 TO 54.8 15.6 -91.4 00:40:20:0 51.1 TO 54.8 15.657.1 00:17:42:0 49.2 TO 51.5 10.350.8 00:18:00:0 47.5 TO 50.7 9.350.8 00:49:30:0 47.5 T3 50.7 9.332.7 00:09:00:0 44.8 TO 47.7 6.432.7 00:08:50:0 44.3 TO 47.7 6.430.5 00:58:30:0 44.4 TO 47.2 6.028.6 00:57:58:0 44.0 TO 46.7 5.722.5 00:04:26:0 42.5 T3 45.1 4.7

DIVERSITY SITE

EAIN RQIE -1EME _ _ CALCULATED Z RANGE CALCULATED ATN152.4 00:49:26:0 54.2 TO 58.4 24.7152.4 00:49:30:0 54.2 T0 58.4 24.7114.3 00:31:35:0 52.4 TJ 56.4 17.1114.3 00:26:54:0 52.4 TO 56.4 19.1114.3 00:27:00:0 52.4 TJ 56.4 19.1101.6 00:40:32:0 51.7 TO 55.5 17.291.4 00:40:22:0 51.1 TO 54.8 15.657.1 00:18:00:0 48.2 TO 51.5 10.357.1 00:17:46:0 48.2 TO 51.5 - 10.332.7 00:09:00:0 44.8 TO 47.7 6.432.7 00:08:54:3 44.8 TO 47.7 6.430.5 00:58:32:0 44.4 TO 47.2 6.028.6 00:58:00:0 44.0 TO 46.7 5.715.0 00:00:02:0 40.1 TO 42.2 3.4

COMPARISON OF DISTROMETER AND RAIN GAUGE RAIN RATES

AVERAGE DIFFERENCE IN RAIN RATES: ·0.07

MAXIMUM DIFFERENCE IN RAIN RATES: 100.20

Figure 5.3.1 (continued)


5.4 EVALUATION

The first-look file is designed to be easily evaluated by the equipment

operator. However, some values will be clearly right or wrong; others

may allow some interpretation. lt is for this reason that the operator

is involved in the evaluation, instead of having the computer check the

results.

The satellite receiver data are easiest to evaluate. The two main site

receivers, Fred and Wilma, should record the same attenuation and XPD at

l all times. Any constant difference in the attenuation measurements in-l

dicates a wrong clear weather reference for one receiver. These should

be checked, and adjusted to account for the difference. A non-constant

difference may indicate an error in the slope of one or both calibrations

curves. The calibrations should be checked. Very large values of at-

tenuation in any receiver indicates a loss of lock. This does not affect

attenuation values at other times.

iOver the course of the event, the attenuation calculated from the rain

rate should approximately correspond to the measured attenuation. The

prediction model is not expected to be very exact in each individual time

segment, however. High rain rates should occur shortly after large

measured attenuations.

Chapter 5 - Presentation of results for operator — Verification ofequipment operation 55

The measured Z values should fall within the range predicted from the rain

rate for the same period. Consistently low or high Z values compared to

rain rate suggest errors in the radar calibrations. The timing of the

DAS should also be checked to insure that the sampling is occurring at

the right time. A spurious pulse can cause early triggering, andi the

range normalization will be incorrect.

There should be a good correlation between the rain rate predicted from

Z and ZDR, and the next sampled rain rate. ZDR values should not be

greater than about 4 dB. lf these are unusually high values, the opera-

tion of the DAS should be examined.

Predicted and measured drop size distributions are not expected to cor-

respond too well, as explained in section (3.3.4). The measured dis-

tributions should demonstrate reasonable operation of the distrometer,

roughly matching the form of the predicted distribution.

Although the maximum difference between the measured rain rate and

distrometer-calculated rain rate may be quite large, the average differ-

ence should be rather small compared to the actual rain rates. Adjust-

ments of distrometer calibrations may be necessary.

After checking this data and making any adjustments, the operator should

make a note in the first-look file of any equipment problems found that


might affect the further analysis of the data. The first-look file is

saved to be used for further evaluation, as described in the next chapter.


CHAPTER 6 · EVALUATION OF RESULTS FOR FURTHER DATA

ANALYSISI · ASSESSMENT OF EVENT DATA QUALITY

The first-look file produced during preprocessing provides valuable in-

formation to the researcher performing further data analysis. It docu-

ments not only data validity — proper operation of all equipment, but data

quality - length, intensity, and, to some extent, distribution of the rain

event. Data analysis may be made more efficient and more accurate by the

use of this information.

If the first—look file indicates some equipment problems, data analysis

may proceed, but with the appropriate adjustments. If a satellite re-

ceiver is not working, or if the radar fails for a short period, that

receiver or that time period may be disregarded. Some data may have to

be adjusted for corrected calibration constants. All operations should

be checked from the data and operator comments in the first-look file

before analysis.

However, event data quality is of more importance to the researcher at

this stage. The first·look file can be used to indicate the time periods

of greatest rain rate or highest attenuation. These would be preferable

to long period of drizzle and low attenuation in testing the analysis

routines. Such information, condensed from the whole event, would be

useful in comparing difference events for priority in analysis. After

Chapter 6 - Evaluation of Results For Further Data Analysis -Assessment of Event Data Quality 58

analysis, it could be used to categorize events, e.g. thunderstorms, light

rain, snow, etc.V

_ It is not unlikely, in the case of high rain rates, to have great dif-

ferences in measured rain or attenuation between the main site and the

diversity site. Such intense rain is quite localized and may affect only

a small part of the satellite path.. As part of the data analysis involves

_ synthesizing other paths from the RHI data, (see section 3.5), information

about the two sites may influence selection of these synthesized paths.

Ultimately, it is hoped that the use of the first-look file would provide

the researcher with an understanding of the general nature of an event

and thus make analysis more fruitful. In turn, the analysis could be used

to refine the prediction techniques of the first-look program, to better

evaluate events during the preprocessing stage of data handling.

Chapter 6 - Evaluation of Results For Further Data Analysis -Assessment of Event Data Quality 59

APPENDIX A. FRONT END PROGRAM

This program converts all data, stored on the tape in hex values, to

computer counts. It also calculates the distrometer rain rate from the

drop size distribution, and the tipping bucket rain rates from the re-

corded times of trips.

Appendix A. Front End Program 60

""°°*‘^" "*°"""°‘%2§‘éI'E¥L’ä’¥' LINELENGTH 8203)DIST! LFN=12F LINELENGTH = 120):IRAIN! LFN=14e LINELENGTH = 66):RADAR! LFN=16; LINELENGTR = 66)) F

. CONST TAPEBLKSIZE = S20? FRDLFILL = E FCMLFILL = 15 FPHLFILL = 27 FLKLFILL = 7 FDELFILL = 15 FRTLFILL = L F

TYPE TAPEEUFFER = PACKED ARRAYCO••TA°E3LKSIZE] OF CHAR FDATEARRAY = PACKED ARRAY[1„•?] OF CHAR FTIWEARRAY = PACKED ARRAY[1„„12] OF CHAR FLUMPCODE = PACKED ARRAY[1•„2J OF CRAR FCHANNEL = 0..7 FSUBCODE = 'A'•„'H' F

RADARBIN = ARRAYCCHANNEL] OF INTEGER FDROPSINLUMP = RECORD

DATE : DATEARRAY FTIME : TIMEARRAY FBIN : ARRAY[1„•20] OF INTEGER

END F

·F

POINTHEADERLUMP = RECORD OF CHAR FPARAMETERS ;ARRATi1•:10] OF INTEGEREND F ·

LINKLUMP = R'CORDDATETIMEE: PACKED ARRAY[1„•20] OF CHAR F°OINTCOUNT : INTEGER FRECEIVER : ARRAY[1••10] OF INTEGER F— STATUS : ARRAYC1••}] OF INTEGER

END F

RAINGAUGE = 'A' •• 'E' F~ RTSUSLUMP = RECORD‘

GAUGE : RAINGAUGE FTIME : TIMEARRAY

END F_.RAINTRIPLUMP = RECORD

DATE : DATEARRAY FTRIPS : ARRAY[1..S] OF RTSUBLUMP., END F

FRAINRATERECORD = RECORD

SEC : INTEGER FRR : REAL

END F

RAINRATEFILE = FILE DF RAINRATERECORD F

I

‘

6l

VAR

TB : TAPEBUFFER F E INPUT BUFFER FOR RAV DATA TAPE JBP : INTEGER F BUFFER POINTER — NEXT CHAR IN TBOBP : INTEGER F C OLD BUFFER POINTER J

LXL : LINKLUWP F E LINK DATA LUHP JDTL : DROPBINLUMP F DISTROMETER DATA LUMP JRTL : RAINTRIPLUNP F [ RAIN GASUGE TRIPS J

LC : LUMPCODE_F E TAPE LUMP CODE • MARKS KIND OF DATA]RC g INTEGER F LOGICAL RECORD COUNT JTAPE : TEXT F C TAPE INPUT FILE• S100 RAH DATA JDIST : TEXT F C DISTROMETER DATA DUTPUT FILE JRAIN : TEXT F C RAIN GAUGE TRIPS OUTPUT FILE JRADAR : TEXT F C RADARILINK DATA OUTPUT FILE JK : INTEGER FL : INTEGER F

STATUS : INTEGER F

RADCHKCNT : INTEGER FI

RD : ARRAYCO••127J OF RADAPBIN F

RADARPOINT : INTEGER F C CURRENT POINT NUNBER JPHL : POINTHEADERLUMP FDEL : DROPBINLUMP F

RG : RAINGAUGE FSEC : INTEGER FNSEC : INTEGER FR : RAINRATERECORD F

DR : RAINRATERECORD FRGRR : ARRAYCRAINGAUGEJ OF RAINRATERECDRD F

DISTRAIN : PAINRATEFILE F ELOCLCRAIN : RAINRATEFILE F— LOCSCRAIN : RAINRATEFILE FDIVLCRAIN : RAINRATEFILE F

DIVSCRAIN : RAINRATEFILE FÄ

LOCRR : REAL FDIVRR : REAL F

Ä~ OLDLOC : REAL F

OLDDIV : REAL FOLDDIST : REAL F .

TFUNCTION NEXIN(N:INTEGER) : INTEGER F

VAR DIGIT : INTEGER FV : INTEGER FC : CHAR FD : INTEGER FK : INTEGER F

”BEGIN

V := 0 FFOR K := 1 TD N DO BEGIN

§¤"—‘ä$"’¥ Ä ·IF ('OA <= C) AND (C <= 'R') THEN D := CRD(C) · 48ELSE IF

(‘A'<= C) AND (C <= 'F') THEN D := ORD(C) • SSELS§ 3EGéN_

EN°dRITELN('HAPNING · ILLEGAL MEX CHARACTER') FV := v•1¤'+ D

END FHEXIN := V F

END F .

·

62

FUNCTION SECONDS(D : OATEARRAY 2 T : TINEARRAY) : INTEGER 2VAR V : INTEGER 2 _

S : INTEGER 2

BEGINV := (0RD(DC2])·63) * 10 * (O2D(DC3])·6*) 2S := V * 14600 2V := (ORD(T[Z])•63) * 10 * (ORD(TC3])°65) 2S := S + V·• 3600 2V := (O1D(T{S])·6!) * 10 * (ORD(T{6])•6?) 2S := S * V * SC 2 ‘V := (ORD(T[E])·63) * 10 * (0RD(TC9])•6R) 2SECONDS := S * V 2

END 2

PROCEDURE FMTCML 2VAR K : INTEGER 2

BEGINURITE(RADAR:LC) 2FOR K := 3 TO 66 OO BEGIN

HRITE(RADAR'TB[3F]) 2BP := BP

•·1 2

, END 2HRITELN(RADAP) 2BP := BP + CMLFILL 2

END 2

PROCEDURE FWTRDL 2VAR PN : INTEGER 2

K : INTEGER 2C : CHANNEL 2. B : INTEGER 2

BEGINBP := EP + 1 2PN := HEXINU) 2BP := BP + 1 2IF PN <> RADARPOINTTHEN URITELN('RADAR DATA POINT NUMSER <> TO POINTHEADER')ELSE BEGINC := 0RD(LCE1]) — 6H 2

B :=(0RD(LC 2]) • 65)* 16 2

RADCHKCNT := RADCHKCNT * 1 2FOR K := 1 TO 15 DO BEGIN

Rats':} := '·IE‘(IN(6)·2E := 3 +1 2

END 2END 2 'BP := BP + ROLFILL 2

END 2

(

a

63

j_____ ____ __ __ .. „..„.- E-„·-»--« -· ·—-———l··-*-——·t•·

PROCEDURE FMTRHL F °VAR K : INTEGER F

L : INTEGER FBEGIN ‘_ IF RADCHKCNT = $4 THEN BEGIN

HRITE(RADAR F 'PH') FHRITE(RADAR F PHL.DATETIME) FHäITE(RADAR F PHL•POINTCOUNT : S) FFOR K := 1 TO 5 D3 HRITE(RAOARF PHL•PARAMETERS[K]:5) FURITELN(RADAR) F

HRITE(RADARe'0P ') FFOR K := 5 TO 10 DO URITE(RÄDÄRrPHL•PÄRÄHETERScK]IS) FURITELN(RADAR) F

URITE(RADAR: 'LN ') FFOR K := 1 T0 S O3 HRITE(RADAR;LKL„RECEIVERCK]:6) FHRITELN(RADARFLKL•STATU$[1]:6) FHRITE(RADAR¤'LO ') FFOR K := o TO 10 DO URITE(RADARzLKL„RECEIVER[K]:6) FFOR K := Z TO 3 90 URITE(RADARFLKL•STATU$[K]:6) FHRITELN(RADAR) F_ HRITE(RADARF 'P° O') FFOR K := 0 TO 7 DO HRITE(RAOARF RD[U:K]:6) FHRITELN(RADAR) F

FOR L :=1 TO 127 DO BEGINHRITE(RADARF 'RD 'F L:3) FFOR K := 0 TO 7 DO HRITE(RADARaRDCL;K]:6) F

END URITELN(RADAR) FEND ELSE IF RADCHKCNT > O THEN. HRITELN('** PROBLEM · INCOMPLETE DATA SAM°LE **') FFDR K :=1TO 20 D9 BEGIN

PHL„DATETIME[K := TBCBP] FBP := BP + 1 F .END F

xPHL•POINTCOUNT := HEXIN(6) FBP := BP + 1 FFOR K := 1 TO 3 DO PHL„?ARAWETERS[K] := HEXIN(6) FFOR K := 6 TO 10 DO PHL.PARAMETERS[K] 2= HEXIN(2) F _BP := BP + FHLFILL F

RADCHKCNT := O FRADARPOINT := PHL•POINTCOUNT F

END F

· PROCEDURE FMTLKL F

VAR K : INTEGER F

BEGINFOR K := 1 TO 20 DO BEGIN

LKL•DATETIME[K] := TBCBP] FBP := aß + 1 FEND F ·LKL•POINTCOUNT := HEXIN(6) F

BP := BP + 1 FFOR K := 1 TC 10 DO L<L•RECEIVER[K] := HE(IN(6) FFOR K := 1 TO 3 DO L(L•$TATU5[K] := HEXIN(Z) FBP := B? + LKLFILL F

END F

,64

PROCEDURE FMTDEL F

CONST PI = 3.14159265 FAREA = 0.0046 F E SDR METERS ]T = 30.0 F C SECONDS ]

VAR K : INTEGER FL : INTEGER F

A D : REAL FC : REAL F

BEGINFOR K := 1 T0 B DO BEGIN

D8L.DATECKl := TBCBP] F

END BP := BP + 1 FFOR K := 1 TO 12 DO BEGIN '

DBL.TIFECKJ := TBEBPJ F

:ND BP := BP * 1 Fgs Läfgg i :4: THEN L := 1 ELSE L := 11 FFOR K := 1 10,10 DO BEGIN

E DBL.BIN[L] := HEX!N(4) F_N0L := L + 1 F

IF LCC2] = '3' THEN BEGINHRITE(DISTzD6L.DATE:DBL.TIME) FDR.3EC := SEC0N0S(DBL.DATEFOBL.TINE) F

äR:§R(0:030% j PI)/(AREA * T) F .roä •< E= 1·TO'19 oo ascxnHRITE(DI$TzDBL.BINLK]:5) F

D := 0.25 * K + 0. 25 F

EN° QR.RP := DR.RR * D•D*D * D8L.9IN[K] * C F‘

HRITELN(DIST) F_~°URITE(DISTRAINFDR) FSF :2 BP + DBLFILL F

END F

PROCEDURE FMTRTL F

VAR §G FTA.:

TIMEARRAY F' DA : DATEARRAY F '« K : INTESER FL : INTEGER FDLTS : REAL F

~ BEGINFOR K := 1 TO 8 OO BEGIN

DACK] := TBCBPJ FSP := BP

•1 F

~ ggo E BP * 1 'FOR·L := 1 TO'5 DO BEGINRG := TBCBPI F ·„ BP := BP + 1 F

FOR K := 1 TO 12 DO BEGINTACK] := TBEBPI F

END BP := BP + 1 FIF (1A' <= RG) AND (RG <= 'E') THEN BEGIN

SEC := SECONDS(DA¢TA) FDLTS := SEC • RGRRCRG].$EC F:= SEC F

' N': asctuRSRRC'A'].RR := 90.0/DLTS F

ENO QRITE(LOCLCRAINFRGRR['A']) F'B': BEGIN END F'C': BEGIN

, RSRR['C'].RR := 914.4lDLTS FHRITE(LOCSCRAINFRGRRC'C ]) F

END F'D': BEGIN’

R.;¤=2£•1>'J.na := 916.6/0LTs ;wRITE(DIVSCBAIN:RGRRC'D']) F

END F'E': BEGIN

P3R°C'E'].RB := 90.0/9LTS FHRITE(DIVLCRAIN»RGRRC'E']) F

END FEND F

END§N° ;

BP :2 BP + RTLFILL FEND F

I65

BROCEDURE FMTENL F BEGIN END F

E MAIN PROGRAM ]

BEGIN .DR.$EC := ·3000O F- DR.RR := 0.0 F' REHRITE(DISTRAIN) FHRITECDISTRAINFDR) F

FOR RG := 'A TO 'E' DO BEGINRGRRERG]•SEC := *30000 FRGRRCFG].RR := 0.0 FCASE RG BF

'A': BEGINREHRITE(LOCLCRAIN) F

END @RITE(LOCLCRAIN¢RSRR['A']) FI

'B': BEGIN END F'C': EEGIN

REHRITE(LOCSCRAIN) Ftwu NRITE(LOCSCRAIN1PGRR['C']) F•' I

'D': BEGINREHRITE(DIV3CRAIN) FURITE(DIVSCRAIN¢RGRR['D']) F

END F'E': BEGIN

REURITE(DIVLCRAIN) FURITE(DIVLCRAIN:RGRRE'E']) F

END FEND F

END F

BIND(DIST1 '3000DIST*RAUDATA '1 STATUS) F_REHRITE(DIST) F8IND(RAIN: '3000RAIN*RAWDATA 'F STATUS) FREHRITE(RAIN) FBIND(RADAR¢'3000RAD*RAHDATA 'F STATUS) FREHRITE(RADAR) FRESET(TAPE) FRADCHKCNT := ·1 FRADARPOINT := ·1 FHHILE NOT EOF(TAPE) DD BEGIN

READLN(TAPEFTB) F. BP := 0 FFOR RC := 1 TO 102 DO BEGIN

- OBP := 3P FLCC11 := TECBP] FBP := BP

* 1 FLCEZJ := TBCEP] F

- BP := BP + 1 FIF (('0° <= LC[1]) AND (LCC1] <= '7')) AND(('A' <= LCEZJ) AND (LCC2] <= 'H')) THEN FNTRDLELSE IF LC = 'LK' THEN FMTLKL

- ELSE IF LC = 'PH' THEN FMTPHLELSE IF LC = 'CM' TNEN FMTCML

ELSE IF (LC = 'DA') OR (LC = 'DB') THEN FMTDELELSE IF LC = 'EH' THEN FMTEHL

ELSE IF LC = 'RT' THEN FMTRTLELSE BP := OBP * 80 FEND F

END F

I

a

66

R.SEC := SGCJOU FR.RR := 0.0 F

URITE(DISTPlINFR) FRESET(DISTRAIN) FREAD(DI$TRAINF9R) F _OLDDIST := DR.RR F

FOR RG := 'A' TO 'E' DOCASE PG DF

'A': BEGINHRITE(LOCLCRAIN:R) FRESET(LOCLCRAIN) F

END READ(LOCLCRAIN;RGRR[‘\']) FI

'B': BEGIN END F'C': BEGIN

HRITEILOCSCRAINFR) FRESETILOCSCRAIN) FREAD(LOC$CRAIN:RGRR['C']) F

END F'U': BEGIN

HRIIECDIVSCRAINFR) FRES:T(DIVSCRAIN) FREAD(DIVSCRAIN1RGRRC'D']) F

END F'E°: BEGIN

WRITEIDIVLCTAINFR) FRESET(DIVLCRAIN) FREAD(DIVLCRAIN1RGRRC'E']) F

END F -END F

IF RGRRE'C'g•RR>ZO•O THEN OLDLOC:=RGRR§'C'g.RR ELSE 0LDLOC:=RGRR€'A'].RP FIF RGRR'D‘

.RR>20•O THEN OLDDIV:=RGRRL'D' .RR ELSE OLDDIV:=RGRR 'E'].RR F

SEC := 0 FHNILE SEC < 300000 D) BEGIN

NSEC := $00000 FFOR RG := 'A TO 'E' DO IF RG <> '3' THEN BEGINUHILE RGRPCRG]•SEC <= SEC oo

CASE RG JF'A': READ(L0CLCRAINFRGRRE'A']) F'C': READILOCSCRAINFRGRR 'C']) F'D': READ(DIVSCRAINaRGRR$'D']) F

END'E': READ(DIVLCRAIN:RGRR.'E']) FI

_NDIF (RGRRERG].SEC<NSEC) THEN NSEC := RGRRERG].SEC F

E 1

~ IF RGP¤['C'].RR>ZO•O THEN LOCRR:=RGRR['C'].RR ELSE LOCRR:=RGRR['A'].RR FIF RGRR['D']•RR>20.0 THEN DIVRR:=R5RR[°D'].PR ELSE DIVRR:=RGRR['E']•RP FHHILE DR.SEC <= SEC DO READIDISTRAINFDR) FIF DR•SEC < NSEC TNEN NSEC := DR.SEC FI§€§O%g%S£<>LOCRR) OR (OLDDIV<>DIVRR) OR (0LDDI$T<>DR.RR)

HRITELN(RAIN»SEC:81OLDLOC:8:1FOLDDIV:E:1F0LDDIST:8:1) FOLDLOC := LOCRR FOLDDIV := OIVRR F „OLDDIST := DR.RP F

END F

END SEC := NSEC FEND HRITELN(RAINF$EC:E:L9CRR:3:11DIVRR:8:1FDR.°P:E:1) F

I

I

67

APPENDIX B. PREPROCESSING PROGRAM

This program converts the measured values, in computer counts from the

front end program, to experimental values, as summarized in Chapter 5.

It also produces the first-look file, performing the prediction calcu—

lations.

Appendix B. Preprocessing Program

68

PROGRAM PREFROCESS (IN’UT: DUT°UT:ARCRIVECLFN = 11: LINELENGTH = 8530):RAD\R(LFN = 12: LINELENGTH = 66):RAINCLFN = 14: LINELENGTH = 66):REPORTCLFN = 18):CALISRATION (LFN = 20 )) 3

CONSTNOMAXPTS = 1S 3

AA = 0.015$ 3BB = 1.166 3EPSILON = 0.3228359 3 E 18.5 DEGREES ]GAMMA = 0.0454:45 3 /22 ]LNOM = 10.332 3DIVSITE = O 3DIVRHI = 1 3DIVPATH = 2 3LOCPATH = 3 3LDCRHI = 4 3

TYPE

RECEIVER = (HILMACD:VILM\X:HILMAPH:HILWAIP:HILMAQP:FREDCO:FREDX:FREDPH:DIVCO:DIVX) 3

CHANNEL = 0..7 3

DATEARRAY = PACKED ARRAY E1..8ä OF CHAR 3TIMEARRAY = PACKED ARRAY 1..1 ] OF CHAR 3

POZNTHEADERLUNP = RECORDDATE 1 DATEARRAY 3

·TIME : TIMEARRAY 3ROINTCOUNT : INTEGER 3AVGPHR : REAL 3AZ : INTEGER 3EL : INTEGER 3 ESCAN 1 INTEGER 3 [ SCANSECTOR ]POINT : INTEGER 3 ‘

END 3

LUMPCODE = PACKED ARRAY [1..2] OF CHAR 3

COMMENTLUMP = RECORDMSG : PACKED ARRAY [3..64] OF CHAR

~· END 3

DASPARAMETERLUMP = RECORDPO 1 INTEGER 3

~ DZE 1 INTEGER 3DZO 1 INTEGER 3NI 1 INTEGER 3EINSZ : INTEGER— END 3

MAXRECORD = RECORDVAL : REAL 3» AUX : REAL 3

- TIME 1 TIHEARRAYEND 3

MAXARRAY = ARRAY[1..NOMAXPTS] OF MAXRECORD 3„\

I

'

69

VAR LC 1 LUMPCODE JCML : COMMENTLUMP JDAS : DASPARAMETERLUMP JPHL 1 POINTHEAOERLUMP J

DIVRR : REAL J E DIVEPSITY SITE RAIN RATE 5LOCRR 1 REAL J LOCAL SITE RAIN RATEDISTRR : REAL J E DISTRJMETER CALCULATED RAIN RATE J_ RAINSECONDS : INTEGER J E END OF RAIN RATE PERIOD JDIFFSUM 1 REAL J SUM OP THE DIPF- OP DIVRR AND DISTRRS

u :

R5€ä§2>‘"’ äE§{"¥‘” ‘'§b"éäE?6°ä;‘ééEäE§§€E‘°E

"°‘"”*“"""’MAXDIPP 1 REAL J OF DIFP INDIVRRMAXLOCRR

1 REAL J E MAXIMUM LOCAL RAIN RATE J‘ MAXDIVRR 1 PEAL J E MAXIMJM DIVERSITY RATE Jq%§äT§qE : Tägääägäx J E TIME OF MAX HH:MM:SS-T JMLRRSEC :.INTESER J ' E SECON)S IN MONTH OF MAX JMDRRSEC : INTEGER JZLMAX 1 REAL J E LDCAL PATH WAX Z JZDMAX : REAL J C OVER DIVERSITY SITE MAX Z JZLMTIME : TIWEARRAY J E TIME MAX OCCURED •

LOCAL PATH JZDMTIME 1 TIMEARRAY J E TIME MAX OCCURED · OIVISITY SITE JZDRLMAX : REAL J ZDR TRAT GOES WITH MAX · LOCAL JZPRDMAX : REAL J C ZDR THAT GOES WITH MAX · DIVERSITY JBINWIDTH : REAL J ”BINLENGTH 1 REAL J _DEADZONE : REAL J

RADARPKPWRM : REAL J E RADAR PEAR ROWER CALIBRATION : M JRADARPRPWRE : REAL J [ RADAR PEAR POHER CALIERATION : 5 JRADARM 1 REAL J E RADAR COUNTS TO DBZ CALIERATION : M JRADARB 1 REAL J E RADAR COUNTS TO D21 CALIBRATION : B J

. PEAKPWRCF : ARRAYECHANNELJ OP REAL JCHANCF : ARRAYECHANNEL] DF REAL J

RADAR 1 TEXT J _ARCHIVE 1 TEXT JRAIN : TEXT J EREPORT : TEXT J

- CALIBRATION 1 TEXT J

RRL : REAL JRRATN : REAL JRRZL : REAL JRRZH 1 REAL JRRP1 1 REAL J

· RRP2 J REAL JZRR : REAL J

STATUS 1 INTEGER JCHAN 1 INTEGER JSTIME 1 TIMEARRAY JSDATE : DATEARRAY JSEC 1 INTEGER J

» LNTO : REAL J

NMAX 1 INTEGER J

ATNMAX : MAXRECCRD JHILMAATNMAX : MAXARRAY J’ FREDATNMAX : MAXARPAY JDIVATNMAX : MAXARRAY J

MWA : REAL JMWT : TIMEAFRAY JMFA : REAL JMFT 1 TIMEAFRAY JMDA : PEAL JMDT : TIMEAPRAY J

Rxv : ARRAVERECEIVERI OF REAL JRXM : ARRAYERECEIVERJ OF REAL J

·_ RX3 1 ARRAYERECEIVERJ OF REAL J

·

. 70

L UILMAATN : REAL F»uA~]~—M_A F ”““"""““*"——————~

„„ . ...HILMAISL : REAL FFREDATN : REAL F .FREDISL : REAL FDIVATN : REAL FDIVISL : REAL F

HILYASTAT : INTEGER F'

FREDSTAT : INTEGER F. DIVSTAT : INTEGER F

UILMACHR : FEAL FFREDCUR : REAL FDIVCNR : REAL F

HILHACGD : REAL FFREDCGD : REAL FDIVCGD : REAL F

RRMAX : MAXFECORD FLOCRRMAX : MAXARRAY FDIVRRMAX : MAXARRAY F

ZMAX : MAXRECORD F _LOCZMAX : NAXARRAY F -DIVZMAX : MAXAQRAY F

lFUNCTION $ECONDS(D : DATEARRAY F T : TIMEARRAY) : INTEGER F

VAR V : INTEGER FS : INTESER F

BEGIN VEV := (0RD(D[Z])·48)•10 *

(OR0(D[3])·48) FS := V

•14430 F

V := (0RD(T[Z])'4B)*10 + (ORD(T[3])·48) FS:=S+V=•360"JF‘V := (ORD(T[5])•48)*TO + (0RD(TC5])'4S) FS := S + V

•60 F

V := (0RD(T[3])•4S)*10 * (3RD(TC9])•48) FSECONDS := S + V F

' END F

PROCEDURE $ETMAX(MX : MAXRECDRD F VAR NA : MAXARRAYF F

- VAR N : INTEGER F _TX : MAXRECORD F

BEGIN- FOR N := 1 TG NOMAXPTS OO

IF MX„VAL > MACN]•VAL THEN BEGINTX := MAU!3 FMAIN} :=

‘·1XF

MX := TX FEND F

END F

Z

I

’ ·

7l

°ROCEDURE MAXDETECTOR F

BEGINATNMAX.VAL := MJA FATNMAX.TIME := MUT FSETHAXKATNMAXFNILWAATNMAX) FMHA := -1000.0 F

' ATNMAX.VAL := MFA FATNMAX.TIME := WFT FSETHAX(ATNMAXFFQEDATNWAX) FMFA := -1000.0 F

ATNMAX.VAL := MDA FATNHAX.TIME := MDT FSETMAX(ATNMAXFDIVATNM£X) F‘MDA := -1000.) F

ZMAX.VAL := ZLMAX FlWAX.AUX := ZDRLMAX FZMAX.TIME := ZLMTIME FSETMAXCZNAXFLJCIMAX) FZLMAX := -100).0 F

ZMAX.VAL := ZJMAX FZMAX.AUX := ZDRONAX F .ZMAX.TIM€ := ZDMTIME F .SETMAXCZMAXFDIVZMAX) FZDMAX := -1000.0 F

RRHAX.VAL := MAXLOCRR FF

RRMAX.TIME := MLPRTIME FSETMAX(RRMAXFLOCRRMAX) FMAXLOCRR := •1000.G F

RRMAX.VAL := WAKDIVRF FRRMAX.TIME := MDRRTIME FSETMAX(RRMAXF0IVRRMAX) FMAXDIVRR := -1000.Ü F

END F ·

PROCEDURE FMTDPL F

VAR K : INTEGEB F

'l

BEGINBINHIDTH := 125.0 FREAD(RADARF 0AS•°C) F

~ READ(RADARF DAS.9ZEF0AS.DZO) FREAO(RADARF DA$.NI) FREAD(RADARF 0AS.BINSZ) FREAD(RADAR) FDEADZONE := (DAS.0ZE

*DAS.DZO) * 15.0{2.0 F

IF DAS.BINSZ = O THEN BINLENGTH := 25:.0ELSE BINLENGTN := 510.0 F

END F

RROCEDURE FMTCNL F

VAR K : INTESEQ F

BEGINHRITE(LC) FURITECREPORTF LC) FFOR K := 3 T9 54 90 BEGIN

READ(RADARF CML.MSG) FHRITE(CNL.“1SG) FURITE(RE’0RTa CNL.MSG) F

END FEND F

’ ·

72

PROCEDURE FMTRDL 7

CONST RADARM = Z•SS]O 7RADARE = •TO7•6 7

VAR K : INTEGER 7· BIN 3 INTEGER 7

C : CHANNEL 7Z 3 ARRAICCHANNEL] OF REAL 7RC 3 INT:GER 7

BEGINHRITECARCHIVE: LC) 7READKRADAR7 3IN) 7HRITE (ARCHIVE: BIN :4) 7

FOR C := C TO 7 DO BEGINREAD (RADAR7 RC) 7ICC] := RC * (RADARM I DAS•NI)

* IC * LN(DEAOIONE * BINUIDTHI2.0 *BIN * BINLENGTH)lLN1O• FEAKPNRCFCC] * RAOARB • CHANCFCC] + 7E•S5 7HRITE(AFCHIVE:ICC]:7:Z) 7 _

END 7URITE(ARCHIVE:' ') 7

IF (PHL•%CAN = LOCPATN) AND (BIN = S)TNENIF I S] > ILMAX THEN BEGIN

ILFAX := ICS] 7ZLMTIAE := ¤HL„TIME 7

_NDIDRLMAX := ICS] ° IC7] 7I: 1

IF (PHL•SCAN = DIVSITE) AND (SIN = ZS) THENIF ICS] > IDMAX THEN BEGIN

ZDMAX := ICS] 7ZDMTIME := PAL TIME 7

' ZDRDMAX := ICS] · ZE?] ;END 7

END 7

PROCEDURE FMTLKL 7

CONST CHR = •?Z•O 7CGD = 38.0 7

VAR RX : RECEIVER 7_ RXC 3 INTEGER 7

BEGINHILMACUR 3= CHR 7HILMACG0 := CSD ;FREDCHR := CAR 7FREDCGD := CSD 7DIVCVR := CAR 7DIVCGO := CSD 7IF LCCZ] = 'U' THEN BEGIN

FOR RX := UILMACO TO UILHAQP DO BEGINREAD(RADAR;RXC) 7

EMU RXVCRX] := RXMCRX] * RXC * RXBEBX] 7I

READ(RADAR7HILNASTAT) 7HILMAATN := WILMACUR • RXVCHILMACO] 7HILMAISL := RXVCHILWACO] • RXVCNILFAX]

‘UILMACGD 7

IF WHA < AILMAATN THEN BEGINMwA := AILMAATN 7MAT := PHL.TIME 7

END 7END ELSE BEGIN

FOR RX := FREOCO TO DIVX DO EEGINREAD(RADARaRXC) 7

Evo RXVCRX] := RXNCRX] * RXC * RXBCRX] 7READ(RADAR7FREDSTATVDIVSTAT) 7FREDATN := FREDCHB · nxvtrasoccu 7FREDISL := RXVCFREDCO] • RXVCFREDX] + FRFDCGD 7IF WFA < FREDATN THEN BEGIN

MFA := FREDATN 7MFT := °HL.TIWE 7

END 7DIVATN := DIVCHR • RXVCDIVCO] 7DIVISL := RXVCDIVCO] · RXVCDIVX] * DIVCGD 7IF MDA < OIVATN THEN BEGIN

MDA := DIVATN ;

END MDT := RHL•TIME 7I

URITE(ARCHIVEn'LK 'eHILMAATN3331;WILMAISL3S:17NILMASTAT:Z1FREDATN:531»FREDISL:8:17FREDSTAT:2:DIVATN:8:1;DIVI$L:8:170IVSTAT:27' ') 7

END 7END}

73

PROCEDURE FNTPHL F

- VAR K : INTEGER FAP : INTEGER FD : REAL F

BEGINIF PHL.POINTCOUNT > Ü THEN HRITELN(ARCHIVE) FREAD(RADAFF PHL.DATE) FREAD(RADARF ?HL.TINE) FREAD(RADARF PHL•POINTCOUNT: AP; PHL.AZ¢ PHL•EL) FREAD(RADAR; PHL.SCANF PHL.°0INT) FSEC := SECONDS(PHL.DATE1 PHL.TIME) FPHL.AVGPHR := AP F

IF PHL.POINTCOUNT = 1 THEN BEGINSDATE := PHL„DATE FSTIME := PHL.TIME F

END ELSE IF (PHL.SCAN = DIVSITE) AND (?HL.°CINT = 0) THEN VAXDETECTOR F

URITE (ARCHIVEu'PH':°HL.DATEr PHL.TIMEF PHL.POINTCOUNT:$F°HL.AVGPHR:7:2r PHL.AZ:Sz PHL.EL!Sz 9HL.SCAN:Sa PHL.ROINT:5) F

URITE (ARCHIVEn° ') F

UNILE (SEC>RAINSEC3NDS) AND (NOT EOF(RAIN)) DOREADLN(RAINF RAINSECONDSF LOCRR; DIVRRF DISTRR) F

URITE (ARCHIVE¢'RR 'rSEC:10:LOCRR:10;ZrDIVRR:10:2:DISTRR:10:2) FFOR K := 44 TO 60 DO HRITE (ARCHIVE: ') F

' D := DIVRP• DISTRR F

DIFFSUW := DIFFSUM * D FDIFFCOUNT := DIFFCOUNT * 1 FD := ABS(D) FIF D > MAXDIFF THEN WAXDIFF :=D FIF LOCRR > MAXLOCRR THEN BEGINMAXLOCRR := LOCRR F ‘

MLRRTINE := ?HL.TIME FMLRRSEC := SEC

END FIF DIVRR > MAXDIVRR THEN BEGIN

MAXDIVRR := DIVRR FMDRRTIME := PHL„TI^1E FMDRRSEC := SEC

. END FEND F

PROCEDURE FMTPPL FF

CONST RADAP¤K?HRM = 20.0 FRADAPPKPHRB = 15.0 F

VAR C : CHANNEL FB : INTEGER F —

BEGINREAD(RADARF E) FFOR C := O TO 7 DO BEGIN

READ (RABARF B) F

END BEAKPHPCFECJ := 10.0 * LN(RADARPK°HRM * E * RADAPPKPURB)lLN10 Fzum ; '

;x \

·

74

BEGINLN10 := LN(10-J) FBIND(FAINF'}JO0RAIN*RANDATl 'FSTATUS) FR£SET(RAIN) F' READLN(RAINFRAINSECONDSFLOCRRFDIVRRFDISTRP) F

BIND(RADAPF'$O00RAD*RAUbAT\ 'FSTATUS) FRESETCRADAR) F

?IND(REP0RTF'300ODATA•FST*L00K'FSTATUS) FREHRITE(REPORT) F

IMAX-VAL := ·10C0-G FIMAX-AUX := 0-3 FIMAX-TIME := ' 99:99:99-9 ' FFOR NMAX := 1 TO NOH\x¤TS DC BEGIN

HILMAATNNAXCNMAX] := ZMKX FFREOATNMAXENMAXI := ZNAX FDIVATNMRXCNWAX] := ZNAX FLOCRRMAXENMAXI := ZWAX FDIVRRMAXENMAXJ := ZWAX FLOCZMAXCNMAX] := IMAX FDIVZMAXKNWAX] := IMAX F

END F _ATNMAX := ZNAX F

DIFFSUM := C-O FDIFFCOUNT := 0 F

PHL-ROINTCOUNT := 0 F

MAXLOCRR := *1-0 FMAXDIVRR := *1-0 FMAXDIFF := ·1-0 F .

MUA := *1000-0 FMFA := *1000-0 FMDA := -1000-O F —ILMAX := *1000-0 FZDMAX := ·1000-0 FFOR CHAN := 0 TO 7 DO CNÄNCFECHAN] := 0-0 F

.

RXMEHILMACOJ := 0-0159 F RXBEHILNACO] := *1&&-6 F, RXMEFREDCOI := 0-0159 F RX! FREDCO] := *144-L FRXHEDIVCOJ := O-0159 F RXBCDIVCOJ := *14k-6 F— RXMCUILMAXJ := B-0166 F RXBCHILMAXJ := -128-6 FRXXIFREDXJ := 0-0166 F RXBCFREDXJ := *123-6 FRXMCDIVXJ := 0-0156 F RXRCDIVX] := *128-6 F

» RXMEUILMAPH} := 0-0 F RXSENILNAPH] := 0-0 FRXM wILMAIP} := 0-0 F RX3 HILH\IP] := 0-0 FRXMCHILMAOP] := 0-0 F RXBCUILMlQ!] := 0-0 FRXMCFREDRHI := 0-0 F RXBCFREDRHI := 0-O F

HHILE NOT EOF(RAOQR) DO PEGINREAD(RADßR: LC) FIF LC = °CM' THEN FMTCML FIF LC = 'PH' THEN FMTPHL FIF LC = ')P' THEN FMTOPL FIF (LC = 'LW') OR (LC = 'L0') THEN FMTLKL FIF LC = '°P' THEN FMTPPL FIF LC = 'RD' THEN FMTRDL FREADLN(RAOAR) F

END F

—I

75

\'[ CAROL'S FIRST LOCK RE’0RT ]

HRITELNIREPORT) FURITELN(REFORT) FUäälätuégäsgäggNOMAXPTS:2a' HIGHEST LINK ATTENUATIONS DURING EVENT') F

I -CNRITELN(REPORTF'0IL!A PECEIVER') FURITELN(REPOPT) FHRITELN(REPORT;'ATTENUATICN TIME') F ·URITELN(REPOPT1'•‘•''•••·••

••··') FFOR VILMAATNMAX[NMAX].VAL > 0.0 THEN BEGIN

END QRITELNIPEPORTaATNMAX.VAL:7:I:' '1ATNMAX.TIME) FHRITELN(REPORT) FURITELN(REPORT1'FREO IECEIVER') FURITELN(REPORT) FHRITELNIREPORTF'ATTENUATION TIME') FURITELN(REPOFTa'•'''°'‘''•• "'•') FFOR _FREOATNMAX[NMAX].VAL > 0.0 THEN BEGIN

END BRITELNIREPORT:ATNMAX.VAL:7;1¢' ';ATNMAX.TIME) FHRITELN(PEPGRT) FHRITELN(REPORT:'DIVERSITY RECEIVER') FHRITELN(REPORT) FHRITELN(REFORTr'ÄTTENÜRTIÖN TIME') F .URITELN(REPORT1'''''•'••'‘•

••"') FFOR DlVATNMAX[NMAX].VAL > 0.0 THEN BEGIN

‘EN¤ QRITELNIREPORTpATNMAX.VALzF:1:' ‘;ATNMAX.TIME) FHRITELNCREFORT) FHRITELN(REPORT) F

URITELN(REPOPT) FNQMAXPTS:21' HIGHEST RADAR Z VALUES') F ’URITELN(REPOPT;'MAIN SITE ' LOCAL PATH BIN S') FHRITELN(REPOPT) F Z(S) TIME ZDP(0) PPEDICTED RAIN RATE:; FFOR ggg; zi 1JgO”}OEß§§§§ OO IF LOCZMAXCNMAX].VAL > 0.0 THEN BEGIN I

[ ZRR z; EXP(ZMAX.VAL * LN10I10.0) * 0.00193

~EXP(·1.5O * ZMAX.AUX

• LN10/10.0) FE URITELN(REPORTrZMAX.VALz6:1:‘ 'eZ!AX.TIME:

END_ ZMAX.AUX:6:1:' ':ZRR:6:1) F

URITELNIREPORT) F. H¤ITELN(REPOPT) F

HRITELN(REPORT:'DIVERSITY SITE ' BIN E8') FHRITELN(REPORT) F Z(S) TIBE ZOR(0) PREDICTED RAIN RATEZO FFOR := g xgvägäääzäg OO IF DIVZMAX{NWAX].VAL > 0.0 THEN BEGIN I

ZRR zé EXR(ZMAX.VAL*LNI0l10.0) * 0.U01°?* EXR(•1.S0 * ZMÄX.AUX * LN10lT0.0) F

HRITELN(REPORT1ZMAX.VAL:é:1:' 1IMAX.TIMEz

END_ ZMAX.A'JX:6:1F' 'FZPR:6:1) F _

HRITELN(REPORT) F__0 HRITELNIPEFGPT) F

(

, ·

76

HRITELN(REPCRT) 2HRITELN(REPCRT1NONAXPTS:2:' NIGHEST RAIN RATES') 2HRITELN(REFOFT) 2

. HRITELN(PEPORT:'MAIN SITE') 2HRITELNIREFOPT) 2HRITELN(REPOFTa'RAIN RATE TINE CALCULATED Z RANGE 'r

' CALCJLATED ATN') 2wRITELN(RgpgRy,:....-.... ----:;....•. -.....-- ...... •’

.........•.... ;FOR NMAX := 1 TO NONAÄPTS DO IF LOCRRMAXENMAX].VAL > 0.0 THEN BEGIN

RRMAX := LOCRRMAX.NNAX] 2RAIL := 10.0 * LN(230.0 * EXP(1.&~LN(RRMAX.VAL)))lLN10 ZRRZH := 10.0

~ LN(ZZ0.0 * EXP(1.6•LN(RRMAX.VAL)))lLN10 2IF RRMAX.VAL <= 1J.O THEN BEGIN

RRATN := AA * EX°(?B*LN(RRNAX.VAL)) * LNOM 2 'END ELSE 3ESIN

RRL := LNOW • $.152 * LN(RRMAX•VAL/10.0)/LN1U 2RPF1 := GAMNA * RB * LN(RRNAX.VALl10.Ü) * COS(EPSILON) 2RRF2 := (1.Ü ' EXP(°1.Ü * RRF1 * RRL))/RRF1 2EYDRRATN := AA * EXP(RS*LN(RRNAX.VAL)) * RPFZ 2 E

1 IHRITELN(REPORT;RRWAX.VAL:S:1r' ‘aRRMAX.TIME;' '1

END Q RRZL:6:11° TO '1RRZH:6:1:' 'rRRATN:6:1) 2I

HRITELN(REFCRT) 2HRITELNIREPORT) 2HRITELN(REPORT) 2

URITELN(REFCPT) 2URITELN(REPORT1'DIVERSITY SITE') 2URITELN(REPORT) 2• URITELN(REPORT;'RAIN RATE TIME CALCULATED Z RANGE '1

' CALCULATED ATN') 2wQITEL~(REp0py’:-....---- ...•7;------ ------ -- ----.-

ul

FOR NMAX := 1 TO NONAXPTS DO IF DIVRRHAX[NMAX].VAL > 0.0 THEN BEGINRRMAX := DIVRRMAXINNAXJ 2 _RRZL := 10.0

•LN(Z30.0 • EXP(1.4*LN(RRMAX.VAL)))/LN10 3

RRZH := 10.0 •LN(220.0 * EXP(1.6*LN(¤RMAX.VAL)))/LN10 2

IF RRMAX.VAL <= 10.0 THEN BEGINRRATN := AA * EXP(BB*LN(RRMAX.VAL)) * LNOM 2

END ELSE BEGINRRL := LNON • 3.152 * LN(RRMAX.VAL/10.0)/LN1O 2RFF1 := GAMMA A BB * LN(RRMAX.VALl10.0) * COS(EPSILON) 2RRF4 := (1.0 · ElP(·1.0

~RRF1

~¤¤L))/RRF1 2

ENURRATN := AA * EXR(RB*LN(RRMAX.VAL)) * RRF2 2I

HRITELN(REPORT:RRiAX.VAL:B:1:' 'eRRMAX.TIME1' '1 _

END_ RRZL:5:14' TO '«P¤ZH:6:12' '4RPlTM:6:1) 2

ilI'HRITELN(REPOFT) 2HRITELN(REPOPT) 2HRITELN(REPORT) 2

AVGDIFF := DIFFSUM/DIFFCOUNT 2HRITELN(REPOPT:'COMPARISON OF DISTROMSTER AND RAIN GAUGE RAIN RATES°) 2HRITELN(REPORT) 2URITELN(REPORT;'AVERASE DIFFERENCE IN RAIN RATES: °:AVGDIFF:7:2) 2URITELN(REPOFT) 2=N¤URITELN(PEPOPT1'MAXIMUN DIFFERENCE IN RAIN RATES: '2MAXDIFF:7:2) 2

I

4

77

APPENDIX C. °DUMMY DATA' GENERATION PROGRAM

This program reads a series of rain rates, one for each 4.5 minute_radar

scan cycle, and produces corresponding radar, link, and weather instru-

ment data, in the form of the collection procedure. The data thus gen-

erated is stored on tape and can be used directly as input to the front

end program of Appendix A, to test the processing system. _

Appendix C. °Dummy Data' Generation Program

78

HARETRPEPase 1

Line Stat Level1 1 0 PROGRAH HakeTare 6 { aake a reder/1ink/rain/distroaeter test data tare12 1 0 .

. 3 1 0 ·1$I:”·l·•1i{•P·1rR+r£1+•U+ }4 1 05 1 06 1 0 CUNST cn0 =

'0’6 { Channel codes }/ 1 1 cnl = '1' 6

8 1 1 cn2 = '2' 69 1 1 cn3 =

’3’6

10 1 1 cn4 ¤’4'

6 .11 1 1 cn5 = '5' 612 1 1 cn6 =

’6'6

13 1 1 cn7 = '7' 6 .14 1 1 z15 1 116 1 1

· 17 1 110 1 1 TYPE17 1 1

‘

20 1 1 { Standard Tunes }21 1 122 1 1 Bste = 0••255 623 1 124 1 1 Channel ¤ 0••7 625 1 126 1 1 liaeünits ¤ (hh6hl••h•a1•sh•s1) 627 1 1

. 28 1 1 PointC0unt = inteuer6271 1

30 1 1 Luawüode • Arras[1••2J of Char 6J1 1 132 1 1 hhvalues ¤ 6rraeL0••15J of inteser 6J3 1 134 1 1 Receiver ¤ (U11aaC0•UilaaX•U11aaPh6U1laa0P6H11aaIP635 1 1 FredCo6Fr•dXaFredPh•01vC0601vX) 6

' 36 1 137 1 1 Rainöause ¤ (LoctCR8•LocBKUP•LocSCRG60ivSCRG»h1vlCRG) 638 1 1

. 39 1 1 Rxötatus = (Ui1aaStat•FredStat•01vStat) 640 1 141 1 1 HPHT1aeRec = Record42 1 1 date 1 inteeer 643 1 1 tiae 1 Arras[T1aeUnitsJ 06 bete 644 1 1 End 645 1 146 1 1

, 47 1 1 Datehrras = Arrae[1•«7l of Char 6 { DDMKKYY }48 1 1 Tiaehrrau = Arrau[1••101 of Char 6 { HN1HH1SS•T }49 1 1 TiaeRecord = Record50 1 1 Ja 1 char 651 1 1 date 1 Uateerrae 652 1 1 Ju 1 char 653 1 1 tiae 1 Tiaekrrav 654 1 1 Jc 1 char 655 1 1 I·.n11 G

_ 56 1 1

4

79

HkkETkPE Pase 9

Line Stat Level57 1 1du 1 159 1 160 1 1 Hssüode ¤ (ok•TxTi•e0ut6RxTi•e0ut6InCo••1n9•

. 61 1 1 DataError6F•tError6LxError) 662 1 1 Hsskanse = 0•„127 663 1 1 Radarössbuffer e Record64 1 1 cod 1 cher 665 1 1 data 1 Arraeüäsekansel of inteeer 666 1 1 End 667 1 168 1 1 Tavekecord ¤ record69 1 1 luar 1 Arrae(1••80] of char 670 1 1 end 6/1 1 172 1 1 devicecude = ltaeeecartl 673 1 1 inout = (dinndoutl 674 1 1 statecode = 1 reade•ea1tins•loadinal 6/5 1 176 1 177 1 1 Taeetntlßlk ¤ RECORD78 1 1 device 1 Deviceüode 679 1 1 lrc 1 bete 6 -80 1 1 fill 1 bete 681 1 1 is 1 bete 682 1 1 ds 1 bete 6 ~83 1 1 state 1 Statetode 684 1 1 Ports 1 •rrae[0••3] of bete 185 1 1 •rv 1 bete 686 1 1 vrv 1 bete 697 1 1 crv 1 bete 6 ~88 1 1 lrsize 1 bete 189 1 1 rnb 1 bete 690 1 1 bc 1 lnteeer 191 1 1 Hrtßnable 1 boolean 692 1 1 EOT 1 boolean 693 1 1 BH1 1 boolean 6

· 94 1 1 0nL1ne 1 boolean 695 1 1 Rudine 1 boolean 6

_ 96 1 1 Fübetect 1 boolean 697 1 1 Codßtat 1 (C•dOK»Nohtte•rt6Uithktteeeteüentaxl 698 1 1 Subßode 1 bete 6‘ 99 1 1 Blkäize 1 inteeer 6

100 1 1 end 6101 1 1102 1 1 °103 1 1 { 1ave tuev Records J104 1 1

' 105 1 1 Rex1estLu•e = Arree£1•«40J ot Bete 6106 l 1107 1 1 RadarPattern = Record { A radar bin data lunr}108 1 1 code 1 Lueetode 6109 1 1 Ja 1 char 6110 1 1 Nat 1 Pointßount 6111 1 1 Jb 1 char 6112 1 1 bin 1 6rrae11•„l6J of lnteeer 6

. 6_ 80

HAKETAPEPggq 3

Line Stnt Level113 1 1 End 1114 1 1115 1 1 RBt1äI‘SUb(l011Q ¤ (A•11rC•DrE•FrG•N) 1‘116 l 1117 1 1 Radartusp = record118 1 1 data 1 ARRAY(RadarSubCode] of TaeeRecord 1119 1 1 end 1120 1 1121 1 1 Uhanhrrav ¤ Arrav[Channe1J of RadarLus» 1122 1 1123 1 1 ConnentLunr = Record { Urerator consent }124 1 1 code 1 Luspßode 1125 1 1 tise 1 T1•eRecord 1126 1 1 ass 1 ArrayC1••60] of Char 1127 1 1 End 1128 1 1129 1 1 PointHeaderLunp = Record { Radar Point Header }130 1 1 code 1 Lunpßode 1131 1 1 tine 1 Tinekecord 1132 1 1 Net 1 Pointßount 1 '133 1 1 Ja 1 char 1134 1 1 avgeur 1 integer 1135 1 1 az 1 inteser 1136 1 1 el 1 inteeer 1_137 1 1 scan 1 bete 1138 1 1 en 1 bete 1139 1 1 P0 1 bete 1140 1 1 0ZE 1 bete 1141 1 1 ‘DZ0 1 byte 1 ‘142 1 1 NI 1 hate 1143 1 1 B1nSz 1 byte 1144 1 1 Junk 1 bete 1145 1 1 End 1146 1 1147 1 1 L1nkLu•e = Record { Receiver Link Data 1_ 148 1 1 code 1 Lunrßode 1149 1 1 tine 1 Tinekecord 1150 1 1 Npt 1 Pcintüount 1151 1 1 Ja 1 char 1

· 152 1 1 anale! 1 Arrayfkecelverl of inteeer 1V 153 1 1 status 1 hrrayfkxßtatusl nf Rute 1154 1 1 End 1155 1 1156 1 1 Tripkecord = Record157 1 1 Ja 1 char 1158 1 1 sause 1 char 1159 1 1 Jb 1 char 1160 1 1 tise 1 Tinekrras 1161 1 1 End 116:· 1 1163 1 1 RainTr1vLuse ¤ Record { Rain Hause Trirs 1164 1 1 code 1 LuseCode 1165 1 1 Jc 1 char 1166 l 1 date 1 Datehrrav 1167 1 1 trip 1 Arrav11••5J of Trirkecord 1168 1 1 End 1

I

8l

HAKETAPE Paee 4

Line ätnt Level169 1 1'170 1 1 Distroneterlunr = Record171 1 1 node 1 Luneßodn 1172 1 1 tina 1 linekecord 1173 l 1 Net 1 Polntüount 1174 1 1 Ja 1 char 1175 1 1 Dronßln 1 Arrav[l••l0J of Integer 1176 1 1 End 1177 1 1178 1 1179 1 1 _180 1 1181 1 1102 1 1183 1 1 ”104 1 1

‘

105 1 1 { llttttttltttttttltttttttttttltttlttttttttttttttttIttttttt }186 1 1 ( 8 t }187 1 1 1188 1 1189 1 1190 1 1 VAR191 1 1192 l 1 ( Lunws }193 1 1194 1 1 HTL 1 HexTestLunr 1195 1 1 CHL 1 C0•nentLune 1196 1 1 PHL 1 PointHeaderLunv 1197 1 1 RDL 1 Chanhrrae 1190 1 1 HLA 1 Dietroneterlune 1 \

199 1 1 DL8 1 01etr0neterLune 1200 1 1 RTL 1 RainTri»Lunr 1201 1 1 LKL 1 L1nkLune 1202 1 1 ‘203 1 1 cn 1 channel 1204 1 1 sc 1 Radaräubüode 1

' 205 1 1206 1 1 NRadarPo1nt 1 Pointüount 1

. . 207 1 1 Susten 1 T1neRec0rd 1208 1 1209 1 1 tv 1 Tavekecord 1210 l 1 tcb 1 Tareüntlßlk 1211 1 1212 1 1 LN10 1 real 1213 l 1 RR 1 real 1214 1 1 1 lti 1 inteser 1215 1 1 eti 1 integer 1216 1 1 sec 1 integer 1217 1 1 kk 1 lnteeer 1210 1 1 L 1 integer 1219 1 1 sn 1 integer 1220 1 1221 1 1 rdnb 1 ARRAY1ChannelJ 01 Radarßsgßuffer 1222 1 1223 1 1 HTriw 1 integer 1224 1 1

l

8 2

HAKETAPEPase 5

Line Stet Level» 225 1 1 rrf 1 TEXT 6

226 l 1 _227 1 1220 1 1229 1 1230 11231

1 1 ( I I }232IA

12331 1234 1 1 Procedure bateT1•e(Uar·t1ne 1 HPNT1•eRec) 6 External 6235 1 1236 1 1 Procedure F•tRbL(Var n 1 Radarüseßuffer 6237 l 1 Var rld 1 ChanArrav 6238 1 1 Var net 1 Puintüountl 6 External 6239 1 1240 1 1 Procedure F•tCHL(Var cul 1 Coeeentlune 6 .241 1 1 Var tr 1 TaeeRecord) 6 External 6242 1 1 »243 1 1 Procedure F¤tPHl(V•r rhl 2 Pointkeadertune 6244 1 1 Ver tr 1 Taeekecordl 6 External 6245 1 1246 1 1 Procedure F•t8ist(Uar del 1 Distroeeterlune 6247 1 1 Var tr 1 Taeekecordl 6 External 6248 1 1249 1 1 Procedure F•tL1nk(Uar lkl 1 Linkluer 6230 1 1 Var tr 1 Tanekecordl 6 External 6251 1 1 . '252 1 1 Procedure FetR¤in(Uar rtl 1 Rainfriwluor 6 \253 1 1 Var tr 1 faeeßecordl 6 External 6254 1 1255 1 1256 1 1257 1 1258 1 1 Procedure TaeeInit(d1r 1 In8ut 6257 l 1 dev 1 Oeviceüode 6' 260 1 1 Var tcb 1 taeecntlblkl 6 External 6261 1 1» 262 1 1 Procedure T•ee0ut(Uar tr 1 Taeekecordl 6 External 6« 263 l 1

_ 264 1 1 Procedure TPRee1nd(Var tcb 1 Taeeßntlßlkl 6 External 6265 1 1266 1 1 Procedure TP8kStat(Uar tcb 1 Taveüntlßlkl 6 External 6267 l 1268 1 1 Procedure TPReset(Var tcb 1 Tareüntlßlkl 6 External 6269 1 1270 1 1 Procedure TP5ark 6 External 6271 1· 1272 1 1273 l 1274 1 1 Procedure StartTare(d1r 1 In8ut 6275 1 1 dev 1 Deviceuode 6276 1 1 Var tcb 1 taeecntlblk) 6277 1 1

· 278 1 1 var taeereade 1 boolean 6279 1 2 c 1 char 6

. 280 1 2

Ee

83

NANETAPE Pase 6

Line Stat Level201 1 2 BEGIN

T

282 1 2 Tare1n1t(dir6devrtcb) 6203 2 2 uriteln 6204 3 2 Tapekeadv 1= false 6205 4 2 Repeat206 5 3 1PCkStet1tcb) 6287 6 3 11 not tcB«0n1ine Then urite1n(’TAPE ERROR ~ UNIT NOT

0N~LINE’) 6280 0 3 16 idiredout) and ( not (tcB•UrtEnah1e))287 7 3 Then ur1te1n(’IAPE ERROR — TAPE NOT RRITE ENAHLED') 6290 10 3 If (d1r=din) and (tcb•UrtEnebIe)291 11 3 Then ur1t•1n(’Uarn1ne — Tape is Brite Enahled') 6292 12 3 Tarekeede 1= tch•dn1ine and (not(dir=dout) nr tcb«UrtE

nable) 6 ‘.

293 13 3 if not 1•peReade then Resin294 15 4 urite1n1'P1ease correct the probleas and hit retur

n key') 6295 16 4 read1n(c) 6296 17 4 End 6297 10 3 until Tarekeads 6290 19 2 1f not tcb•bot Then TPReuind(tch) 6299 21 2 ERB 6300 22 1301 22 1302 22 1303 22 1304 22 1 —305 22 1 3 _306 22 1 ( 1 1 }

T

307 22130022 1

309 22 1310 22 1311 22 1 Procedure FixTiaeRate 6312 22 _ 1

‘‘

313 22 1 var s 1 inteser 6314 22- 2 a 1 inteser 6

_ 315 22 2 h 1 inteser 6. 316 22 2

317 22 2 BEGIN° 310 22 2 s 1¤ sec and 60 6

319 23 2 a 1¤ (sec div 60) aod 60 6320 24 2 h 1= sec div 3600 6371 Pfr 2322 23 2 Ssstea•tiaet1] 1= chr(1h div 10) + 40) 6323 26 2 Sustea•t1aeC2] 1= chr((h aod 10) 6 40) 6324 27 2 0sstea•tiae[33 1=

’1'6

325 28 2 Svstea6t1aeC4] 1= chr((a div 10) + 48) 6326 29 2 Swste••tiae15] 1= chr((a add 10) 1 40) 6327 30 2 Suste••tiae£6] 1=

’1'6

328 31 2 Sustea•tiae17] 1= chr((s div 10) + 48) 6329 32 2 0vstea•t1ae£0] 6= chr((s aod 10) 6 48) 6330 33 2 Sustea•tiae[9] 1=

’1'6

331 34 2 5sstea•t1ae£10] 1='0’

6332 35 2 ENB 6

_ 333 36 1334 36 1 '335 36 1336 36 1

I

84

HAKETAPE Pase 7

Line Stat Level337 36 I .330 36 1 Procedure Setlineßate 6339 36 1340 36 1 const st = '00I0060060’ 6341 36 2 sd ¤ ’0lJAN05' 6342 36 2343 36 2 Benin344 36 2. SH§tGI•tÜIE 6= st 6345 37 2 5es£e•6da£e 6= sd 6346 38 2 Snste•6Ja I=

’' 6

347 39 2 5esbe•6Jb 6= ' ' 6340 40 2 5H§t9I•J0 6¤ '

’6

349 41 2 End 6350 42 1351 42 1352 42 I353 42 1354 42 1355 42 1 Procedure kaiolnitielizelkk I real) 6356 42 1357 42 I Benin350 42 2 uriteln(’Rain Initialize') 6359 43 2 ltl 6= round19060/RR) 6360 44 2 ati 6¤ reund(91464/RR) 6361 45 2 uriteln 6362 46 2 ur1teln(’ ltie ’•ItiII»’ st1= '6st161) 6363 47 2 erlteln 6_ .364 48 2 End 6 „365 49 I366 49 1 4367 49 1360 49 I369 49 1 Procedure GenBist1RR I real) 6370 49 1_ 371 _ 49 1 Const Pl ¤ 3614159265 6372 49 2 T ¤ 3060 6 ( seconds ~ cullectlon tieeI

' 373 49 2 AREA = °•0046 6 { Distroneter Head area· }

374 49 2375 49 2 Var d 1 real 6376 49 2 lan I real 6377 49 2 b 6 inteser 6370 49 2 NSUB0 6 real 6

~379 49 2 dsd I AkRAY[16620J of inteser 6380 49 2 nun 6 real 6

6 301 49 2 v I real 6382 49 2

_ 303 49 2 BEGIN384 49 2 uriteln 6385 50 2 ur1teIn(<D1stro•eter’) 6306 51 2 urlteln 6307 52 2 Ian l= 461 t exv<~0621tIn(RR)) 6‘ 380 53 2 NSUB0 Ia 8000 6309 54 2 FOR b !¤ I to 19 do BEGIN

- 390 56 4 d 6= 06258b 6 06125 6391 57 4 v 6= 9665 ~ 1063 t exr(~066 t d) 6372 58 4 nun I= round(NSUB0 3 0625 3 exe(~la•td)) 6

6

85

HAKETAVE Pase 8

Line Stat Level393 59 4 dsdtbl 1- kound(T K AREA K v I nun) 6394 60 4 END 6

- 395 61 2 dsd[20J 6¤ 0 6376 62 2397 62 2 d1a1code 6¤ ’DA’ 6378 63 2 dla1Ja 6= '

’6

399 64 2 For D 1= 1 te 10 do dla1DrorB1n[hJ 1= dsd[bJ 6400 66 2 d1b1c0de 1= ’D0' 6401 67 2 dlb1Ja 2¤

’' 6

402 68 2 For b 6- 11 to 20 du d1b10rne8inKb—10] 6= dsdßbl 6403 70 2 END 6404 71 1405 71 1406 71 1407 71 1408 71 1 Procedure 6en1ink(kR 6 real) 6409 71 1410 71 1 Lonst CUR = *92eÖ 6411 71 2 808

-3810 6 .

412 71 2 COH ¤ 010159 6413 71 2 Eoß = ~l4414 6414 71 2 XN ¤ 010166 6415 71 2 XD ¤ 'Ä2Ü•Ö 6416 71 2 LNO•

= 101832 6417 71 2 AA ¤ 010155 6418 71 2 BB = 11166 6417 71 2 P1

-3114157265 6

420 71 2 '421 71 2 Var saeaa 1 real 6 \

422 71 2 eesilon 6 real 6423 71 2 len 6 real 6424 71 2 f 6 real 6425 71 2 f2 1 real 6426 71 2 atn 6 real 6427 71 2 isl 1 real 6‘423 71 2 x 6 real 6429 71 2 co 6 real 6

. 430 71 2431 71 2 BEGIN

· 432 71 2 urlteln 6433 /2 2 urite1n('L1nk Data') 6434 73 2 aaeaa 6- 110/2210 6435 74 2 ersiloo 1- 1815 I PI/18010 6436 75 2437 75 2 len 6¤ LNo• « 31152 K 1H(RR/l0•Ö)/[H10 6433 76 2 .f 1- saeaa I 88 I 1n(RR/1010) K cusleesilnn) 6439 77 2 f2 1- (1 ~ exr(~ f K leo)) / f 6440 78 2 atn S- AA I exe(00!1n(RR)) K f2 6441 79 2 co 1- OUR ~ ain 6442 80 2 lsl 6= 33148189 ~ 1710 1 lnlatnl/LN10 6443 81 2 x 1¤ cu + CUD ~ isl 6444 82 2445 82 2 uriteln 6446 83 2 er1te1n(' ¤o= '6co6661•’ x= '6x6661) 6447 84 2 uriteln 6

_ 443 85 2

686

HRLETAPE Pase 9

Line Stat Level449 05 2 lkl.code 1¤

’lK’5

450 36 2 lk1•Ja 1=’

' 5451 07 2 1kl.analos£H1laaCOJ 1= roundllco ~ Buß)/Coü) 5452 08 2 lkl•analo¤(FredCo] 1= roundllcu — 000)/Coü) 5453 U9 2 lkl.anal¤s[DivCoJ 1= rouad((co - Cou)/Cohl 5454 90 2 1kl•anal0a[U11aaXl 1= roundllx — XB)/XM) 5455 91 2 1kl.analos£FredXJ 1= roundltx — XB)/XM) 5456 92 2 lkl•ana1¤¤(OivX] 1= round((x - XB)/XM) 5457 93 2 lk1.analus[UilaaPH3 lv 2047 5458 94 2 lk1.ana101£U11•a[P] 1= 2047 5459 95 2 1kl.anal0s[H11aaüP] 1= 2047 5460 96 2 1k1•aaa1oeCFredPN] 1= 2047 5461 97 2 '

462 97 2 lkl.status[U11•a0tatJ 1= 3 5 V463 90 2 lk1•atatus£Fred3tatJ 1= 3 5464 99 2 lkl.statua[01vStat3 1= 3 5465 100 2 ENO 5466 101 1467 101 1’468 101 1469 101 1 Procedure GenRadar(RR 1 real) 5470 101 1471 101 1 Coast H =‘125.0 5472 101 2 L ¤ 25550 1473 101 2 HZ = 15.0 5474 101 2 P1 = 3114159265 5475 101 2 NI é 64 5476 101 2 Radarß = ~l07•6 5

‘

477 101 2 Radarh ¤ 2•35 5473 101 2479 101 2 Var r 1 real 5480 101 2 zdr 1 real 5401 101 2 z 1 real 5432 101 2 xz 1 real 5”483 101 2 cf 1 real 5434 101 2 c 1 channel 5

· 405 101 2 b 1 inteser 5· 486 101 2 dbz 1 real 5A 407 101 2 LNRR 1 real 5

400 101 2 x 1 real 14119 101 2490 101 „ 2 BEUIN491 101 2 urlteln 5492 102 2 ur11e1a('Radar Uata') 1493 103 2 LNRR 1¤ ln(RR) 5494 104 2 zdr 1= 11045 S exe10•3255 S LNRR) 5495 105 2 eriteln 5496 106 2 ur1telnl' zdr ¤ ’5zdr5611) 5497 107 2 z 1= (230.0 I exr(1•4 t LNRR) 1 220.0 S exr(1.6tLNRR))/2.0I

498 108 2 FOR c 1= 0 Tu 7 DU MEGIH499 110 4 cf 1= zdr/2•0 S (1.0 ~ coslP1S(c—3)/410)) 5500 111 4 dbz 1= 10.0 S lutz)/LN10 ~ vl 5501 112 4 ur1te1n1' dbz1'5c115’) = '5dbz565l) 5

. 502 113 4 rdab£c].cad 1= chr(c+40) 5503 ll4 4 rdab£c]•data[0l 1= roundl(exel54•0SLNl0/1050)-l5•0)/20

•0) 5504 115 4 For b 1= 1 tu 127 Du Beain

I

87

NAKETAPE Pase 10

L1ne Stat Level505 117 6 r 1= BZ 6 8/210 + Ltb 6506 118 6 rd•b(c1•da1aCb] 1= round(1db2 1 5460 —507 119 6 Radarh ~ 20•0tIn(r1/LN10 — 786551/(kadarü/H11)6500 119 6 End 6509 120 4 ENO 6510 121 2511 121 2 nhI•code 1¤

’PH’6

512 122 2 ehl•Ja 6= '’

6513 123 2 rh1•av¤evr lv 2047 6514 124 2 eh1•a2 1¤ 1023 6515 125 2 rh16eI 1¤ 1025 6516 126 2 wh1•scan 1= 0 6517 127 2 rh1•en 1= 0 6518 128 2 vh1•P0 6= 1 6519 129 2 rh1•BZE 1¤ 1 6520 130 2 vh1•BZ0 1= 1 6521 131 2 rh1•NI 1= 64 6 _522 132 2 »h1•01nGz 1= 0 6523 133 2 ENU 6524 134 1525 134 1526 134 1527 134 1520 134 1 Procedure H¤keIr1r(rs 1 Ra1n0auae1 6529 134 1 '530 134 1 BEGIN531 134 2 1F NTr1r

=”0YNEN BEGIN _\

532 136 3 rt1„cnde 1¤ 'R1’ 6533 137 3 rt1•da1• 1= Sss1e••date 1534 138 3 rt1•Jc 6¤ ' ' 6

‘

533 139 3 ENG 6536 140 2 NIrir 1¤ Nirir + 1 6537 141 2 rt1•tr1r£NIr1rl•Ja 1=

’' 6

538 142 2 rt1•tr6r[N1r1r]•Jb 1=’

' 6' 539 143 2 rt1•trir(NTr1rJ•sause $= chr(0rd(ru)+65) 6

. 540 144 2 rt1•1r1r[NJrirJ•t1•e 1= 0sste••t1•e 6 V. 541 145 2 IF Ntrir = 5 FHEN BEGIN542 147 3 F•tRe1u(rt1»1r1 6543 148 3 NTr1v 1= 0 6544 149 3 ENB 6545 150 2 END 6546 151 1547 151 1540 151 1549 151 15110 1261 1551 151 1552 151 1553 151 1 Besin 1 Hain Prusrau J554 151 1555 151 1 LN10 1= In(10•0) 6556 152 1

~ 557 152 1 betiinehate 6 N553 153 1 $tarhTare(dout61ave6tcb) 6. 559 154 1

560 154 1 sec 1¤ 0 6

6

88

NRKETAVE Pase 11

Line 5161 Level561 155 1 rh1•NP1 1¤ 1 1 '562 156 I NIr1r 1= 0 1563 157 1564 157 1 rese1(’kAINRATE•BAT’•rrf) 1565 158 1 FOR kk != 1 T0 15 B0 BEGIN566 160 3 readIn(rr11RR) 1567 161 3 wr11e(’Ra1n Rate ’•rr!511) 1 ·560 162 3569 162 3 Gen11nk(RR) 1570 163 3 0enRadar1RR) 1571 164 3 Gen01s1(RR) 1572 165 3 Rainlnitlalizutßk) 1573 166 3 —574 166 3575 166 3 FOR k 1= 0 T0 269 DO BEGIN576 168 5 FlxT1•e0•1e 1577 169 5 NRa0arPoin1 1= rhI•NPt 1570 170 5579 170 5 sn 1= sec und 111 1500 171 5 IF s• ¤ 0 TNEN NakeTr1»(LocLCRG) 1501 173 5 IF sn ¤ 1 THEN HskeTr1v101vLCRG) 1502 175 5 6• 1= sec nod 611 1583 176 5 IF sn = 0 INEN HakeIriv1Loc00RG) 1504 178 5 IF sn = 1 IHEN NakeTr1n(0Iv5GRG) 1505 100 5506 100 5 IF (aeu nod 60) ¤ 0 IHEN BEGIN507 102 6 d1a•NP1 1= rh1•NP1 1580 103 6 dla•11•e 1= Gesten 1 —\509 104 6 F•1B1s11d1a•1r) 1590 105 6 dIb•NP1 1= NRadarP¤1n1 1591 106 6 dlb•11•e 1= Ssstsn 1592 107 6 F•1B1s1(d1h•1r) 1593 108 6 ENG 1594 109 5

„ 595 109 5 IF k ¤ 0 IHEN BEGIN rhI•scan 2= 0 1 vhI•»n 1= 0 1 ENB 1

596 194 5 I1 k = 31 INEN BEGIN vhl•scan 1= 1 1 whI„rn 2= 0 1 E· ND 1‘

597 199 5 IF k ¤ 71 IHEN »hI•scan 1= 5 1. 590 201 5 IF k = 01 TMEN BEGIN rh1•scan 2= 2 1 vhI•wn 1= 0 1 E

ND 1599 206 5 IF k = 131 IHEN BEGIN rhI•scan §= 3 1 shI•rn 1= 0 1 E

NB 1600 211 5 IF k = 151 INEH rhI•scan 1= 5 1601 213 5 IF k ¤ 156 THEN BEGIN rh1•6can 1= 4 1 rN1•rn I= 0 1 E

ND 1 ‘

602 210 5 IF k ¤ 196 INEN vhl•sc¤n 1= 5 1e

603 220 5 IF k ¤ 201 THEN BEGIN rh1•scan 1= 3 1 Ph1„vn I= 0 1 ENB 1

604 225 5 IF k =_221 THEN BEGIN rhI•scan 1= 2 1 rhI•rn 1= 0 1 EN0 1

605 230 5606 230 5 IF (not udd1sec)) and (vhI•scan<>5) IHEN BEGIN607 232 6 Ph1•11•a 1= Svsten 1600 233 6 F•1|*|·|L (vhl 1 tr) 1— 609 234 6 1k1•NP1 1= NRadarPoin1 1610 235 6 IkI•t1•e 1= Sssten 1611 236 6 F•1L1nk(1k1•1r) 1612 237 6 FOR cn 2= 0 IO 7 B0 Fn1k0L(r0•b1cnJ•vdl«RRadarPu1n

1) 1613 239 6 rhI•NP1 1= »hl•NP1 1 1 1614 240 6 ' rh1•»n 1= nh1•¤n 1 1 1615 941 6 END 1

I

89

» ' 1 --·—-

—-- --

-~-.—... ..--—t—•--•«¤•n"""—„^Y1;l

HAKETAPE Pggg jz

Line Stat Level'" 617 242 5 sec I¤ sec + 1 I

618 243 5 END I619 244 3 uriteln I620 245 3 uriteln I621 246 3 uriteln I622 247 3 END I623 248 1624 248 1 TPH•rk I625 249 1 TPHII·k I626 250 1 End •

I

90

REFERENCES

1. VPI&SU Satellite Communications Group(l984), Systematic Investi-gation of Propagation Impairments Using a Dual Polarized Radar, _

Part I: Technical and Management Proposal, Response to RFP, INTEL433.

2. M. I. Skolnik, Introduction to Radar Systems, McGraw-Hill BookCo., New York, New York, 1980: Chapters 1, 13.

3. R. F. Harrington, Time—Harmonic Electromagnetic Fields,McGraw-Hill Book Co., New York, New York, 1961; Chapter 6.

4. M. P. M. Hall, Effects of the Troposphere on RadioCommunication, Peter Peregrinus Ltd., Stevenage, U.K., 1979;Chapter 3.

5. J. H. Andrews,"A Multiple Polarization Plane ZDR Radar Data Ac-quisition System," Thesis, VPI&SU, Blacksburg, VA, July 1983.

6. L. J. Battan, Radar Observation of the Atmosphere, University ofChicago Press, Chicago, Illinois, 1973; Chapter 7.

7. T. Pratt, C.0zbay, C. Friberg, "Canting Angle Measurements UsingMultiple Polarization Radar," Preprints 21st Conf. on RadarMeteor., AMS, Edmonton, Alberta, Canada, Sept. 1983.

8. J. J. Marshall and W. McK. Palmer, "The Distribution of Raindropswith Size," J. Meteorology, Vol. 5, pp. 165-166, 1948.

9. D. Atlas, et. al., "Doppler Radar Characteristics of Precipitationat Vertical Incidence," Univ. of Chicago LAP Tech. Report No.22,May 1971.

10. C. W. Ulbrich and D. Atlas, "Assessment of the Contribution ofDifferential Polarization to Improved Rainfall Measurements,"Radio Science, vol. 19, pp. 49-57, Jan./Feb. 1984.

11. T. A. Seliga, K. Aydin, and H. Direskeneli, "Disdrometer Meas-urements During a Unique Rainfall Event in Central Illinois andTheir lmplication for Differential Reflectivity Radar Observa-tion," Preprints 21st Conf. on Radar Meteor., AMS, Edmonton,Alberta, Canada, Sept. 1983.

12. L. J. lppolito, R. D. Kaul, and R. G. Wallace, Propagation EffectsHandbook for Satellite Systems Design, NASA, Washington, D.C.,June 1983.

References 91

13. W. L. Stutzman and W. K. Dishman, "A Simple Model for the Esti-mation of Rain-Induced Attenuation Along Earth-Space Paths atMillimeter Wavelengths,°° Radio Science, vol. 17, pp. 14-65-1476,Nov./Dec. 1982.

References 92

master of science · these factors have caused a saturation of the standard telecommunications...

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