a) Introduction
b) Calibration
i) Intensity
ii) Azimuth, Elevation and Range
c) Data Logging
i) Interface
ii) Integration
iii) Compression
iv) Position and Time Information
d) Computer Data Conditioning
a) Introduction
The S-Band Alberta Hail Radar has been of prime importance in
understanding the physical nature of hailstorms (see e.g.
Chisholm (1970),
Marwitz and Berry (1971),
Warner (1971),
Barge (1974),
Humphries (1974),
Barge and Bergwall(1975)). More recently,
Goyer (1975a, 1975b) suggested that radar offers some
encouragement in the difficult task of evaluating weather modification
experiments.
However, due to the nature of the radar records, previous analyses of radar data
proceeded extremely slowly. Fortunately, such tedious analysis procedures are
coming
to an end with the availability of computer recorded radar data.
Careful implementation of the new digital data system is of utmost importance, especially in consideration of many sophisticated innovations (hardware and software) necessary for the computer to record data. Investigations were therefore conducted to determine the precision of the data, specifically, the precision of intensity level (reflectivity) recording and precision of range and azimuth records. To carry out this study, the calibration of the radar-computer system and the alignment of the radar antenna were considered crucial. In addition, aII aspects of the computer facility necessary to record the data were investigated. The following sections outline the results of these careful quality control considerations.
b) Calibration
i) Intensity
The philosophy of S-band radar calibration for computer recording
proceeds in a manner similar to calibrations for the analog displays. A known RF
signal
is injected into the radar antenna and recorded on files within the computer
system.
lt is on these files that information is stored to relate digital calibration
data values
to known input power levels.
Raw radar data values are usually compressed by the computer prior to magnetic tape storage; however, this part of the computer system is not used during calibration. Instead, calibration data values are stored on disk as a result of commands introduced by a keyboard operator. A simple block diagram showing components relevant to computer calibration is shown in Fig. 1.
An input calibration signal is injected simultaneously into both pre-amplifiers; it is amplified logarithmically and then range integrated. This aspect of the system is the same during analog or digital calibrations. For the computer calibration the input signal is at least 150 usec in duration. This signal is amplified by video amplifiers before passing to signal conditioners. The signal conditioners adjust voltage levels to ensure proper operation of the analog to digital (A/D) converters.
The analog to digital converter outputs are 8-bit data values; however, averaged radar data are stored as 7-bit values. To prevent overflow of the final 7 - bit value, digital limiters at the output of the converters restrict the range of digital data values from 0 - 255 to 0 - 204. The signal conditioners and video amplifiers prior to the A/D converters are adjusted such that a digital data value of about 202 corresponds to an input signal level of -30 dBm, while a digital data value of about 5 corresponds to -90 dBm. The digital data values between 0 and 204 inclusive are stored by input computer buffers. From these buffers, azimuth integration of information within each range bin is carried out by adding twenty values together (each value corresponds to one radar pulse) and then dividing by 20. Because the maximum value at the input to the azimuth integration section is 204, the maximum calibration value available for storage is 204. Values from zero to 204 are stored on disk as a table of 8-bit information corresponding to the known calibration signals. The azimuth integration is similar to that carried out upon raw radar data with one difference; during logging only ten (rather than 20) raw data values are added and then divided by 16. This means that the maximum raw data value available for storage is 10/16 (204) = 127.5, which can be stored as a 7-bit quantity when truncated. The interpretation of the 7-bit raw data values using the 8-bit calibration table is shown in section d). Although 20 pulses are averaged, and calibration values are averaged over the duration of the calibration pulses (at least 20 range bins in duration equivalent to about 140 u sec), it has been noted that the recorded calibration value is independent of the amount of averaging. This indicates adequate stability of the RF signal generator.
A keyboard operator, interacting with a graphics display, controls the complete calibration. A sequence of events for recording the 8-bit calibration values on disk is as follows:
Resulting from this calibration scheme are two tables stored on disk files: one table for the main radar channel and another table for the orthogonal channel. These tables are for use in interpretation of raw data values stored on magnetic tope. An example of data stored in one of these tables is shown in Table 1, and illustrated in Fig. 2.
Table 1. Eight-bit calibration for 15 July, 1975
Input (-dBm) Orthogonal signal channel Main signal channel
8-bit value 8-bit value
-99.50 0.00 0.00
-90.00 11.56 6.50
-85.00 28.12 23.12
-80.00 44.31 37.37
-75.00 62.31 53.75
-70.00 76.12 69.06
-65.00 93.12 86.44
-60.00 106.31 102.00
-55.00 123.62 118.56
-50.00 139.50 136.81
-45.00 155.75 152.75
-40.00 173.87 172.19
-35.00 187.50 188.00
-30.00 203.50 201.81
-28.00 204.00 203.87
-28.00 204.00 204.00
c) Data Logging
i) Interface
Shown in Fig. 5 are components used to transfer radar data from the A/D
converters directly to the computer's memory (direct memory access, or DMA). The
data transfer is controlled by the end-of-convert (EOC) pulses frorr the A/D
converters, which signify that a 16-bit word of data is ready. Data logging is
initiated
by a program, which once started, proceeds until one complete sweep (currently
147 bins) of data is transferred. At the end of a sweep, the logging program
repeats
the process for the next sweep. Synchronization (so that the first word of data
in an
input buffer corresponds to the first bin of data) is accomplished indirectly.
When
the logging program begins and the data transfer started, the first word to be
transferred could be from any of the bins of a sweep. After one sweep is transferred
(which
could actually be the last part of one sweep and the first part of the next), the
program
takes about 35 micro-seconds to restart the data transfer; consequently some EOC
pulses
are missed if they occur before data transfer is re-initiated. The first word
transferred
would then come from a bin later in the sweep. This "sliding" will continue
until the
last word transferred is the last bin of a sweep. In this case the next EOC
pulse will
not occur until the beginning of the next sweep, over one millisecond later, and
so no
EOC pulses will be missed. The synchronizing process takes about thirty
milliseconds
in the worst case, and since actual integration is begun manually after the
logging
program has started, synchronization will be complete before any data are processed.
The data are presented to the computer by the A/D converters as 16-bit words, with the low-order bytes (eight bits) corresponding to the main polarization component, and the high-order bytes corresponding to the orthogonal polarization component. Shown in Table 2 is an example of a data word. The interface stores these words in an input buffer in computer memory. Since one sweep of data may not be fully processed before the next sweep begins, two input buffers are used alternately.
Table 2. Example of data word
Data word:
A A A A A A A A B B B B B B B B
AAAAAAAA value from orthogonal component
BBBBBBBB value from main component.
Table 3. Example of data word after integration
Data word:
0 AAAAAAA 0 B B B B B B B
AAAAAAA - integrated value of orthogonal component
BBBBBBB - integrated value of main component.
Data of interest are characterized by the main component of the received signal. When this value is zero, it is not necessary to store data from this location. To indicate the discontinuity introduced by removing data, a "pointer" is stored before the first word of a contiguous sequence of non-zero data words. This pointer is a negative number related to the bin number of the data location following the pointer. Pointers can be distinguished from data words since data words are always positive values (sign bit set to zero). An example of data before and after compression is shown in Table 4. For a full ray of data one pointer (just before the first data word) is included. Therefore, it can be seen that this method of compression can never result in more than one extra word to be stored for each ray, since a pointer is never added unless at least one data word is removed.
Table 4. Example of data compression
Before After
Word I A -147 Pointer (-l 47 + 148 1)
2 B A Data from bin I
3 c B 2
4 0 c 3
5 0 -140 Pointer (- 1 40 + 148 8)
6 0 D Data from bin 8
7 0 E 9
8 D F 10
9 E
10 F
The compression procedure is actually performed during the
summation
of the last sweep of each ray, and the compressed rays are stored in a large
(currently
1.5K words) buffer, called the output buffer. Data in this output buffer are
written
to tape when the buffer is almost filled. Since a buffer may not be completely
filled,
the end of valid data in the buffer is signified by a special word, called the
end
flag. Because transfer of the data to tape may not be completed before new data
is
ready to be stored in the buffer, two output buffers are used alternately.
iv) Position and Time Information
A "header" is placed at the beginning of each compressed ray of data in
the output buffer. This header is four words long, and contains the antenna
position
and the time of day appropriate for the end of the first sweep of data which
comprises
the ray. The header shown in the ray of Table 5 is always stored, regardless of
the
amount of data in the compressed ray.
Table 5. Example of a ray of data
Bits Meaning
High Low
Word 1 1OAAAAAAAAAAAAAA Antenna Azimuth
Word 2 10EEEEEEEEEEEEEE Antenna Elevation
Word 3 0LLLLLLLLLLLLLLL Low word of time
Word 4 0HHHHHHHHHHHHHHH High word of time
Word 5 1111111101101101 Pointer (-147 + 148 = 1)
Word 6 0DDDDDDD0DDDDDDD Data from bin 1
The antenna positions are stored as 14-bit numbers in the format presented by the synchro-to-digital converters. The two remaining bits are set by the hardware as a one and a zero in the sign bit and the next highest bit respectively. Thus, these two words will always appear as very large negative numbers, and so a ray of data can be easily isolated on the data tape.
The next two words in the header contain the time of day expressed Os
two 15-bit unsigned numbers representing the number of "ticks" (60 ticks per
second)
since midnight.
A ray of data is shown in Fig. 7 as an A-scope display. Power
levels
in dBm together with raw data values are shown. The power levels and raw data
values
are related according to Fig. 6.
Because data are also collected by an analog system and recorded on
film,
lt is possible to compare the PPI and film data sources. The crosses on Fig. 7
are main
signal power levels taken from the film data. Clearly, the agreement between the
computer recorded values and the film recorded values is good.
The reduction of radar data from the orthogonal signal channel proceeds
in the same manner. Fig. 8 is a plot of 7-bit calibration information for the
orthogonal signal channel . The similarity between Fig. 6 and Fig. 8 demonstrates the
similarity between the two radar signal channels.
lt is well known that the Circular Depolarization Ratio (CDR)
represents
the difference between the power levels of the main component and the orthogonal
component. The CDR is displayed directly on the cathode ray tube as a PPI
display.
For comparison, the difference in power levels obtained from the raw computer
data values, using Figs. 6 and 8 was calculated. This calculation was actually
performed in conjunction with a conversion of main signal power level to
equivalent
radar reflectivity values. A ray of data showing-the calculated CDR is shown in
Fig. 9. The CDR values recorded from film are shown by the crosses.
More extensive calculations are required to compute the equivalent
radar
reflectivity (Ze) from the raw data values. Firstly, the raw data values are
converted
to power levels according to Fig. 6. Using the radar equation, calculations of
the
equivalent radar reflectivity factor can proceed. The radar equation can be
expressed as
If I is the intensity of precipitation being measured, and log
amplifier
signals are averaged, P, a log 1; however, measurements related to log Tare
desired.
Austin and Schaffner (1970) investigated the effect digital conversion
has on the determination of I,, the true average power, or log I,, received from
a
precipitation Smith (1964) were used to generate the samples. The 10 numbers in each
sample were averaged before and after quantization and compared for quantization
widths of 2, 4 and 6 dB. If log I is the average computed before quantization
and
log-I, the average computed after quantization then the difference is found to a
function of the quantization width. This result, shown in Fig. 11, is seen to
be
virtually the same relationship found by Austin & Schaffner except they were
comparing
the true average power with the quantized average. The quantization width for
the
Alberta system is about .5 dB which means that a correction of .25 dB must be
applied.
If Tog-l,, is the overage of k independent intensity levels then
according
to Smith the most probable value of IO Tog-1k Sh'ftS from IO log I,, toward 1 0
log I 2.51 dB
as k increases. For the Alberta S-band radar there are 4 independent samples per
range bin and 1O pulses per degree of azimuth. -The computer averages IO
pulses for
each range bin which means 40 samples of the return power are averaged. Not all
the samples are independent, however, since decorrelation in azimuth occurs over
one beam-width. Pulse to pulse frequency shifts of the magnetron and shuffling
of
precipitation also leads to further decorrelation. Thus the number of
independent
samples contributing to each computer overage lies between 8 and 40. When k is
about 16 the most probable value of Tog 1 k is about 10 log I,, - 2.5 dB, which
is virtually
invariant for values of k >8. The effect of quantization yields a final
correction of
2.75 dB.
Therefore, Ze a 'P + 2.75
Extreme caution must be exercised in use of equation (1).
Other radars
may have different electrical parameters such as antenna gain and
transmit-receive
waveguide attenuations.
d) Computer Data Conditioning
It was indicated in section b) that calibration information necessary
to
reduce recorded raw data is initially stored on the computer's disk.
These 8-bit
data form a table which compare pulse to pulse averaged calibration values to
input
signal levels. Since the raw radar data are azimuth averaged and stored as 7-bit
values, efficient reduction of raw data must begin by transforming the 8-bit
calibration
information into a table of calibration information corresponding to 7-bits.
Fig. 6 is
a typical plot of 7-bit calibration information. These 7-bit calibration
values
are then applied to the raw radar data such that the raw data can be reduced
to power
values in dBm.
Z, (d BZ) = C (d BC) + 20 1 og (r/ I km) + P, (d Bm)
where C = + Z,, (dBZ) - P., (dBm)
According to Smith (unpublished manuscript)
Z. - 1024 (C) In 2 PRF I (I km)' I mw
7 1 mw f@ G@ 9 I K 1
for G = 43.3 d B = 104-
0
and 0 = 1.15 2 x 10-2 radians
z& - (I 024) (3) (I 0") 693) (480) 1 O' m'
(31) (8. 29) (1 01") (I . 82) (i 05) .93
2.35 x 1012 mm
and C = +1 23.7 - P.,
Nominally P., +54dBm
and Z,, (d BZ) +69. 7 + 20 1 og r (km) + 'P, (d Bm)
Acknowledgements
Many thanks are due to Ms. S. L. Olson for her diIigence in
preparation
of the diagrams.
Footnotes
Because of the range integrator characteristics, the position of the calibration
pulse
in range can determine the amplitude of the first two and last two range bins at
the range integrator output. This occurs because of the finite rise time of the
calibration pulse. In the calibration pulse averaging, the calibration program
eliminates
the first and the last of the bins from the pulse. Therefore the pulse must be
positioned
so only the first and last bins of the range integrator output are affected by
the
calibration pulse rise time.
Pulse to pulse integration is performed upon each range averaged bin of data. A
ray of data re presents up to 1 50 range bi ns averaged over X pulses. For the
Alberta Hail Radar X usually equals 10.
The volume is defined by the cross section of the beam and one-half of the pulse
length.
References