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Alberta Hail Radar - Computer Considerations
Alberta Hail Radar - Computer Considerations
B. L. Barge, R. G. Humphries and M. R. Johnson
Contents
Contents
ii) Azimuth, Elevation and Range
iv) Position and Time Information
a) Introduction
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
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:
calibration program made operative in the computer
calibration program asks that the signal generator be set to inject a power level of -90 dBm into the antenna
signal generator is hand-set to appropriate power level
calibration controller examines pulse quality
calibration program averages pulse, and stores value in table
steps 3 - 5 are repeated in 5 d B steps to -30 d Bm
calibration controller stores table of digital calibration levels and their corresponding input power levels on disk.
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 tape. 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
ii) Azimuth, Elevation and Range
Azimuth and elevation data are transmitted to the computer by synchros and synchro to digital converters. The output voltage signals from the synchros are related to the direction of the radar antenna. The angle information is converted into 14 bit digital form by the synchro to digital converters. The corresponding resolution of this information is 1.3 minutes of arc. After a first sweep of radar data is collected by the computer, the azimuth, elevation and time (resolved to 1/60 sec.) are recorded. This information is assigned to the corresponding ray. The position and time data are therefore valid for the end of the first sweep in each ray.
Azimuth
The S-band antenna was aligned in azimuth by transmitting an RF signal towards the radar from a distant location of known azimuth. After the radar antenna was positioned to maximize the received signal, the azimuth synchro was rotated to obtain the appropriate indications on the PPI displays. The angle calibration can be checked in real time and during analysis by observing the echo from a tower located at 200.7 degrees azimuth and 21.9 statute miles in range. The tower is indicated by a dot on the PPI in Fig. 3 and on the computer output in Fig. 4.
Elevation
The elevation calibration was roughly determined by mechanically leveling the antenna with the aid of a machinist's level. A remote transmitter located on top of a 90 ft mast located 1300 ft from the radar was also used for precise elevation calibration. When the S-band received the maximum signal from the remote transmitter the elevation angle was 2.1 degrees. The elevation synchro was adjusted to output the appropriate angle information on the PPI displays and into the computer when the radar was pointed at the remote transmitter. At present there is no target suitable for checking the elevation calibration in real time or during analysis.
Range
For each radar pulse the return signal is logarithmically detected and then integrated in 7 usec intervals or bins which correspond to 1.05 km in range. The computer determines the range of an echo by counting bins. This procedure will be described in detail in the next section describing the compression of radar data. Again the tower at 200.7 degrees azimuth and 21.9 statute miles in range can be used to verify that the range information is correct.
c) Data Logging
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.
ii) Integration
Integration is performed on each range bin individually, and separately for each component of the data. Data from each range bin of a number of sweeps (currently 10) is summed. Since the sum of several eight-bit values can become too large to represent with eight bits, the intermediate sums are stored as 16-bit words. Thus, one buffer is required for each component being integrated, and these buffers are called intermediate sum buffers. For each bin the most significant seven bits of the two components are combined into a 16-bit word.
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.
iii) Compression
Since much of the volume scanned by the radar provides no echoes of interest, not all of the possible data locations presented to the computer need to be stored on magnetic tape. To reduce the amount of data stored, data compression is applied to the intermediate sum buffers when integration is completed.
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.
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.
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
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)
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 (1970) 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.
Acknowledgements
Acknowledgements
Many thanks are due to Ms. S. L. Olson for her diligence in preparation of the diagrams.
Footnotes
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
Austin, P.M., and M.R. Schaffner, 1970:
Computations and experiments relevant to digital processing of weather radar echoes. Preprints of Papers, Fourteenth Radar Meteor. Conf. , Tucson. Amer. Meteor. Soc. 375-380.
Barge, B. L., 1974:
Polarization measurements of precipitation backscatter in Alberta. J. Rech. Atmos., 8, 1-2, 163-173.
________, and F. Bergwall, 1975:
Hail growth processes suggested by polarization diversity radar data. Progress Report, Current Research on Alberta Hailstorms, 1974 - 1975. Atmospheric Sciences Division, Alberta Research Council. 26-52.
Chisholm, A.J., 1970:
Alberta hailstorms: A radar study and model. Unpublished Ph.D. thesis, Dept. of Meteorology, McGill University, Montreal. 237 pp.
Goyer, G. G. , 1975a:
Overall strategy for the evaluation of a hail suppression experiment. J. Rech. Atmos. 9, 49-57.
Goyer, G. G. , 1975b:
Time-integrated radar echo tops as a measure of cloud seeding effects. J. Appi. Meteor., 14, 7, 1362-1365.
Humphries, R. G., 1974:
Observations and calculations of depolarization effects at 3 GHz due to precipitation. J. Rech. Atmos., 8, 1-2, 155-161.
Marwitz, J.D., and E.X. Berry, 1971:
The airflow within the weak echo region of an Alberta hailstorm. J. Appi. Meteor., 10, 487-492.
Smith, P. L., 1964:
Interpretation of the fluctuating echo from randomly distributed scatterers: part 3. Sci. Rept. MW-39. Stormy Weather Group, McGill University, Montreal. 70 pp.
Warner, C., 1971:
Visual and radar aspects of large convective storms. Unpublished Ph.D. thesis. McGill University, Montreal, 116 pp.
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