I’m sure that by now you’ve seen plenty of weather radar images—high resolution digital images of what we might informally call rainfall intensity. I’m also sure you get the basics of radar—microwave pluses are transmitted in known and controllable directions, and echoes from objects such as planes, ships, and rain (and many other types) are received. The objects can be located in space using the known direction of the beam, and by multiplying the speed of light by half the elapsed time between transmission and reception to get range (half because it’s a round trip).
Let’s fill in some details to see what WR66 and WR73 were actually doing, what the PDP-8 interface did, what hardware and software signal processing was done, and what the rainfall intensity in those images you’ve seen actually means. We’ll see that measuring rainfall with radar is not at all like finding planes and ships, and that there’s a big difference between what a radar set can directly measure, what we’re trying to measure, and what we’d actually like to measure.
Unlike planes and ships, raindrops do not reflect microwaves because they are much smaller than the wavelength, 10 cm for WR66 and 5 cm for WR73. Instead the beam wiggles electrons in the drops, which causes a tiny amount of energy to be absorbed as heat and most to be reradiated in all directions, a process called scattering. The scattered energy is not directionally uniform, however—a significant amount, called backscatter, is radiated directly back towards the radar. Scattered power is proportional to the sixth power of the drop diameter, and inversely proportional to the fourth power of the wavelength, according to a formula derived in 1871 by Lord Rayleigh, who used it to explain why the sky is blue.
Frozen water is different. Snow backscatters much less power than raindrops. Hail is very different—hailstone diameter is no longer much smaller than wavelength, ice can act as a lens, and power radiated back to the radar can produce echoes much stronger than even severe rain.
The backscattering of a unit volume of space, called reflectivity and denoted by the symbol Z, is proportional to the sum of the sixth powers of the drop diameters in the space. If we define a reference value Z0 as the reflectivity of a one cubic meter volume containing a one-millimeter raindrop, we get dbZ = 10 log(Z/Z0). We use log ratio because reflectivity has enormous dynamic range, easily five orders of magnitude, and the radar receiver uses a log amplifier. We use decibels because we’re effectively dealing with power ratios. dbZ is what we’re trying to measure, and what the intensity scale in weather radar images actually is.
I say “trying to measure” because the only thing that the radar receiver can directly measure is power. Measured power is a function of:
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transmitted power
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antenna gain—how much power ends up in the desired direction, rather than off to the sides
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reflectivity, i.e. dbZ
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range according to an inverse square law if the volume of rain fills the beam, or inverse fourth power if it does not
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attenuation of power caused by intervening rain absorbing some of the energy
Clearly one must accurately know the transmitted power and antenna properties. Range is easy, and I’ll say more about attenuation below. Speed was meticulous about radar calibration, monitoring transmitted power with a bolometer and periodically measuring antenna gain. I remember going up to a high floor of the old Hancock building in Boston across the river from the Green Building for antenna calibration. We used the old Hancock building because it was tall and you could open the windows. From the radar room the antenna would be moved in various directions, we’d record received power from the open window, and Speed would make a plot showing gain as a function of angle from beam center.
Attenuation is negligible at 10 cm, noticeable at 5 cm, and very significant at 3 cm. Airborne radar generally uses 3 cm because the dish is small enough to fit on the plane, but attenuation means that you can’t see very far into severe weather. At Weather Radar we’d study attenuation by comparing WR66 and WR73 returns when pointing in the same direction, and part of WR73 software signal processing tried to correct for attenuation.
With careful calibration we could get dbZ from measured power, but what we really wanted to measure was rainfall rate, e.g. mm/hour. The contribution to rainfall rate of a raindrop is proportional to drop volume, i.e. third power of diameter, times terminal fall velocity.
Fall velocity is very complex due to aerodynamics—drops deform into little parachute shapes. I remember encountering Speed in the stairwell on the 18th floor sending drops of various sizes down to the ground floor to measure fall velocity. I was surprised that it couldn’t just be computed from basic physics, and maybe it can be with today’s computers, but back then it was strictly empirical. He could determine velocity and drop size using a device called a disdrometer, invented by our Swiss colleagues Jurg Joss and Albert Waldvogel.
Fall velocity is roughly proportional to the diameter of the drop, so that rainfall rate is roughly proportional to the sum of the fourth powers of the drops in a unit volume. Estimating rainfall rate from dbZ requires knowing the drop size distribution, and that’s the main reason the Joss- Waldvogel disdrometer was invented. Before that invention, radar meteorologists used specially treated paper that turned some color (purple?) when wet, leaving marks whose size could be catalogued by, you guessed it, grad students.
Drop size distribution depends on the nature of the storm and where in the world you are. Lots of empirical work has been done over the years to develop generally useful formulas to estimate rainfall rate from dbZ (the R-Z relation). Quite a bit of early (1950s), large disagreements between what was expected from measured distributions and what was measured by radar were due to miscalibration. Some of the best early work on R-Z was done with meticulous care by Polly and Speed.
One more thing to keep in mind—radar waves do not travel in a straight line. The index of refraction of the atmosphere depends on pressure, temperature, and humidity, and therefore changes with altitude. With typical atmospheric conditions a radar beam travels in a circular path whose radius is about 4/3 the radius of the earth. Under unusual conditions the beam can actually curve so much that it strikes the ground at substantial distances, generating ground echoes far from the radar. This is called anomalous propagation. If you’re looking at a radar image and notice patterns that look like the shape of topographic features, for example Cape Cod from a Boston-based radar, that’s anomalous propagation. Storms don’t accidentally look like that.
In addition to unusual atmospheric conditions, echoes can be returned from buildings, mountains, birds, insects, and the like. One was always advised to approach weather radar images with due skepticism of the cause, and Speed was famous for doing so. A strong echo from Mount Monadnock in New Hampshire always appeared on our PPI’s 100 km range ring, and seeing it gave confidence that radar azimuth and timing were correct.
The rainfall reflectivity of a given volume element varies rapidly with time due to various factors. The only way to get a useful measurement of dbZ is to average the signal at every point over a number of transmitted pulses. With very early weather radars, due to the limitations of 1950s electronics, this could only be done one point in space at a time using what was called a pulse integrator. Next came the analog sweep integrator, which used an analog delay line to integrate the signal along all ranges as the antenna moved in azimuth. The result was what was being photographed when I arrived in 1973.
By the early 1970s digital sweep integrators were being deployed. These sampled the signal in small increments called range bins, what today might be called pixels or voxels, and summed in each bin A/D converted samples. Typically 16 or 32 pulses would be summed in hardware and made available to software for further processing.
The Air Force digital integrator we inherited had 100 range bins, with spacing that could be programmed to 0.5, 1.0, or 2.0 nautical miles, equal to 0.93, 1.85, or 3.70 km. The integrator would start those 100 bins after skipping a programmable number of sample periods. It had a relay to choose what the Air Force thought was forward or side radar, and for us was WR66 or WR73. I can’t tell from the source code how many pulses it integrated (I was very naïve about comments), but I’m thinking 16.
At round trip speed of light, 0.5 nmi is 6.17 microsecs. That’s well within the capabilities of available sample-and-hold and successive approximation A/D converters of that era. Flash A/D converters hadn’t been developed yet, but weren’t needed.
Both radars had a 1 degree beam, often called a pencil beam. At 10 cm WR66 needed the 18 foot dish to get a beam that narrow; WR73 at 5 cm needed only 8 feet. During recording the radars would be swept in azimuth a rate of 1 degree per integration period, that is 1 degree per 16 pulses. We used a pulse repetition frequency (PRF) of 250 Hz, so 16 pulses is 64 ms, and the radar would sweep at 15.6 degrees/sec, or 23 seconds per rotation. Double those values for integrating 32 pulses. After a full rotation the radar could be stepped in elevation for 3D coverage. The PDP-8 could control both sweep speed and elevation.
PDP-8 software would dump the integrator to a memory buffer for further processing. When a radar is first selected, a noise level is determined by setting the integrator to 1 nmi samples, skipping 215 sample periods, and averaging the 50 most distant bins. Those 50 bins are beyond the range of any expected echo, partly due to curvature of the earth and partly to the inverse square power law. A noise threshold was established slightly above the measured noise level, and any range bin below this threshold during normal processing would be considered to be no echo.
During normal processing, after noise thresholding the bins would be corrected for the inverse square power law. Since we’re dealing with log power, this was done by simple addition using a memory-resident table. The bins would then be run-length compressed for writing to DECtape. Because most bins have no echo, the compression reduced the storage requirements substantially.
Both radars transmitted a 1 microsecond pulse, called the main bang. WR66 could put out a megawatt for that time, which is 250 watts average power at PRF 250. WR73 could do around 250 kW. The receiver was incredibly sensitive, capable of detecting returns at or below one picowatt. Since the transmitter and receiver shared the antenna and waveguide, the receiver had to be electronically isolated during the main bang to avoid being destroyed.
The integrator that Ken designed for GATE was far more sophisticated. It executed microcode instructions to allow variable-length bins and signal processing beyond just integration. We generally programmed it for 0.25 km bins in close, 0.5 km at mid range, and 1.0 km at far ranges. The bin sizes were set to approximately match the 1 degree beam spreading as a function of range. We experimented with various signal processing methods to distinguish high-variability rain echoes from low-variability ground clutter.
Sometime after I finally left the project n 1980, WR66 was augmented for doppler. This could be done because the klystron is a coherent amplifier, so the phase shift from pulse to pulse is stable and tiny phase shifts can be determined by suitable signal processing. Magnetrons are incoherent, so WR73 couldn’t be used for doppler. It’s fascinating to note that the doppler effect for electromagnetic radiation is caused by relativistic length contraction and time dilatation. You’d think that these effects are negligible at terrestrial speeds, and indeed they are very small, but detectable by electronics. The doppler signal processing was designed by Alan, a brilliant engineer and great colleague of mine in the later years.
Next up the PDP-8/IX. What, why, and how.
