Friday April 17, 2015

This class is still a work in progress.  There is a little bit of discussion that will be added at the very end of the notes.

In this lecture we'll have a look at examples of ground-based measurements of the optical emissions produced by lightning and what information may be extracted from these data. 

Lightning is a pretty bright light source and a simple photodiode can, in many cases, be used to detect lightning optical signals. 



A typical filter and silicon photodiode (the diode, at right, is a PIN 10 DF diode manufactured by United Detector Technology).  This particular photodiode has an active (sensing) area of 1.0 cm2.  It can also be fitted with a blue filter (at left in the photograph above) which results in fairly flat wavelength response across the visible and part of the near IR portions of the spectrum (a representative spectral response curve is shown below).


Photodiodes like this are often operated in the photoconductive mode (the diode produces a current that is proportional to the intensity of the incident light signal) and are back biased.  This results in faster time response.  This is explained further in the next few figures.



A PIN photodiode (and this is my very incomplete and perhaps erroneous understanding of them) consists of a "p-doped" region, a middle intrinsic (undoped) region, and an "n-doped" region.  The term "doping" means impurities have been added to a semiconductor material (silicon).  An n-doping material (such as phosphorus) effectively adds negative polarity charge carriers, the p-doping material (boron or aluminum) positive charge carriers.  Charge diffuses from the doped regions across the intrinsic region in the middle.  Movement of the charge carriers creates an electric field which, once it grows to sufficient strength, limits further diffusion and further charge buildup.

Photons which strike the intrinsic region of the photodiode produce photo ions which then move under the influence of the E field.  Back biasing the photodiode increases the size of the intrinsic region and accelerates the motion of the photo ions.

We'll do a quick calculation to estimate a typical lightning photo current, ip.  We'll assume a sensing area of 1.0 cm2, a responsivity of 0.2 A/W and an incident irradiance of 1.6 W/m2 (more about this value later in the lecture notes).


A current this small is readily converted to a measurable voltage using one of the basic op-amp (operational amplifier) circuits below.  A photodiode will detect the transient signal from lightning as well as the daylight background signal.  A capacitor would often be inserted between the photodiode and the negative input to the op amp to block the slowly varying daylight signal.


The two circuits are identical except for the orientation of the photodiode and the polarity of the biasing voltage.  The orientation in the left figure gives a positive-going output signal.  The right circuit produces a negative polarity output.  A feedback resistance of 50 kΩ and a photo current of 32 μA would produce an output voltage of 1.6 volts.

Now we'll look at some actual data.  Most of the results will come from Guo and Krider (1982)  which used a fairly straightforward sensor design.



In this case a silicon photodiode was used together with a few optical components to produce a system with 360 degree azimuthal response and fairly flat angular response between 0 and about 25 degrees elevation angle.  This field of view would be sufficient to see the entire lightning channel between the ground and cloud base unless the lightning was close to the observing location.

The next 5 figures appeared in the Wednesday Apr. 15 class.




Examples of recorded fast electric fields (E, shaded blue) and associated optical signals (O, highlighted in yellow).  This was a four stroke cloud-to-ground discharge that occurred at 13 km range.  The first return stroke is shown at the bottom of the figure.  The first 50 μs or so of the record is the stepped leader.  This is followed by an abrupt rise to peak.  Notice that the E field signal is still increasing in amplitude at the end of the record.  This indicates some of the electrostatic field component is present which is typical of a return stroke field recorded at a range of about 10 km.   These waveforms were photographed on moving film.  The dark black timing marks were from an LED that would flash on and off to code the absolute time onto the film.

Here is some more recent data (Quick and Krider, 2013) recorded with modern waveform digitizer (the darker curve is the optical signal, the fainter trace is the fast electric field). 



Signals from a first return stroke, subsequent return strokes (NGC is a channel with a new ground contact point, PEC a pre-existing channel), and a cloud discharge are shown.




A typical return stroke optical signal.  We can use a measurement of the peak optical signal amplitude (in volts) to determine the peak irradiance, Lp (in W/m2).  Then if the range to the discharge is known we can estimate the peak optical power output, P (in Watts) from the return stroke.



We treat the lightning discharge as a point source and assume the optical power output during the strike will expand evenly outward in a sphere.  We measure the peak irradiance, Lp, a distance D from the source (W/m2 on the surface of the expanding sphere).  So to estimate P we simply multiply the measured values of Lp by the area of the sphere.


Here's a cumulative distribution of peak optical power estimates.  50% of 1st return strokes have a peak optical power output of about 2 x 109 Watts or more (the other 50% have a peak power of 2 x 109 Watts or less.  Peak power emitted by subsequent strokes is almost a factor of 10 less. 

Peak irradiance from a return stroke at 10 km range would be about



You may remember this is the value used to compute an expected photodiode output current. 

 Next we will consider the linear portion of the rising front on a lightning optical waveform.

We will assume that this is produced by the geometric growth of the return stroke channel as it propagates from the ground up toward the bottom of the cloud (the signal amplitude grows as the channel gets taller).  We'll also assume the channel is straight and vertical and that the return stroke velocity is constant.

Optical emissions from the length of the channel between the ground and H(t) determine the amplitude of the signal observed at distance D at time t.


The equation is pretty general at this point, we allow l(z,t) to vary with z and t.


You can think of the channel as being a string of point sources.  The power emitted by each point source is l(z,t-r/c) dz.  Isotropic means the intensity of the emitted lightning does not depend on direction.  We divide the light emitted by each segment dz by the area of a sphere 4πr2  and integrate over the length of the channel to determine the irradiance at distance D.

We'll make a couple of simplifying assumptions

Then the integral becomes

we'll replace H(t) with a time multiplied by velocity term


Here you can clearly see that L(t), measured at distance D would increase linearly with time.
Next we differentiate this expression


dL(t)/dt is just the slope of the linear portion of the optical signal waveform.  We assume the distance to the discharge is known and assume a value for the return stroke velocity.  This provides us with an estimate of the mean radiance per unit length for a return stroke discharge.



Actual measurements of mean radiance per unit length.  A return stroke velocity of 8 x 107 m/s was assumed.  Discharges were 5 to 35 km from the measuring site.

Final Exam Question
I promised I would give you one of the questions on this semester's Final Exam early.  This after having said next Monday's homework assignment would be the last of the semester and later remembering there was at least one more question that I wanted to give you.


Assume that a return stroke is propagating upward at a constant speed v.  Show that the height of the visible channel, H(t), that an observer a distance R away would see at time t is



This is Eqn. (3) in Guo and Krider (1982).

Next we will look at a couple of examples of a completely different type of ground based optical measurement.  The figure below at left is from adapted from Jordan and Uman (1983) and shows how light signals coming from narrow vertical segments of a lightning channel from a natural subsequent return stroke might vary with altitude.  The signals were recorded on film with a high speed streaking camera like has been used to measure return stroke velocity.  A example of a streaking photograph from an entirely different event is shown at right (photo credit: Dr. Vince Idone, State Univ. of NY at Albany).  The image recorded on film was then digitized.  The figure at left actually shows film density versus altitude (the film density values were roughly proportional to the logarithm of light intensity).






The streaking camera shutter was triggered (opened) by the first return in a flash and remained open for 0.5 seconds.  Only subsequent stroke signals were captured on film

The downward propagating dart leader can be seen clearly on the 37 m and 78 m records.  The upward propagating return stroke can be see on all 9 records.  Jordan and Uman reported that the amplitude of the return stroke fast initial peak decays exponentially with altitude with a decay constant of 0.6 to 0.8 km.  The relatively constant amplitude portion of the signal following the fast peak is relatively constant between the ground and cloud base.

Changing light signals like these suggest that the return stroke current waveform also probably changes shape with increasing altitude (though Jordan and Uman suggest that the current decays much more slowly than the light signals).  You may remember that the transmission line model assumes that the return stroke current remains constant with increasing altitude. 

Wang et al. (1995) describe a more modern system that they first used to study lightning striking the CN Tower in Toronto (the 3rd tallest building in the world).

(source of this image)

Their sensor is shown below at right. 


Eight rectangular photodiodes (1 mm x 24 mm) are mounted in the focal plane of a camera lens.  The photodiode signals are amplified and connected to a multi-channel 8 bit digitizer ( 0.2 us sample interval and 200 us duration record with 10 ns synchronization between signals).  Waveforms were stored on a computer.  The sensor was placed on the roof of a building located 1.8 km away from the CN Tower.  A roughly 200 m x 200 m area above the tower was imaged (the lowest channel, ch#8, was actually positioned below the top of the top because lightning sometimes strikes below the tallest point on the tower).

An example of data from a normal dart leader - subsequent return stroke discharge are shown below (adapted from the Wang et al. paper).

Note that as you move from left to right (increasing time) you first see a signal from ch#1 (orange), the upper most channel.  This is followed by signals from channels #2 - #6 in order.  We are seeing the dart leader moving downward from the top of the viewing area to the bottom.  Beginning at around 32 microseconds the signals rise very rapidly and go off scale.  The is the faster upward propagating subsequent return stroke.  While there is much less separation between the signals, the return stroke signal from ch#7 appears first, followed by channels #6 - #1 in reverse numerical order.

One last, very nice example from Olsen et al. (2004).



You can clearly see the downward propagating dart leader on the top 3 records followed by an upward propagating subsequent stroke.  This the first subsequent stroke in a 7 stroke triggered lightning flash.  The stroke had a peak current of 28 kA.  The 4 channel photodiode sensor was about 300 m from the strike point; the light signals above come from roughly a 1 m vertical segment of the channel.  Note the significant change in the shape of the return stroke front in just the first 170 m above the strike point.

Measurable time delays from signals from know altitudes can be used to determine both leader and return stroke velocities.   Some additional discussion of that will be added.



"The Optical and Radiation Field Signatures Produced by Lightning Return Strokes," C. Guo and E.P. Krider, J. Geophys. Res., 87, 8913-8922, 1982

"Variation in Light Intensity with Height and Time From Subsequent Lightning Return Strokes," D.M. Jordan and M.A. Uman, J. Geophys. Res., 88, 6555-6562, 1983.

"Luminous propagation of lightning attachment to CN tower," D. Wang, I. Kawasaki, K. Yamamoto and K. Matsuura, J. Geophy. Res., 100, 11661-11667, 1995.

"Observed one-dimensional return stroke propagation speeds in the bottom 170 m of a rocket-triggered lightning channel," R.C. Olsen III, D.M. Jordan, V.A. Rakov, M.A. Uman and N. Grimes, Geophys. Res. Lett., 31, L16107, 2004.