Using the rolling shutter effect to time lightning leaders

2020 July 07

Here is an image I captured during a lightning storm just after midnight in June:

The horizontal banding is due to the rolling shutter effect. The camera’s sensor recorded the top portion of the image during the ambient night-time conditions, while the bottom was recorded during a lightning strike (the bolt is not within field of view). The blue and green pixels were added as part of a processing step to identify lightning flashes.

While I have many similar images exhibiting horizontal banding, this is the only one featuring three levels of illumination. I suspect, though I don’t know, that the section of intermediate illumination is due to light from a lightning leader, which is the slower, downward, branching, initial phase of a lightning bolt. When one of the branches of the stepped leader touches the ground, the much faster and brighter return bolt happens, which can be seen at the bottom of that frame and for the top half of the next frame of the video:

Therefore, if I know the speed of the data readout of the camera’s sensor, I can calculate how long the stepped leader lasted. As I could not find technical data on the CMOS sensor of the camera (or of any consumer-grade camera), I decided to measure the readout speed experimentally. By having the camera record video while it is placed on its side – not the bottom – and a rectangular object is dropped through its field of view, it is possible to induce the rolling shutter effect and have the rectangle appear skewed in the recording.

Comparing consecutive frames of the video gives the velocity of the object in units of pixels per frame. One side of the rectangle appears closer to the ground because it is recorded after the other side of the rectangle; the height difference gives the number of pixels the object traveled in the time it took for the sensor to record the width of the object. Scaling up according to the fraction of the width of the screen filled by the object and dividing by the object’s velocity and by the fps of the recording gives the time it takes to readout a single frame, which I estimated to be somewhat more than 10 ms. This is consistent with the upper-limit of 17 ms readout as the camera is capable of recording at 60 fps, and readout time does not depend on frame rate (though for some cameras it may depend on resolution of the video).

Using a value of about 12 ms for the readout time of the sensor, it appears that the stepped leader lasted for about 4 ms: that is, it took 4 ms for one of the branches to navigate from the cloud to the ground. (By comparing with the next frame it seems the return bolt persisted for 31 ms. I’ve found that cloud-to-cloud lightning often persists for multiple frames, so I believe this bolt was cloud-to-ground.) Text sources online say that a typical time is 10 - 20 ms, and the two timed videos I was able to find show a stepped leader taking 14 ms and 0.6 ms, so my timing is at least loosely consistent.

Based on this timing, it seems unlikely that this could be two unrelated bolts: over 20 minutes of video, to see two bolts within 4 ms would take on the order of \sqrt{20 \text{ minutes} / 4 \text{ ms}} \approx 550 lightning strikes, which is far more than I recorded in this time. I also find it unlikely that it represents two return bolts of the same strike. I’ve recorded secondary return bolts to be dimmer and 50 - 150 ms after the initial return bolt, consistent with what I’ve read online; however this doesn’t rule out the possibility of a very fast return bolt or some other scenario entirely.

Because the vertical span illuminated by the lightning leader is on the order of the same height or smaller than the typical cloud-to-ground distance seen by my camera from this vantage point, if the timing of this lightning leader is typical then it would be impossible for my camera to capture a downward-moving lightning leader in motion. The lightning leader moves from the cloud to the ground faster than the camera’s sensor can readout the same span. If I wanted to capture a leader in motion I would need to place the camera upside-down, so that as the leader is going cloud-to-ground the sensor is going ground-to-cloud, and they could meet halfway. Unfortunately the top of my camera is not flat so this is impractical.

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