Assistant Secretary of State for Arms Control, Verification and Compliance Rose Gottemoeller, in a speech at Stanford, praised one of my students, Tamara Patton, for her outstanding work on modeling Pakistan’s Khushab Plutonium Production Complex:
I recently learned about some interesting work of a Master’s Candidate at Monterey Institute, Tamara Patton. Patton is focusing her research on the production capacity of Pakistan’s Khushab Plutonium Production Complex. She is using freely accessible geospatial tools to gather and analyze information about the complex’s capacity levels. The really interesting part comes when she takes the open source satellite images of the complex and turns those into 3-D models using a freely available program called Google Sketch-up. This program constructs the models with dimensions that Patton ascertained using tools in Google Earth and basic trigonometry. The model is then placed on the map and textured using observable features. This modeling can be used both as tool of analysis and as a means of clearly visualizing and communicating results.
Tamara is modeling Khushab for her honor’s thesis, using images generously supplied by the GeoEye Foundation. She hasn’t finished yet, but it looks like she will decisively settle the little spat about the size of the second Khushab reactor. (I am strongly encouraging her to submit her final thesis for publication in a peer reviewed journal. It’s one hell of a model.)
Until then, you can see one of Tamara’s early presentations on Using Geospatial Analysis Tools for Nonproliferation Research. Enjoy!
Extra special bonus. At 24:30, you can watch Philipp Bleek eat soup.
I wonder if they could use this software to better evaluate air flow, so to prevent another Stealth Hawk crash, like what happened to Seal Team 6 in Pakistan.
Thanks for the shout-out, Jeffrey. I don’t recall what I was eating, but if soup, it must have been remarkably chewy. More likely some sort of leftover stir fry.
More importantly, Tamara’s doing outstanding work, great to see this getting so much attention here and elsewhere.
In my imagination it was clam chowder. Don’t know why.
I have a few thoughts Jeffrey – or Tamara (assuming that you’re wise enough to read your supervisor’s blog and make suitably nice noises about it!).
At the end of the presentation there was a question from the audience about possible errors in an analysis based on shadows. For what it’s worth I suggest the following for consideration:
1. Errors on the ground. The analysis assumes that a shadow falls onto perfectly horizontal ground, but if the ground is sloping in any way then the shadow will appear elongated or shortened. For a sufficiently long shadow it may be possible to use Google Earth’s terrain height (I don’t know how accurate this is) to measure the vertical height of the shadow’s end compared to its base; and you can then assume a perfect inclined plane between the end and the base. Alternatively there may be some other way of knowing or estimating the slope e.g. if the shadow falls on a bund or a roof of know pitch. Either way, if you’re able to estimate or determine the slope (and the direction of the slope) of the ground on which the shadow falls then correction is easy with some projective geometry. The readiest source for this would be a good book on making sundials, in which case read the pages on calculating where the shadow of the gnomon falls on an inclined plane, or for vertical sundials where the shadow is projected onto a non-south facing wall.
2. Errors of the building. The assumption in all of these calculations is that the building has vertical walls, or that there is at least a section of horizontal roof whose shadow is cast on the ground. If this isn’t the case then you can still do an analysis of an inclined wall by treating it as the gnomon of a sundial.
Another error of the building is, as mentioned in the presentation, the fact that the satellite photo is rarely taken from overhead, and therefore there may be a foreshortening of the “depth” dimensions. This doesn’t affect a height calculation, but it would affect calculation of the building’s horizontal dimensions. I got the impression from the presentation that one of the software tools can automatically correct for this, but if not then it’s just a question of knowing the satellite’s height and the point over which it was (lat and long) when the photo was taken, together with the lat and long of the building, and then using a few cosines to correct the foreshortening.
3. Errors of the astronomy. Here there are lots of opportunities to avoid errors, and all of the below plus many more would be well covered by a good book on astro-navigation:
a) I’d suggest discarding your own measurement of solar azimuth as an input for determining the sun’s altitude and instead use the photograph’s date and time stamp directly in order to get the sun’s altitude and azimuth for the building’s location.
b) The sun’s altitude (as calculated by astronomy software) is based on the centre point of the sun. But the sun isn’t a point source, and the longest part of the shadow is cast by the lower limb, which is about 16′ (the sun’s diameter averages about 32′, but you can look up an exact number if needed) lower in the sky than the centre. This means that a shadow is marginally longer than the sun’s astronomical position would suggest. When the sun is lower in the sky the effect of this error is greater, so it’d be good practice to stick to photos taken when the sun is high, and then to correct for the sun’s diameter.
c) Refraction: The sun always appears to be higher in the sky than it really is because of atmospheric refraction. For astro navigation the rule of thumb is not to take any sights if the object is lower than about 25 – 30 degrees above the horizon because the error can be as large as 0.5 – 1.0 degrees (depending on atmospheric temperature and pressure). Again, then, it would be good practice to stick to photos taken when the sun is high, and to add a refraction correction.
d) If you really want to go to town then you can correct for the fact that the sun isn’t infinitely far away, and hence there is a small parallax error in the projection of the shadow.
4. Errors of Google Earth. There’s an inherent limitation in the resolution of the picture of the shadow in Google Earth, so clearly the analysis cannot be any more accurate than this limiting feature. Since the error is proportionately less for long shadows (one pixel is a smaller percentage of a long shadow) this would seem to argue for using photos when the sun is low. However, 3b and 3c above caution against this. I guess there’s an optimum angle at which the error in the sun position matches the error in the measurement of the shadow, but unless you’ve the authority to direct the National Reconnaisance Office (or Google) on when they should be taking their pictures I guess all you can do is live with what you’ve got and try to calculate the resulting error.
The other possible Google Earth “error” I can think of is the time and position of the satellite when it took its photo. Astronomical software and ephemeris tend to be based on UTC, which is synchronised to atomic time (TAI). But it’s possible that some of the satellite timings are given in GPS time, since GPS time is used so frequently as a synchronising standard for international communications. The difference between TAI / UTC and GPS time is currently 19 seconds. This may not seem much but it makes a lot of difference to foreshortening calculations when a satellite is moving at many 1000s of kph.
Sorry for a long post of pedantry, but I hope you (Tamara) find something useful in this for your thesis. I certainly wish you all the best with it.
Thanks for your detailed and very helpful post, Hairs. A bit of pedantry is exactly what this project needs before I put it out there, and I intend to look into each of the aspects you mentioned.
Thanks especially for your notes on how satellite positioning affects the measurements. I had originally thought orthorectifying the images would improve accuracy, but as you mentioned, the satellite’s position doesn’t seem to affect height calculations as long as you have a full view of the entire shadow. And fortunately, there’s enough variability in the vantage points of publicly available images of the site that I can try to get as close as possible to that “optimum angle” you describe.
Regarding the solar azimuth measurement, I would have liked to use the time stamp to determine this value, but to my knowledge, while Google Earth provides the date of each image, it doesn’t provide the time. This is the reason I developed the “work-around” methodology I discuss in the presentation. I’ve also tried referencing the dated image in Google Earth with the image files available on GeoEye or Digital Globe, but I ran into a wall as there are often multiple image files for each date. Do you happen to know where the time info is available (or do I perhaps just need to go to Google or GeoEye/Digital Globe directly)?
Once you have the date, you can find the original image in the Digital Globe database.
The “optimum angle” is not so much a reference to the satellite as to the height of the sun – you want it to be low enough to give nice long shadows (such that a single pixel of error in measurement becomes insignificant as a fraction of the shadow’s length) but not too low from the point of view of atmospheric refraction or the error related to the diameter of the sun.
With regard to the satellite’s viewing angle, a shadow on flat ground should be foreshortened by the same amount as a building’s roof, so the same technique that can correct for the building’s foreshortening can be used to correct the shadow. For shadows on sloped ground, a correction for the ground’s obliquity and a correction for foreshortening are independent (just like you can correct the foreshortening of a randomly viewed cube independently for length, width and height) so just apply your corrections one by one and they should still be OK.
As for the satellite photo times, I’ve always relied on Allen Thomson posting the times on ACW whenever there’s been something interesting (e.g. box on Euphrates, box in Burma) to analyse! 🙂
By the way, my own experience is that the errors are small compared to the derived height of any significant structure – but if someone wants an error analysis then at least you’ve got some options to put before them.
Thanks for the note on time, Jeffrey.
And yes, sorry I should have said there’s enough variability in both the satellite vantage point and the sun angle/shadow lengths among the images that I can try to find a happy medium. Though finding this “optimum angle” sounds like it could be an interesting research project in itself.
Regarding ground errors, I’m lucky in that the Khushab site seems to be located on very even terrain. The distortions are so slight that when I turned on the “real terrain” information in SketchUp, I didn’t have to adjust the model at all. But of course this is reliant on the accuracy of Google Earth’s terrain data, which as you mentioned merits caution. I will look into the foreshortening issues you noted, and the sundial concept certainly sounds worth checking out. Thanks again!
For those that couldn’t make it, Tamara’s outstanding work was followed by a “cluster bomb” of questions delivered by MIIS students in the audience (conventional weapons verification, prompt global strike and ICBMs, Iran, etc). AS Gottemoeller said to one of them “I’d like to see your analysis on my desk” and she was NOT joking…feeling good.