Something special happened in the garden on 26 September, 2015.. A rare vagrant showed up to pose, difficultly, for its photo well out of its normal range from South America to Central Mexico. I was out on my back, (quite literally, I was hawk watching) when I noticed an unusual bird land high in our live oak. Thinking there was a new garden visitor, I checked it out with the binocs. I realized it was something new for the garden but otherwise apparently just another bird. I lifted my camera and squeezed off a few shots, made especially difficult because I was lying down and the bird was behind twigs and small branches. It didn't help that I was hand pointing and manually focusing at that. When I checked the view screen and determined some shots ought to be good enough for an ID I stopped. Little did I know, and now regret, that I didn't make more effort to get into a better position. Oh well...
Later while trying to ID the bird I was frustrated and unable to find anything like it in any of my guidebooks. Closest I could come was a Sulphur-bellied apparently way out of range. A visit to Whatbird gave better advice and the possibility of Piratic or Variegated and the need to take this to the pros. Emails to TOC and TRBA fed flames of excitement as the news of a rare sighting became known.
As I write this note, the status is a probable Piratic according to the ABA. No word from TOC but with their more stringent reporting requirements I imagine it will remain a toss between Piratic and Variegated. Seems my photos were not detailed enough and I did not get a view of the back or wings. As the two bird possibilities have rather different sizes, (6 inches for Piratic versus 7 1/4 for Variegated) I have made a rather detailed analysis of the size of the bird in the photo, see below. Updates will be made here when finalized. Personally, I feel certain that the Piratic as the most reasonable choice (again, see my size analysis below). According to the TOC checklist only 5 confirmed sightings of this bird have been made previously in Tx. What fun!
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Given the optics I was using, it is possible to calculate the field of view of the lens from its focal length and sensor size. Needed information for this also includes a good knowledge of the distance to the bird and the pixel length of the bird from tip of the bill to tail.
In order to collect the needed data, I went back to my observing location, removed the tele-extender (assuming that Nikon lenses are properly calibrated to Nikon cameras) and re-focused on the branch where the bird had been. With the correct focus I made a photo of the lens range-finder to document the correct range. I also tape measured the horizontal distance to the foot of the tree below the area the bird had sat (to my best estimate). Plugging the data into a spreadsheet allowed me to calculate the birds' length at 5.9 inches with a correction for foreshortening.
The data above suggests some level of uncertainty and I stressed over this for some time. In particular the distance measurements, extent of foreshortening, and to a lesser extent the bird length. Camera optics are given from the manufacturer and I assume are precise. For the range finder, I took the photo and imposed fine 1-meter divisions to help with a proper estimate. Even so, I imagine the distance estimate has a plus or minus 1-meter resolution. The taped measure to the tree is better, but here again there is a plus or minus 1 to 2 feet error as to where exactly the spot is directly below the bird. Finally, bird lengths are measured with the bird on its back in a lab and my bird was in a natural pose. Mercifully one photo showed the bird more or less with its bill outstretched. I assume the length could be up to 5% greater than the pixel length, but obviously no shorter.
Foreshortening results from the lookup angle to the bird. Were the bird sitting normal to my line of sight, the angle would give the proper foreshortening. As the bird was turned somewhat towards me, the foreshortening may be less. Had the bird been turned directly parallel to my line of sight and tilted similarly to my lookup angle then there would be no foreshortening. Foreshortening uncertainty thus runs the range from none to the maximum angle calculated.
I also look at the lookup angle as a test for my distance uncertainty ranges. I judge from my observing chair that the lookup angle is about 35 degrees or so. Calculated angles that vary dramatically are improbable, and in any case, the distance to the bird can never be shorter than the horizontal distance to the tree. My uncertainty ranges result in possible lookup angles between 22 to 41 degrees which seem reasonable.
Finally, I implemented a simple Monte-Carlo uncertainty analysis in the spreadsheet to handle the various uncertainties explained above. The analysis used 2000 iterations through the uncertainty ranges randomly selected with a flat distribution. This process gives results for every possible combination of input with a probability distribution for the results obtained.
The graphic below summarizes my analysis. Included is a histogram of the resulting length calculations and the probability distribution curve. Imposed on the graph I have indicated the range in published bird length for the Piratic and Variegated flycatchers. It is clear that, given my estimates in uncertainty, the Piratic is indicated as the flycatcher in question. There is a 98% probability that the bird photographed is SMALLER than the smallest published size of a Variegated. The Piratic size range crosses the 50 percentile in my analysis.