Aircraft-specific truncation to address different blind spots

[James Hodson]

Good morning,

I am working on analysis of an aerial transect distance-sampling survey for moose in the Northwest Territories.  I was hoping to get some feedback on the approach I used to deal with different blind spots between aircraft to see if it makes sense or violates any model assumptions. The survey used two different aircraft, one was a Cessna 180 and the other was a Found Bush Hawk.  The Bush Hawk has bubble windows on all four doors which extend down almost to the floor.  When I plotted our detection distances by aircraft I found that the Bush Hawk didn't really have a blind spot under the plane, whereas the Cessna 180 seemed to have blind spot out to 150 m:   

 

To address this I filtered out observations <150 m from the Cessna (FUGR).  I also filtered out observations >650 m for the Bush Hawk, and greater than 800 m for the Cessna.  This was to ensure that I was using observations from an equal strip width for each plane (650 m wide).  I then subtracted 150 m from the remaining Cessna observation detection distances.  This approach retained 139 of the 151 original moose observations.  It yielded the following adjusted histogram (each aircraft separately, and the combined histogram for both aircraft below it):

 

I then fit Half Normal and Hazard Rate models without adjustment terms to the data.  The fit of both models was pretty decent, but the Half Normal model performed slightly better based on AIC:

AIC -167.90

Distance sampling Cramer-von Mises test (unweighted)
Test statistic = 0.0445782 p-value = 0.908257

Abundance Estimate: 1804 (cv 0.17)

AIC -166.99

Distance sampling Cramer-von Mises test (unweighted)

Test statistic = 0.0481351 p-value = 0.887509

Abundance estimate: 1677 (cv 0.18)

 

I also tried models with left and right data truncation for both aircraft. Data was left truncated at 200 m and right truncated at 800 m, retaining 96 of the 151 moose observations.  The Half Normal model fit the truncated data well (CvM p-value = 0.96), but the abundance estimate was much higher (N=2977 and cv = 0.21).  The Hazard Rate model with the same truncation did not fit quite as well (CvM p-value  = 0.78) but yielded an estimate a bit closer to my approach outlined above (N = 1851 and cv = 0.2). 

Any advice on which approach might be best to use would be much appreciated!

Thanks

[Laura Marshall]

Dear James,

I think your approach of pre-processing the data to left-truncate where there is a restricted view from the plane and subtract this distance from the remaining distances is appropriate. This allows you to combine the data from the two planes. The assumption you are then making (assuming a single-platform analysis) is that you are detecting everything at that left-truncation distance, as if it were on the transect. One suggestion I have is to use plane as a covariate in the detection function model. You have not said if the two planes were surveying across a single area of interest or whether there was any stratification? That suggestion is particularly important if there is stratification present and the planes were surveying different strata and you want estimates at the stratum level. 

I do not think left-truncation of the data from both planes would be appropriate as the other plane looks like g(0) will be less than 1 at that distance and it also looks like it would create a more spiked detection function.   

Best wishes,

Laura

Laura Marshall

Distance Development Team