Teil C - Annex 
63 
Process instruction for calculating distance correction for radar equipment (after Hup- 
pop et al. 2002) 
The distance correction method described in the following is just an example. Each radar unit 
has to be corrected individually and the formula below is by no means generally applicable. 
Whether or not a bird is detected by radar depends on quite a number of factors (Eastwood 
1967, Bruderer 1997a, b). The volume covered by a radar beam increases with distance. On 
the other hand, the energy density of emitted radar beams decreases by the factor 4nR 2 
(R = distance). The same energy loss occurs with the radar beams reflected by birds. This re 
sults in a complex relation between distance and the probability of an object being detected 
by radar. In order to compensate the distance-related “sensitivity” of radar equipment regard 
ing quantitative assessments, e. g. regarding altitude distribution, the number of echoes 
recorded has to be corrected. Huppop et al. (2002) decided not to apply an experimental 
approach to equipment calibration (e. g. by using a model plane). Instead, they tested an 
empirical approach using already collected data, which was based on the assumption - 
confirmed by visual observations - that, firstly, there exists no land-sea gradient in bird density 
off Helgoland and, secondly, flight directions within the distance covered by radar are evenly 
distributed. Accordingly, distance correction for detectability was performed for the 50-150 m 
altitude range according to Buckland et al. (2001) using the programme Distance 3.5 
(www.ruwpa.st-and.ac.uk/distance/index.html). The 50-150 m altitude range was chosen for 
two reasons: it is an altitude characterised by high bird densities and the observation angle 
from the horizontal plane is almost unchanged. This helps to minimise errors attributable to 
the fact that the radar cross-sections of birds vary according to azimuth (= angle of vision) 
(e. g. Fig. 3.3 in Eastwood 1967). 
A half-normal model with cosine series expansion (Buckland et al. 2001) was used, with three 
parameters to be estimated (a1 - 3), which constitute a good compromise between a good fit 
(assessed according to the Akaike Information Criterion) and easy handling of the model: 
, i-x 1 /! a , 3 ) ,, , v- J n x 
V = e 1 1 ■ (1 +X a : - cos ^ —) 
i-z J 
where x = distance from the radar (m), and y = detection probability, w = transect width (here: 
2,500 m). The result of our modelling is shown in Fig. 9. Accordingly, the sum of all echoes for 
each 100 x 100 m field of the total radar range up to 1,800 m was corrected for distance, with 
the maximum of the correction curve = 1 (corresponding to the assumption that all birds have 
been discovered within this distance). 
This method is entirely satisfactory for the determination of relative flight intensity up to dis 
tances of just under 2,000 m. At larger distances, the density of values per 100 x 100 m field 
is too low. This distance correction has to be performed for each individual radar unit because 
of production-related differences and different equipment settings.