(A rough outline of a presentation given at the AFO/Wilson/GCBO Meeting Symposium on Weather Radar Ornithology held at Galveston, Texas, April 2000.) John E. Black

Physics Department

Brock University

St. Catharines, ON L2S 3A1 CANADA

A guide to making these estimates is presented in the Nexrad interpretation table.

In Figure 2, the base reflectivity image for the Buffalo WSR-88D for the 0.5 degree elevation beam at 10:58 PM on the night of May 15 is shown. The arrow marks the location of the 3-cm radar. Note that the strength of the base reflectivity is indicated in dBZ. The value of Z can be obtained from dBZ by a simple calculation. In Figure 3, we show the overlap between the two radars. As can be seen the 3-cm radar is in an excellent position to observe birds in the WSR-88D beam between the heights of 250 and 950 m. The center of the WSR-88D is at 585 m above St. Catharines.

Now the other quantity of interest is density of birds aloft (birds/km^{3}). As we
shall see, this is the quantity measured by the WSR-88D base reflectivity. Figure 5 gives
you some idea of what is meant by density. I have also indicated that if all the birds in
a volume 1 km by 1 km by 1 km (10 football fields by 10 football fields by 10 football
fields) were to land then the density on the ground would be the same number of birds in a
1 km by 1 km square. Something we will look at a little later.

The 3-cm results for the night of May 15/16, one of the busiest nights in the spring of 1999, are shown in Table 1 and Figures 6 and 7. The 3-cm radar is limited to heights above 250 m by clutter from nearby buildings. It is also a poor detector of birds above 950 meters.

Note that in monitoring migration numbers it is the migration traffic rate accumulated over the entire night, not the density, that tells us how many birds have passed overhead in one night.

From Eastwood (67) one expects radar cross-sections ranging between 8 cm^{2} for
the small Old World Warbler the Chiffchaff *(Phylloscopus collybita*) and
34 cm^{2} for a European Starling (*Sturnus vulgaris*). The radar
cross-sections are a complicated function of mass of the target and the size of the
target. My estimates are 22 cm^{2} for a Swainson’s Thrush (*Catharus
ustulatus*) and between 7 and 15 cm^{2} for different North
American Wood Warblers.

I found that averaging the density values over a 1-hour period produced the best agreement
between Z and density. In fact the radar cross-section of 17.5 reported for 500-700
(R^{2} = 0.75) is probably the most reliable values obtained in this study.
(The Z values are from Ron Larkin and Rob Diehl). Figure 8 shows the scatter diagram
for this case. There are two nights that clearly lie off the curve. The point with a
non-zero Z and no 3-cm birds, Tom Niziol of the National Weather Service at Buffalo
suggests is probably Anomalous Propagation. The other point with birds on 3-cm and very
low Z value on NEXRAD was associated with a cloud deck extending from 600 m to 4000 m
and highly variable dBZ values in the vicinity of St.Catharines.

We do not expect perfect agreement between Z and density for a number of reasons. From night to night, or even hour to hour, we do not always expect the same mixture of bird types, and therefore the same average radar cross-sections, up there (i.e. Warblers Vs Thrushes Vs Sparrows for example). In fact, based on Eastwood's estimates we can expect a factor of between ½ and 2 times some average cross-section. Secondly, we are not comparing the same volumes of birds with the Weather Radar (which takes a snapshot as it were) and the 3-cm radar (counts Birds in a volume that flows above the 3-cm in 20 minutes). Thirdly, we do not know to what extent the beam is bent by the atmosphere, and this may change from night to night, so we are not sure what precise range of heights is seen by the weather radar. These various factors then should lead to some scatter in the data. We see, however, there is a consistency in the radar cross-sections determined from the comparison, and they lie in precisely the regime we would expect if the birds were scattering as single targets.

Finally, we ask how many birds are flying over a 1 km line on the ground each hour, the migration traffic rate (MTR). It can be shown (Black and Donaldson (1999)) that the average bird density times the speed times the range of heights gives the MTR in birds/km/hr. On the night in question, the speed was about 50 km/hr, and the range of heights is the same as that used in the previous calculation; hence, the MTR was about 2500 birds/km/hr. Over a ten-hour night we would then have 25,000 birds/km. Recall that a total of 49,000 birds flew over a one-km line through Brock University on the night of May 15/16 based on the 3-cm radar result so we are doing reasonably well with our simple estimate.

Finally, note that the extent of the pattern of Figure 2 is about 300 km and that 300*25,000 or 7,500,000 birds/km/hr cross a 300 km line through Buffalo and perpendicular to the migration. According to our simple formula then, if the MTR continued unabated for 10 hours, about 7,500,000 birds would cross over the region covered by the Buffalo WSR-88D on the night of May 15/16.

These calculations can be summarized as follows: if we ask how many birds with
10 cm^{2} radar cross-sections are overhead at 46 km then the dBZ value at
46 km from the radar can be used to estimate the density in the beam as
3.0*Z birds/km^{3}. 2.0*Z is a measure of the birds that would land in an area
of 1 km^{2} if the birds were to simply drop from the sky and 100*Z is a measure
of the birds crossing a 1-km line per hour for a typical speed of 50 km /hr.

The above formulae apply to birds at 250-950 m. Corrections to the formulae would be needed to include birds below 250 meters and above 950 meters. I can estimate, (at least roughly based on dBZ at 24 km from Buffalo), the contribution to the MTR of birds below 250 m. I find the contribution to MTR from 50 m to 250 m is roughly two thirds the contribution from 250-950 m! I can estimate also from work with the King City radar the contribution above 950 m at least another third. So 4Z is a rough estimate of birds at all heights that would land in a square kilometer. Which brings me to a more sophisticated estimate. One that is not perfect however, but should give you an idea of how to refine the calculation.

By the way, the King City radar is a 5-cm radar. Estimated cross-sections would be smaller than for the 10 cm radar. About 5 cm squared might be a better figure to make it equivalent to what we have done for the WSR-88D.

- Black, J.E., 1998: Nocturnal Bird Migration and the Niagara Escarpment
*. Brock Physics Report,*PR-1998-2. - Black, J.E., and N. Donaldson 1998: A Comparison of Bird Migration Observed on a
Small Conical Radar and that Observed on a Large Doppler Radar Located near King
City, Ontario, Canada in the Spring of 1998.
*Brock Physics Report,*PR-1998-3. - Black, J.E., 1999: Ontario Spring Bird Migration on Weather Radar.
*Birders Journal,***6**, 310-315. - Crozier, C.L., P.I. Joe, J.W., Scott, H.N. Herscovitch and T.R.Nichols, 1991:
The King City Operational Doppler Radar: Development, All-Season Applications and
Forecasting.
*Atmosphere-Ocean*,**29**, 479-516. - Eastwood, E. 1967: Radar Ornithology, Methuen, 278 pp.
- Gauthreaux, S.A. Jr., and C.G. Belser, 1998: Display of Bird Movements on the
WSR-88D: Patterns and Quantification.
*Wea. Forecasting*,**13**, 453-464. - Lowery, G.H., Jr., 1951: A quantitative study of the nocturnal migration of
birds
*. Univ. Kans. Publ. Mus. Nat. Hist*.,**3**, 361-472. - Rinehart, R.E., 1997: Radar for Meteorologists (third Edition) Rinehart Publications, P.O Box 6124, Grand Forks, ND 58206-6124, U.S.A, 428 pp.

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