Application of Weather Radar to Monitoring Numbers of Birds in Migration


(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

Introduction

In the spring of 1997, 1998 and 1999 I operated a 3-cm radar at Brock University and electronically counted birds passing overhead between 250 and 950 m. The 3-cm radar beam intersects the same volume of space that is sampled by the WSR-88D located at Buffalo, New York. I will discuss the comparison I made of the base reflectivity and the numbers of 3-cm birds and how the WSR-88D can be used to estimate numbers of birds aloft and their migration traffic rate.

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

The 3-cm Conical Radar and the Buffalo WSR-88D

The 3-cm radar is located on the roof of the physics building at Brock University in Ontario at a distance of 46 km from Buffalo(Figure 1). It is operated in the conical mode described in Eastwood (1967). The returned pulses are accumulated electronically for 20 minutes. Then a computer program determines the bird current density (birds/km2/hour), the bird’s speed (km/hr) and the direction of flight of the birds as a function of height. The density of birds (birds/km3) as a function of height is then calculated from the bird current density divided by the speed. The process is repeated every half hour over the night. Details of the 3-cm radar are given in Black (1998, 1999)

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.

Bird Density and Bird Migration Traffic Rate

It is worthwhile here to discuss briefly these two important concepts. In Figure 4 is illustrated what is meant by Migration Traffic Rate(birds/km/hour)(MTR) in this presentation. This is the quantity measured by the 3-cm radar. It is a flow of birds crossing above a 1 km line through the 3-cm radar in the course of one hour between heights of 250 m and 950 m, there will be birds above and below these heights.

Now the other quantity of interest is density of birds aloft (birds/km3). 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.

Comparison of Results from the 3-cm and WSR-88D Radars

The theory of the WSR-88D can be used (Rhinehart (1997) and Black and Donaldson(1998)) to show that, if the weather radar detects individual targets and there is no interference between them, then for a pixel of strength Z (T3)

Z*28.0 = average bird density (birds/km3) * average radar cross-section (cm2),

where the average is over the returned pulse volume.

From Eastwood (67) one expects radar cross-sections ranging between 8 cm2 for the small Old World Warbler the Chiffchaff (Phylloscopus collybita) and 34 cm2 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 cm2 for a Swainson’s Thrush (Catharus ustulatus) and between 7 and 15 cm2 for different North American Wood Warblers.

The theory then suggests that a plot of Z*28.0 obtained from the WSR-88D against the bird density obtained from the 3-cm radar should yield a slope which is the average radar cross-section of the targets in the beam. I have explored this relationship in a series of experiments extending back to 1997. The slopes are tabulated in Table 2.

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 (R2 = 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 ˝ 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.

Simple Estimates of Density and MTR from the WSR-88D

From a study of the average density in the full range of heights covered by the beam (250-950 m), we find values in the range of 9.2 to 34 cm2. I would suggest that 9.2 cm2 would be a good choice of cross-section in estimating birds aloft since it comes from the average over almost the entire beam. The other numbers give higher cross-sections because we are underestimating the density in not including the very high densities in the 250-350 m height regime. So I would suggest that a reasonable estimate of the bird density based on the Z value at 46 km from the WSR-88D would be; (T4)

average bird density in the NEXRAD radar beam(250m-950m) at 46 km = 3.0*Z.

Another way of looking at this is simply to say that this is the estimate of density we would expect if the average radar cross-section of targets in the beam was about 10 cm2.

There is a second question of interest here. How many birds would land when such a pattern as Figure 2 is present on the weather radar? There are several approaches to this problem, but a simple view is to think of the case of a location 46 km from the radar site. Here the average density in the beam is roughly, from Figure 2, 14 dBZ or 75 birds/km3. Now the region sampled by the 3-cm is about 0 .70 km thick at 46 km (recall it extends from 250-950 m). Thus, if all the birds above a square km from 250-950 m were to land we would have 0.7* 75=50 birds landing in a square km on the ground or:

average landing density (250m-950m)at 46 km = 2.0*Z.

I have found that roughly this number should be doubled to make a crude estimate of all birds from 50 m to 2000m. A useful estimator for stopover ecology this would allow some idea of how many birds would make use of a particular area.

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 cm2 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/km3. 2.0*Z is a measure of the birds that would land in an area of 1 km2 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.

Sophisticated Estimates of Density and MTR Using the Canadian Weather Radar

With a little work one could, using the above scheme, manually process the WSR-88D data to obtain an hour by hour picture of density and MTR. The more sophisticated approach is to process the weather radar data using a computer. Norman Donaldson and I have done this with data from the Canadian 5-cm weather radar at King City located north of Toronto (about 96 km north of my 3-cm radar.) for the night of May 15/16 1999. Here instead of taking Z at 46 km in one direction we average over all pixels at each distance and plot the result over time. This gives us a measure of average density*radar cross-section as a function of range form the radar and hence height above the radar.We could convert to density by dividing by say a 10 cm squared cross-section to get density of birds assuming they were of 10 cm squared* cross-section. The next transparency shows the speed from the VAD data as a function of height. Then the final transparency shows the product of speed and Z, a measure of the MTR. We could sum all of this to get the total traffic over all heights over the night. I am hoping to pursue this approach further in the next few years and have a look at traffic of birds for the past 6 years of operation of the King City Radar. In the future there will be more Canadian Radars forming a nice line for monitoring numbers of birds breeding in Canada!

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.

Acknowledgements

The author has benefited greatly from numerous conversations about targets on weather radars with Norman Donaldson of the Cloud Physics Research Division, Atmospheric Environment Service, King City, Ontario, and Thomas Niziol of the National Weather Service at Buffalo, New York.

References


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