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Inventory of Wintering Geese with a Multispectral Scanner

Laurence L. Strong, David S. Gilmer, and James A. Brass

Abstract: We used a multispectral scanner with an instantaneous-field-of-view (IFOV) that was larger than a goose to inventory winter concentrations of lesser snow geese (Chen caerulescens) on a water background. A simple linear mixture model of the image-forming process was inverted to estimate the proportion of the IFOV covered by geese. The mixture model prediction of the number of geese was 2% less than a manual count of geese on aerial photographs acquired simultaneously. We suggest that it is possible to inventory white geese and dark geese in mixed concentrations on water from visible and shortwave infrared reflectance measurements. Shortwave infrared (1,420-2,440 nm) reflectance measurements may be used to discriminate among dark species of geese.

Table of Contents



Concentrations of waterfowl at major staging and wintering sites have sometimes exceeded 1 million birds. At no other time in their life cycle do waterfowl concentrate at such high densities. Geese, in particular, may congregate in numbers that represent a major portion, if not the entire population, of a species (Raveling 1984). Typically, waterfowl population surveys are made visually from aircraft (Henry et al. 1972). However, visibility and observer bias (Caughley 1974) create serious problems when mixed species occur or when concentrations exceed a few thousand birds.

For many years biologists have examined various remote sensing tools for censusing waterfowl. Photography has achieved some success (Heyland 1978), but the technique is limited by the spectral range of the film and by cumbersome chemical processing. Interpreting photographs requires labor-intensive manual counting unless an optical digitizer and computer processing are used (Gilmer et al. 1988). Best et al. (1982) used aerial thermal infrared (8,700-11,500 nm) imagery from a predawn winter survey to delineate the areal extent of Canada geese (Branta canadensis) concentrations on water; the total number of geese, calculated as the product of area of concentration and goose density determined from aerial photographs, produced an estimate that differed from actual numbers of geese by 11%. Radar has been used to detect migrating flocks of geese, but its use for inventory is theoretical and experimental (Schaefer 1968).

Multispectral sensors measure reflected and emitted electromagnetic energy over a wider portion of the spectrum (300-14,000 nm) than do photography and video cameras (300-900 nm). This provides additional spectral variables for discriminating among waterfowl and their habitat components. Schwaller et al. (1984) presented spectral reflectance contrasts between Adelie penguins (Pygoscelis adeliae), their rookeries, and other habitat components, and they discussed the potential of using satellite multispectral sensor data to inventory penguin rookeries on a regional scale. Payne (1983) made spectral reflectance measurements (457-1,139 nm) of 9 species of birds and their primary habitats and examined the use of waveband ratios to discriminate birds from their habitat components. He reported low commission errors using a ratio of 981 and 744 nm to discriminate the birds from their habitat. However, he was unable to differentiate among bird species within light or dark groupings. Payne (1983) envisioned a remote sensing device with spatial resolution much smaller than the target bird.

To our knowledge, the use of airborne multispectral sensors for avian census has not been described, primarily because spatial resolution is not sufficient to resolve individual birds. Spatial resolution is a function of aircraft altitude, the optical system, and the size of the sensor's detector elements. The instantaneous-field-of-view (IFOV) of the sensor can be expressed as an angular or linear quantity (Slater 1980:517-522). The IFOV, when expressed in degrees or radians, is the smallest plane angle over which the detector is sensitive to energy flux. The IFOV, when expressed in linear or area units such as meters or hectares, is an altitude-dependent measure of the spatial resolution of the scanner. At an altitude of 1,000 m above the terrain, most multispectral sensors have a ground IFOV ranging from 1.5 to 2.5 m in diameter, much larger than a goose. The individual measurements are processed to form spatial arrays which are termed images. A pixel is a single data sample in an image to which a radiance value is assigned.

The need to quantify the composition of a scene in which the targets are smaller than the IFOV of the sensing device has led to the development of image processing models referred to as mixture models (Strahler et al. 1986). In these models, the reflectance measured by the instrument is a sum of the interactions of light with the mixture of scene elements weighted by their relative proportions. A primary objective of mixture models is the estimation of the target proportions that are present within an IFOV. Mixture models are successful for a variety of resource inventories including waterfowl habitat (Work and Gilmer 1976), rangeland vegetation and soil cover (Pech et al. 1986), and agriculture (McCloy 1987).

Our objectives were to (1) estimate the spectral bidirectional reflectance factor for 4 species of geese: lesser snow, Ross' (Chen rossii), white-fronted (Anser albifrons frontalis), and cackling Canada (Branta canadensis minima); (2) identify wavelengths for discriminating among geese and habitat components; and (3) detect and enumerate snow geese on water with remotely sensed scanner imagery from pixels that contain mixtures of water and geese.

We thank J. M. Hicks, M. L. Casazza, J. P. Fleskes, K. A. Gonzales, E. H. McCollum, D. V. Derksen, D. R. Raveling, and numerous staff members at Klamath Basin, Sacramento, and Havasu National Wildlife Refuges for helping with and providing materials for laboratory and field measurements. Also, our thanks to D. Bundy and the Environmental Protection Agency for flight coordination and collection of the airborne multispectral scanner data; L. L. Biehl end F. J. Tannis for assistance with the literature search; and V. C. Vanderbilt, D. H. Card, P. J. Curran, B. E. Ekstrand, C. A. Hlavka, C. J. Markon, J. S. Meyers, R. C. Wrigley, and C. L. Wyatt for valuable discussions. Assistance in manuscript review was provided by G. A. Bouret, L. M. Cowardin, P. J. Curran, C. A. Hlavka, D. J. Twedt, V. C. Vanderbilt, and R. C. Wrigley. Financial assistance was provided by the U.S. Fish and Wildlife Service and the National Aeronautics and Space Administration.


Laboratory Measurements

To measure spectral reflectance, we obtained samples of 4 species of geese at hunter check stations, at a commercial plucking plant, and by salvaging birds found dead on National Wildlife Refuges. Sample size for adult and immature birds, respectively, was white-fronted goose n = 7, n = 17; cackling Canada goose n = 14, n = 3, unknown n = 4; Ross' goose n = 9, n = 3; and snow goose n = 10, n = 12.

We used a Barringer reflectance spectrometer, model Refspec IIA, to estimate the bidirectional spectral reflectance factor from the dorsal surface of geese. A bidirectional spectral reflectance factor is defined as the ratio of the radiant flux actually reflected by a sample surface to that which would be reflected into the same reflected-beam geometry by an ideal (lossless), perfectly diffuse (lambertian), standard surface irradiated in exactly the same way as the sample (Nicodemus et al. 1977). This nomenclature is part of a unified approach to the measurement and analysis of reflectance measurements. For brevity we will refer to these measurements as reflectance in the remainder of the paper.

In preparation for spectral measurements, the birds were aged, cleaned of dirt and blood, and blotted of any moisture. Frozen birds were thawed the night before measurement. The light source for the laboratory measurements was a 500 W incandescent quartz halogen lamp mounted in an aluminum reflector. Individual geese were centered under the objective lens. The dorsal surface, consisting of the back and folded wings, occupied the instrument's entire field of view. Measurements of a white Fiberfrax calibration standard were made frequently while measuring the geese. Reflectance of the geese was calculated by taking the ratios of the measurements of geese to the standard and then correcting the result to absolute reflectance using a pressed BaSO4 powder standard.

Mean, variance, and 95% confidence intervals were calculated for each goose species and age class at 2-nm increments from 450 to 2,440 nm. We used a t-test with unequal variance to test for significant differences in mean spectral reflectance at each wavelength among species and between adult and immature birds within a species. We constructed curves of the difference between the calculated t-statistic and the critical t-value for P = 0.01, P = 0.05, and P = 0.20 as a function of wavelength to identify spectral regions useful in discriminating among species of geese. Because multiple t-tests were performed, the probability of a Type I error over all tests is greater than the chosen significance level. However, to control the frequency of any wrong statement, rather than the frequency with which a wrong statement is made in an individual test, would have resulted in an extremely conservative test. Wavelength intervals > 10 nm long with significant differences (P < 0.05) in reflectance were identified as useful in discriminating among species.

Idealized spectral reflectance curves for water, soil, and green vegetation were used for a first approximation of the contrast between geese and their habitats. The measured reflectance from a surface varies depending on several factors including (1) changes in amount and type of sediment in water (Novo et al. 1989); (2) soil color, moisture content, and surface texture (Huete et al. 1985); (3) amount and structure of vegetation (Jackson and Pinter 1986); and (4) characteristics of the measurements including solar incidence angle, and sensor view angle (Duggin 1985). A reflectance curve for turbid water with a suspended sediment concentration of 300 mg/L was obtained from Novo et al. (1989). We obtained bare soil and winter wheat reflectance curves from Hinzman et al. (1986). Bare soil measurements were of the moist, smooth surface of a silty clay loam. Winter wheat measurements were of tillering canopies 20 cm tall with a green leaf area index ranging from 0.71 to 0.81. We constructed figures of the difference between the mean reflectance curve for a goose species and each of the habitat components so that the spectral contrast among geese and these simple habitat components could be determined.

Multispectral Scanner Imagery

Although some experimental airborne instruments provide continuous spectral reflectance curves and the spatial dimension of images, most operational instruments measure reflectance in a subset of wavelengths similar to the multispectral scanner used in our study. Multispectral scanner data and photography of snow geese at Klamath Basin National Wildlife Refuge near Tule Lake, California, were obtained at solar noon on 11 April 1988 from a twin-engine Aero Commander. We used a multispectral scanner with a 2.5-milliradian IFOV and scan angle of 42.5 that was configured to measure reflected radiance in 10 discrete wavelength intervals or spectral bands between 380 and 1,100 nm. The spectral bands included 7 in the visible portion of the spectrum (380-420, 420-450, 450-500, 500-550, 550-600, 600-650, 650-690 nm) and 3 spectral bands in the near infrared (700-790, 800-890, 920-1,100 nm). Two additional detectors were equipped with a 1,550-1,750-nm filter and used low and high gain settings to obtain data in the shortwave infrared.

Multispectral scanner data and photography of snow goose concentrations were acquired at 605, 915, 1,220 and 1,525 m above the ground. Most geese were resting on the water in imagery acquired at 1,220 and 1,525 m above the ground. However, the majority of geese were flying in imagery obtained at altitudes below 1,220 m due to disturbance from the aircraft. We selected imagery from the 1,220-m altitude for analysis because it provided the greatest spatial resolution image of geese resting on water.

Scanner imagery had a nominal ground IFOV of 3.05 m in diameter at nadir. We placed white, grey, and black panels (4.6 × 4.6 m) along the flightline to calibrate the scanner imagery to reflectance factors. Simultaneously with scanner data, we used a 22.9- × 22.9-cm format metric camera with natural color (Kodak 2448 film) and a 152-mm focal length lens to photograph geese; the photography had a nominal scale of 1:8,000.

The relative spectral response or digital output from the scanner for pixels containing water, mixtures of water and geese, and the calibration panels were determined for each spectral band. Only in a spectral band (650-690 nm) from the red portion of the spectrum did the digital numbers for the calibration panels encompass the range of digital numbers for pixels of water and mixtures of water and geese. Thus, we calibrated only the red spectral band to reflectance by using a simple linear relationship between reflectance of the calibration panels measured in the laboratory and the digital number of the calibration panels.

Mixture Model

A simple linear model for the reflectance, R, of a pixel composed of a mixture of water and snow geese is

R = (Rw)(Pw) + (Rg)(Pg),

where Rw and Rg are the reflectance from water and a goose, respectively, and Pw and Pg are the proportion of the pixel that is water and geese, respectively. The domain for the model is a line joining the reflectance of water and a goose. Because the proportions of the 2 elements of the pixel have the unit sum constraint, the proportion of either element is simply one minus the other.

We estimated red reflectance for snow geese (Mean of X = 79.8, SD = 6.77) by averaging the reflectance measurements over the 650-690-nm spectral interval from the mean white (adult snow and adult Ross' geese combined) adult goose spectral reflectance curve obtained in the laboratory; red reflectance for water was estimated from the imagery. We estimated global water reflectance as the average reflectance from a large sample of pixels which contained only water. We used the median reflectance from a rectangular block of pixels enclosing the flock to estimate local water reflectance at each flock. Using the image measurement of reflectance, the estimates of reflectance for water and a snow goose, and the simple relationship between the proportions of the 2 elements, we estimated the proportion of the pixel covered by geese.

The number of geese per pixel, N, was calculated as

Equation: N = (Ap)(Pg) ÷ Ag

where Ap = area of a pixel, Ag = dorsal area of a goose, and Pg = proportion of pixel covered by geese. The area of a goose (Mean of X = 633.6 cm², SD = 173.9) was estimated as the product of length and width of the dorsal surface of a sample (n = 14) of adult snow geese. The shape of a goose might be better approximated using an ellipse rather than a rectangle, but the latter provided an approximate compensation for excluding the neck and head from the calculation of area. Pixel area at nadir was calculated as the product of the angular IFOV of the scanner and the aircraft altitude. We corrected the area of off-nadir pixels for scan angle effects (Richards 1986:45).

We located flocks in the scanner data by viewing the image on a display monitor. We estimated the number of geese in each flock by processing rectangular blocks of pixels that enclosed each flock with the mixture model procedure. Pixels with mixture model predictions of <1 goose were excluded from the calculation of number of geese.

We compared mixture model predictions with manual counts of the number of geese. Two frames of photography were enlarged to a scale of 1:2,545, and 48 flocks of geese were identified. A technician, without knowledge of the mixture model estimates, used the procedures described in Gilmer et al. (1988) to count the number of geese in each flock once. The mixture model predictions and the manual counts of geese were compared using each flock as a single observation in a regression analysis.


Laboratory Measurements

Spectral reflectance curves for the 4 species of geese can be grouped into 2 patterns which correspond to light- and dark-colored birds (Fig. 1). Reflectance curves of dark geese (white-fronted and cackling Canada geese) had a sigmoid shape with similar slopes from 450 to 1,450 nm. Reflectance increased from a minimum, 9-11%, in the visible wavelengths to 48-49% in the shortwave infrared at 1,450 nm. Reflectance curves in the shortwave infrared from 1,450 to 2,440 nm had several absorption features. Reflectance was at a maximum, 57-61%, at 1,850 nm and at a minimum, 35-37%, at 2,350 nm. Snow and Ross' geese had similar curves that were high in the visible wavelengths, increasing to a maximum of 83-84% in the near infrared and decreasing to 63-65% at 1,450 nm. The shape of the reflectance curves for white geese and dark geese were similar in short infrared wavelengths between 1,450 and 2,440 nm.

Mean reflectance of adult and immature birds was not significantly different at any wavelength for white-fronted and cackling Canada geese. However, the plumages of adult and immature snow geese were significantly different in the visible and near infrared wavelengths, 481-839 nm. Plumages of adult and immature Ross' geese were significantly different in the near infrared, 1,001-1,089 nm.

White-fronted geese (n = 24) and cackling Canada geese (n = 21) had similar mean reflectance in the visible and near infrared wavelengths, but mean reflectance for the 2 species was different at shortwave infrared wavelengths (Fig. 2). Significant differences in reflectance were measured at 1,421-2,413 and 2,425-2,437 nm. Mean reflectance of adult snow geese (n = 10) and Ross' geese (n = 9) was not significantly different at any wavelength. When we compared white-fronted geese with the pooled sample of adult snow and Ross' geese (referred to as white geese [n = 19]), mean reflectance was significantly different in the visible, near infrared, and shortwave infrared, 450-1,863 nm, and also from 1,909 to 1,971 nm. When we compared cackling Canada geese with adult white geese, mean reflectance was significantly different in the visible, near infrared, and shortwave infrared, 450-1,907 nm, and also from 1,989 to 2,411 nm and from 2,425 to 2,435 nm.

White geese contrasted greatly with the 3 idealized habitat components at all wavelengths (Fig. 3). Contrast of white geese with water was at a maximum in the near infrared. Contrast of white geese with vegetation and soil was greatest in the visible wavelengths, and differences in reflectance diminished as wavelengths increased. The contrast between white geese and, green vegetation was greater than that between white geese and bare soil, except in the near infrared wavelengths. Dark geese had greater contrast with the habitat components in the short infrared than in visible or near infrared wavelengths. Dark geese had low contrast with soil, vegetation, and water in the visible wavelengths. Strong atmospheric water absorption bands centered at 1,380 and 1,880 nm (Gates 1980:193) prevent the collection of remotely sensed reflectance measurements at these wave lengths.

Mixture Model

Using the local estimate of water reflectance at each flock, mixture model predictions an manual counts of the number of geese in a flock were highly correlated (R2 = 0.95, SE = 124.8). The mixture model prediction of the total number of geese in all flocks was 11.8% greater than the manual count. Examination of the mixture model prediction image and aerial photography revealed several pixels with a predicted density of 1 goose which were commission errors related to variation in turbidity and hence water reflectance within the flock's location. By excluding these pixels from the predicted number of geese in each flock, the statistics from the regression of mixture model predictions and manual counts were improved (R2 = 0.97, SE = 99.5), although the residual variance was not significantly different (P = 0.07) (Fig. 4). However, the mixture model prediction of total number of geese in all flocks, excluding pixels with <2 geese, was 2.1 % less than the manual count. The intercept for the regression of model predictions versus manual counts did not differ from zero (P = 0.62), nor did the slope differ from 1.0 (P = 0.69). Flocks that were outliers in the regression included 1 flock interspersed on islands with brighter reflectance than water, and 2 flocks of flying birds. The manual count for the number of geese in very dense flocks could also be in error.

Spatial variability in water turbidity and hence water reflectance was an important source of variability in the estimation of number of geese. The average red reflectance, at each flock, of pixels containing only water ranged from a minimum of 8.34% to a maximum of 10.20%. Although mixture model predictions using the global estimate of water reflectance accounted for 79% of the variation in manual counts of the number of geese, the prediction of total number of geese was almost double the manual count.


Spectral Reflectance Measurements

The shape of the spectral reflectance curves for the various species of geese is similar to reflectance curves of birds measured by Ellis (1980) and Gates (1980:259). Absorption due to water is present in the curves at about 1,100, 1,450, and 1,900 nm (Gates 1980:258). Absorption due to cysteine, a primary component of keratinized feather cells, can be seen in the reflectance curves around 1,720, 2,000, 2,200, and 2,300 nm (Williams and Norris 1987:248). Other physical explanations for the curves include the absorption characteristics of melanins and lipochrome pigments, feather chemistry, possibly oils from the uropygial gland, and reflectance and refraction of light by structures of the feather.

The magnitude of spectral reflectance for geese was within the range defined by spectral reflectance estimates for a tundra swan (Cygnus columbianus) and a Muscovy duck (Cairina moschata) as measured by Gates (1980:259). Spectral reflectance of white geese was lower than spectral reflectance of white herons, particularly in the visible and near infrared wavelengths (Ellis 1980). Spectral reflectance of dark geese (white-fronted and cackling Canada geese) was greater in the visible and less in the shortwave infrared than dark herons (Ellis 1980). Shortwave infrared reflectance of the geese was similar to Beasley and Ankney's (1988) estimate of 55% for the 1,450-2,600-nm interval for both color phases of lesser snow geese. Some of the variability in reflectance estimates among investigators is probably due to differences in the incident- and reflected-beam geometry of the measurements. Payne's (1983) reflectance estimates could not be directly compared because Payne's data were not corrected for the detector response function.

A combination of spectral band reflectance measurements in the visible, near infrared, and shortwave infrared wavelengths would allow discrimination among white geese and dark geese, water, green vegetation, and soils if these existed as the sole element in the IFOV. Payne (1983), envisioning a remote sensing device with a spatial resolution smaller than a bird, also concluded it was possible to discriminate birds from their habitat with visible and near infrared reflectance measurements, but it was not possible to discriminate among bird species within light or dark groupings. Our reflectance measurements suggest it is possible to use shortwave infrared wavelengths to discriminate between white-fronted and cackling Canada geese. The explanation for the difference in shortwave infrared reflectance between dark species of geese is unknown; it might be due to feather chemistry, which can have large annual and intrapopulation variance (Bortolotti and Barlow 1988). Visible and near infrared wavelengths can be used to discriminate between adult and immature white geese early in the fall before immatures obtain adult plumage.

It is difficult to design a multispectral remote sensing instrument with the spatial resolution to resolve individual birds from an altitude sufficient to avoid disturbance of wildlife (Wyatt et al. 1984). The data volume from such a device would be so large that real time processing of the data rather than analysis of images in the lab has been suggested (Anderson et al. 1986). However, because of the large number of factors that influence reflectance measurements (Duggin 1985), developing robust a priori classification rules can be difficult (Wyatt et al. 1984). Given the current state of knowledge and technology, our approach has been to understand and analyze the image-forming process for a remote sensing device where the IFOV is larger than the target.

Calibrating multispectral sensors for the radiance from a scene composed of geese on water will improve the discrimination capability of the image data; thus, a variable gain and offset capability is needed. Because the range in reflectance from a scene of geese on water is small when detected by a sensor with an IFOV larger than a goose, a high gain setting should be used to increase the reflectance resolution of the data. A variable offset is needed to control the recorded minimum radiance value. The appropriate gain and offset parameters will vary by spectral band and with the optical properties of water and geese.

Calibrating the digital numbers to reflectance factors will require calibration targets with optical properties that encompass the reflectance range from water to combinations of water and geese. This will be difficult in the shortwave infrared wavelengths because few targets absorb infrared radiance more efficiently that water. If the scanner is properly calibrated with gain and offset appropriate for a scene composed of geese on water, extrapolation outside the range of calibration targets might be possible.

Mixture Models

Pech et al. (1986) and McCloy (1987), analyzing remotely sensed images with mixture models, found that shadows introduced nonlinearities between actual proportions of objects and estimated proportions from remotely sensed data. For our study, the solar elevation angle, 56.5, was large relative to the height of resting geese; thus, the area of shadows from resting geese was minimal. Shadows of flying geese were easily detected on the turbid water.

Mixtures of geese resting on water and flying create a problem because the area of a flying goose and that of a resting goose is different. Also, pixel size will vary with the altitude of the flock. Efforts should be made to establish minimum altitudes for aircraft above which disturbance of geese will be minimized.

Our laboratory measurements suggest that by using visible and shortwave infrared reflectance measurements in a mixture model analysis it is possible to inventory white and dark geese in mixed concentrations on water. The domain for the model would be a triangle with the vertices defined by the reflectance of white geese, dark geese, and water (Fig. 5). The mixture model could be expanded to a higher dimensional space by including additional spectral bands. At least n - 1 spectral bands are required to estimate mixtures of n objects. Estimating proportions can be inaccurate if the reflectance of any object in the model is similar to a weighted average of the others (Work and Gilmer 1976). If each was the sole component of a pixel, shortwave reflectance measurements could discriminate between cackling Canada geese and white-fronted geese. However, adding a vertex to the model for cackling Canada geese would probably result in inaccurate estimates of the proportions within a pixel because the reflectance of a cackling Canada goose is similar to a weighted average of water and white-fronted geese. Complex scenes composed of a mixture of species of geese, water, soil, green and senescenced vegetation, and shadow, where multiple reflections and transmission of light are significant, would yield nonlinear relationships between physical proportions and response (Huete et al. 1985).

Inventory of white geese and dark geese in mixed concentrations on a water background should be possible using visible and shortwave infrared reflectance measurements from an aircraft or satellite in a mixture model analysis. Although white geese can be inventoried with aerial photography, inventory of dark geese on vertical aerial photographs is difficult because of the small contrast between water and dark birds in the visible and near infrared wavelengths.

Estimating the mixture model parameters and the image analysis is less labor intensive than manually counting geese on aerial photographs. The method (1) could be used operationally for staging and winter area concentrations of geese on water backgrounds; (2) could be used to estimate the total number of white and dark birds; and (3) will require further research if waterfowl concentrations consist of ducks, geese, swans, pelicans, and other waterfowl. A multistage sampling design with aerial photography would be needed to estimate the number of birds by species.

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This resource is based on the following source (Northern Prairie Publication 0800):

Strong, Laurence L., David S. Gilmer, and James A. Brass. 1991. Inventory of wintering geese with a multispectral scanner. Journal of Wildlife Management 55(2):250-259.

This resource should be cited as:

Strong, Laurence L., David S. Gilmer, and James A. Brass. 1991. Inventory of wintering geese with a multispectral scanner. Journal of Wildlife Management 55(2):250-259. Jamestown, ND: Northern Prairie Wildlife Research Center Online. (Version 21FEB2003).

Laurence L. Strong, TGS Technology, Inc., NASA Ames Research Center, Moffett Field, CA 94035. Present address: U.S. Fish and Wildlife Service, Northern Prairie Wildlife Research Center, Route 1, P.O. Box 96C, Jamestown, ND 58401.

David S. Gilmer, U.S. Fish and Wildlife Service, Northern Prairie Wildlife Research Center, 6924 Tremont Road, Dixon, CA 95620.

James A. Brass, National Aeronautics and Space Administration, Ames Research Center, Moffett Field, CA 94035.

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