THE JOURNAL OF RAPTOR RESEARCH A QUARTERLY PUBLICATION OF THE RAPTOR RESEARCH FOUNDATION, INC.

VOL. 38 SEPTEMBER 2004 NO. 3

J. RaptorRes. 38(3):195-207 ¸ 2004 The Raptor ResearchFoundation, Inc.

MODELING RAPTOR MIGRATION PATHW_AYS USING A FLUID-FLOW ANALOGY

DAVID BRANDES 1 LafayetteCollege, Easton, PA 18042 U.S.A.

DANIEL W. OMBALSKI U8 Filt• Inc., StateCollege, PA 16801 U.S.A.

ABSTRACT.--Wedescribe an approach to mathematical modeling of raptor migration under conditions in which terrain updrafts are the primary sourceof lift. The model is basedon the analogyof laminar fluid flow to raptor migration, with the assumptionthat migration flux at a particular location is pro- portional to terrain conductivityand the local energy gradient driving migration. The terrain conduc- tivity parameter is taken to be the relative updraft strength, which is calculatedusing wind direction, terrain slope, and terrain aspectdata determined from a digital-elevationmodel of the area of interest. By imposing a directional energy gradient (a preferred axis of migration [PALM])across the resulting conductivityfield, flow (i.e., migration) is generated, and the predominant migration paths through the region are determined. We apply the model by simulating the spring migration of Golden Eagles (Aquila chrysaetos)through central Pennsylvaniaunder eight different wind scenarios.The locationsof the simulatedmigration tracksdepended on wind direction, PAM direction, and the spatialarrangement and orientation of terrain features. Migration tracks showed a marked tendency to converge toward a small number of prefbrred pathwaysas the migration proceeds.The overall pattern of simulated mi- gration wasconsistent with availablecount data. Model restiltsshowed that south/southeastand north/ northwestwinds provided the best conditions for rapid migration acrossthe region, as was suggested by field data. KEYWORDS: GoldenEagle; Aquila chrysaetos;migration; pathways; modeling;, updrafts; terrain.

MODELACION DE LAS RUTAS DE MIGRACION MEDIANTE EL USO DE UN MODELO DE ANAL- OG• DE FLUIDODE FLUJO RESUMEN.--Describimosun enfoque para la modelaci6n matematica bajo condiciones en las cuales las corrientes termicas son la fuente primaria para elevarse.E1 modelo esta basadoen la analogia del fiqjo laminar aplicado a la migraci6n de rapacesasumiendo que el fiujo migratorio en una localidad particular es proporcional a la conductividaddel terreno y el gradiente de energia local que guia la migraci6n. E1 parametro de conductividad del terreno es asumido como la fuerza relativa de las corrientes ascendentesel cual es calculado usando la direcci6n del viento, la pendiente del terreno, determinados a partit de un modelo de elevaci6n digital del area de interis. Mediarite la imposici6n de un gradiente direccional de energia (un eje seleccionado de migraci6n) a trav6s del campo de conductividad resultante, el fiqjo (migraci6n) es generado, y las rutas de migraci6n son determinadas a travis de la regi6n. Aplicamos el modelo para simular la migraci6n de primavera del aguila dorada (Aquila chrysaetos)a travis del centro del Pennsylvaniabajo ocho escenariosde vientos diferentes. Las localidadesde simulaci6n de las rutas dependieron de la direcci6n del viento, del eje de migraci6n y del arreglo espacial y de la orientacion de las caracterlsticasdel terreno. Las rutas de migracion

E-mail address:[email protected]

195 196 BRANDESAND OMBP•LSK• VOL. 38, NO. 3

mostraton una marcada tendencia hacia la cobertura de un pequefio numero de rutas preferidas tal como la migraci6n ocurre. E1 patrtn general de la migracitn simulada es consistentecon los datos de los conteosdisponibles. Los resultadosdel modelo demuestran que los vientos sur/surestey norte/ noresteproveen las mejores condicionespara una r•pida migracitn a travfisde la regi6n tal como lo sugieren los datos del campo. [Traduccitn de Cfisar M•rquez]

It is widely held among raptor biologists and cussedby Haugh (1974). Updrafts are often the hawk watchersthat some mountain ridges concen- primary sourceof lift during early spring and late trate raptors in greater numbers than others (e.g., fall migration in temperate latitudes,and on over- Haugh 1974). Why this is true is an interesting castdays. We apply the model to simulatethe early question, especiallyin areas like the northern Ap- spring Golden Eagle (Aquila ch•Tysaetos) migration palachians,where there is a network of ridges and through central Pennsylvania and determine its many hawk watcheswhere counts have been con- primary migration pathwaysthrough the region. ducted (Zalles and Bildstein 2000). The factors The paper concludeswith a discussionof the util- that concentrate migrant raptors on one ridge, ity, limitations,and possibleadditional applications while leavinga nearbyridge of similarmorphology of the model. with few migrants, have only been discussedin a METHODS qualitativesense. Detailed quantitativemodeling of topographic and landscape structure effects on Model Equations. Fluid flows are modeled with the continuity equation (massconservation) and a momen- raptor-migrationpathways at the regional scalehas tum equation or equation of motion. Continuity alsoap- not been conducted. plies to migrating raptors, meaning that the same num- Here we describe a raptor migration model ber of raptors arrives at a location as leavesthat location based on a fluid-flow analogy and digital-elevation For laminar flow (e.g., groundwater flow), the equation data. The overall premise is that raptors migrating of motion is linear and is known as Darcy's law (Bear 1972): over the landscapeare analogousto fluid flowing Oh through a variablyconductive medium. Fluid flows q•: K-- (1) are driven by directionally-orientedenergy gradi- Os ents, much as raptors are driven by an innate urge where q• is the flux velocity (dimensionsof length [L]/ to migrate in a particular direction, termed the time IT]) in the s-direction(s is a spatialcoordinate x, y, preferred axisof migration (PAM; Kerlinger 1989). or z having dimension L), Kis the hydraulic conductiwty Fluid flows tend to channel along connectedpath- (dimensions of L/T), a material property which de- scribesthe easeof flow, and h is the fluid energyper unit waysof high conductivity(i.e., "the path of least weight (the symbolh is usedbecause energy is expressed resistance"). Similarly, raptors use pathwaysalong as an equivalent height (h) of water with dimension L) which migration can be obtained at the lowesten- Restated in words, the velocity of fluid in a particular ergy cost, by using thermals, ridge updrafts, and direction is directlyproportional to the local conductiwty (K) and the energy gradient in that direction. Analogous other sourcesof lift (Kerlinger 1989). Productive equations describea variety of physicaltransport phe- inland count sites like Hawk Mountain, PA (Broun nomena (e.g., heat, electricity). 1935) and the Goshute Mountains, NV (Hoffman The first assumptionin our model is that an equation 1985), are often on long or converginggeographic of the same form applies for raptor migration; that •s, features known as "leading lines" (Mueller and migration velocityat a particular location is directly pro- portional to "terrain conductivity"(defined below), and Berger 1967). In our analogy,these can be thought the magnitude of the local energy gradient driving rin- of as thin layersof sand (high conductivity)in an gration. Clearly, raptor migration is complex and qmte otherwise silty or clayeymedium (low conductivi- possiblynonlinear, but it is not unreasonableto assume ty). Becausethe equationsof groundwaterflow are this form as a first approximation. For example, migra- tion should be rapid where terrain conductivityis high well developed,the analogyis useful in creatinga in the desired direction (i.e., the PAM) and the energy quantitative model of raptor migration. gradient (i.e., urge to migrate) is strong.Conversely, m•- The model is applicableto conditionswhere up- gration should be slowwhere terrain conductivityis low drafts or deflection currents resulting from hori- and the energy gradient is weak. Other combinationsof conductivityand energy lead to intermediate migration zontal surfacewinds deflecting off sloping terrain rates. are the primary sourceof lift, rather than thermals In groundwater flows (and presumablyraptor migra- or other ephemeral atmosphericphenomena dis- tion acrossa diverselandscape), the parameter Kis high- SEPTEMBER2004 MODELING RAPTOR MIGRATION 197

ly variable in spaceand may range over severalorders of is relatively fiat. For a particular wind direction, we use magnitude. For simulating flow through such a domain, the product of two parametersto determine the relauve it is necessaryto divide the region of interest into a grid updraft strength (conductivity)at each location: (1) the of conductivityvalues, and approximate the derivative cosine of the angle between the terrain aspect and the term in equation (1) (Oh/Os)by diffk•renceat each point. wind direction (ranging from 0 fbr parallel winds to 1 For example, the velocityfrom point i to pointj waswrit- for perpendicularwinds), and (2) the terrain slope.Th•s ten as: algorithm determines the relative conductivity of dif•br- ent points of the landscape as a function of wind direc- - hl = (2) tion. In general, steeplysloping ridges that are oriented perpendicular to the wind direction will provide con- where/• • is a meanconductivity fbr flowbetween points nected areas of high conductivity. i and j (it is standardpractice in groundwatermodeling The calculations can be peribrmed using a digital-el- to use the harmonic mean, because the range of varia- evation model of the area of interest. A digital-elevation tion betweengridpoints is typicallyquite large). Note that model is a two-dimensionalmatrix of elevationsrepre- if h, > hj, the flux calculatedfrom (2) will be positive; senting a topographicmap. At each gridpoint, the local however,if h• > h•,the flux calculatedfrom (2) will be terrain aspect and slope can be determined by calculat- negative, meaning that velocity (migration) is in the op- ing the maximum slope value from the eight principal posite direction (from j to i). Thus, equation (2) gives directions (north, northeast, east, southeast, south, the direction of flow as well as its rate. southwest, west, and northwest). Because the cosine of Now consider a gridpoint (point 0) surrounded by the terrain/wind angle becomesnegative where the ter- four gridpoints (points 1-4) an equal distanceaway in rain slopesaway from the wind, resulting in negative con- the east-westand north-south directions. The continuity ductivity, it is necessaryto correct these off:wind values equation for point 0 is written as: to zero or a small positivevalue (conductivity cannot be <0). Note that in reality, lift may exist due to vemcal q0-14- q0-24- q0-• 4- q0-4= 0 (3) eddies on the off-wind side of a ridge; however, such tur- Substitutingequation (2) into equation (3), and solving bulent features are beyond the scope of the model. The for the energy at point 0 gives: resulting grid of conductivityvalues (one value for each point of the digital-elevation model) serves as the con- hlKo_1 4- ]l•2Ko_2 4- h3Ko_3 4- h4Ko_4 h0 = (4) neetion between the migration model and the modeled region. When equation (4) is written fbr all the gridpointsin Interpretation of Results by Particle Tracking. Once the model domain, the result is a set of algebraic equa- the matrix of equations is solved, equation (2) can be tions that can be solvedsimultaneously (a variety of ma- used to determine the magnitude and direction of the trix solution methods can be used) for the unknown en- migration flux at each gridpoint in the domain. A useful ergy values. final step is to conduct "particle tracking" to trace out To apply the model, a directional energy gradient is individual migration paths through the domain. Pamcle created to drive the flow by assigningdifferent energy tracking is often used in fluid mechanicsto help visuahze values to the model boundaries (for example, a higher and interpret complex flow fields. There are severalpos- value on the southern boundary will cause northward sible algorithms for particle tracking; a simple form con- flow). The magnitude of this applied energy gradient re- sistsof using equation (2) to calculate the velocity in the lates to the biological drive to migrate, and thus, is dif- eight possibledirections from a starting point and then ficult to quantify. However, to the extent that relative dif- choosing the next cell in the highest velocity direction ferences in fluxes or velocities between locations are (termed the D8 method; O'Callaghan and Mark 1984) desired rather than the flux value at each location, the The calculation is repeated from the new cell, and then magnitudes of the boundary energy values are essentially continued until a model boundary is eventuallyreached arbitrary, so long as these values create flow in the de- One can also determine the travel time or velocity of a sired direction. Throughout the paper we are interested particular path through the flow field aspart of the track- in such relative differences in migration and do not at- ing algorithm. te•npt to predict actual numbers of migrants. Model Application. In this paper we apply the model The ConductivityField. The secondassumption in our to simulate the spring Golden Eagle migration through model is that the conductivity(K), or easeof migration, Pennsylvania. This season, species, and location were at a particular location on the landscapeis given by the chosen as an initial test for the model because the mi- updraft strength, which can be parameterizedfrom the gration occurs during a period of minimal thermal hft, terrain orientation and slope, and direction of surface count data are available for comparisonwith model sim- winds. Empirical support for the correlation between up- ulations, and the flight occurs through a relatively small draft strength and migrant airspeed is given by Kerlinger region of highly-variable terrain. To test the model, we (1989). He found that lift (wind component perpendic- summarizedGolden Eagle data from spring hawk watch- ular to the ridge) was the most important predictor of es in northeastern North America, separated into full- air speedfor raptorsmigrating along the KittatinnyRidge time and part-time sites(Table 1). Recent •hll-time count at Hawk Mountain, PA and Raccoon Ridge, NJ. data fi-om TusseyMountain hawkwatch, 11 km southwest Updratts will be strong where wind is perpendicular to of State College, PA, show a substantiallylarger spring the terrain and the terrain is steeply sloped and weak Golden Eagle flight than at the long-term Lake Ontario where the wind is parallel to the terrain, or the terrain shoreline sites. Data from other part-time sites in the 198 BRANDESAND OMBALSKI VOL. 38, NO. 3

Table 1. Summaryof spring Golden Eagle migration count data, northeastNorth America. Basedon data reported •n Hawh MigrationAssociation of NorthAmerica Hawh MigrationStudies and BIRDHAWK (listserv.arizona.edu/archives/ birdhawk.html). Hawk Mountain data provided by L. Goodrich (pers. comm.).

ANNUAL COUNT MAXIMUM

RANGE DAILY SITE NAME DESCRIPTION LOCATION YEARS (MEAN) COUNTSa

Full-time sites BraddockBay, NY Lake Ontario shore CentralNY 1979-2002 6-53 (22) 11, 9, 7 Derby Hill, NY Lake Ontario shore Central NY 1980-2002 13-92 (31) 25, 23, 16 Niagara Peninsula Niagra Escarp./Penin. Southern ON 1980-2002 3-13 (7) 4, 4, 3 RaccoonRidge, NJ Ridge NorthwestNJ 1975-76 1-3 (2) 1, 1, 1 Ripley,NY Lake Erie shore WesternNY 1987-99 2-12 (4) 7, 3, 2 TusseyMountain, PA Ridge Central PA 2001-02 119-166 (143) 22, 22, 14 Part-time sites Allegheny Front, PA Edge of AlleghenyPlateau SouthwestPA 1990-2002 2-75 22, 21, 19 Hawk Mountain, PA Kittatinny Ridge Eastern PA 1969-2002 0-2 2, 1,1 Hook Mountain, NY Hudson River bluff Eastern NY 1976-2002 0-5 5,1,1 JacksMountain, PA Ridge Central PA 1995-99 1-11 10, 8, 3 Mount Pleasant,NY Allegheny Plateau West central NY 1992-93 6-34 10, 8, 3 SecondMountain, PA Ridge East central PA 1993-97 0-2 1,1,1 S•delingHill, PA Ridge South centralPA 1997-98 18-43 15, 5, 5 TuscaroraSummit, Ridge South centralPA 1977-2002 0-9 3,2,2 TusseyMountain, PA Ridge Central PA 1995-2000 16-95 20, 16, 15 Valleyfield, QE River crossing Southern QE 1980-2002 2-55 19, 8, 5 White Deer Ridge, PA Ridge Central PA 2000-01 25-33 13, 11, 6 The three highest countson record are listed.

western portion of the ridge-and•valleyregion suggest simulating migration over scalesof severalhundred ki- s•milar numbers of migrating Golden Eagles.However, lometers. Mountain ridgesin this region are on the order Golden Eagles are rarely seen along the Lake Erie and of 2-3 km wide, therefore such terrain features are well Lake Ontario shorelinesto the northwest,or along the representedat the 100-m resolution.The size of the dig- gattatinnyRidge to the east. Basedon a comprehensive ital-elevationmodel (2860 X 4950 gridpointsfor the en- revmw of such data, Brandes (1998) suggesteda narrow tire state) requires that the equationsbe solvedat more spnng migration route through the ridges of central than 14 million locations;to reduce the computer mem- Pennsylvaniawest of Harrisburg, which is distinct from ory requirements,we focusedon a 2400 X 2400 grid (240 the fall migration route acrossthe state,documented ex- km X 240 km) of the central portion of Pennsylvania tensivelyat hawkwatches along the KittatinnyRidge (e.g., (Fig. 1) where Golden Eaglesare known to migrate. Sat- Hawk Mountain, Waggoner'sGap). Available satellite te- ellite telemetry data from the eastern U.S. (Brodeur et lemetry data (Brodeur et al. 1996) are consistentwith a al. 1996) gavean averagespring migration distance of 68 spnng route through central Pennsylvania.Approximate- km/d, indicating it takes Golden Eaglesseveral days to ly 80% of the springGolden Eagle flight at TusseyMoun- traverse the study region. tran occurstkom late February through March with a me- Note the contrastingtopography of the Allegheny Pla- dmn date of 10 March, and only 11 of 285 Golden Eagles teau (northwest portion), the ridge-and-valley (central for which flight path data were recorded during spring portion), and Piedmont physiographicprovinces (south- 2001 and 2002 were crossingand leaving the ridge (D. east) in Fig. 1. Slopes are maximized in deeply incised Ombalski, D. Brandes, and M. Lanzone unpubl. data). canyonsof the AppalachianPlateau, and along the ridges Thus, the model assumptionthat eaglesprimarily use ter- of the ridge-and-valleyprovince. The terrain aspect rmn updraft-dominatedlift is reasonablefor this appli- through the studyarea is dominated by the southeastand cation. northwest directions, due to the southwest to northeast To create the conductivityfield for simulatingspring trend of the Appalachian Mountains. Golden Eagle migration through Pennsylvania,we used Slope and aspectat each point of the digital-elevation the 1:250000 scale (ca. 100-m resolution) state digital- model were determined using the SpatialAnalyst pack- elevationmodel availablefrom the United StatesGeolog- age of the ArcView Geographical Information System ical Survey (http://edc.usgs.gov/geodata/). Higher res- (Environmental SystemsResearch Institute, Redlands, olution data are available, but are unnecessary for GA U.S.A.), and the conductivitywas determined using SEPTEMBER 2004 MODELING RAPTOR MIGRATION 199

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,

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Figure 1. 100-m resolution shaded digital-elevationmodel (dark = high elevation, light = low elevation) of central Pennsylvaniacovering a 240 x 240 Ion area centered on the town of State College. Landscapefeatures are designated by numbers: 1 = Allegheny Front, 2 = Bald Eagle Mountain, 3 = Brush Mountain, 4 = TusseyMountain, 5 = White Deer Ridge,6 = NittanyMountain, 7 = SidelingHill, 8 = JacksMountain, 9 = TuscaroraMountain, 10 = Kittatinny Ridge.

the method oufiined above in the Map Calculator func- west/southwest, north/northwest, and east/northeast) tion of ArcView. All negative conductivityvalues were set rather than all eight, by suinining the respectiveconduc- to a constantvalue of +0.01, severalorders of magnitude tivity fields. This was felt to be a reasonable approach below typical windward terrain conductivityvalues. We sincewinds are deflected locallyby the terrain and often also investigated the application of a nonlinear scalefac- shift over the course of a day as weather systemsmove tor to the conductivityvalues to widen their range of var- acrossthe region. iation; however, this had no significant effect on the sim- To generate flow acrossthe model domain, constant ulated migration tracks.The resultswere exported from energy values were imposed along the southern (high ArcViewas a text array for input to the model, whichwas energy) and northern (low energy) boundaries of the implemented as a FORTRAN prograin. To reduce the region to create a northward (PAM = 0ø) energy gradi- number of required simulations,model runs were made ent. We used energy values of 1000 and 0 for the south for four combined wind directions (south/southeast, and north, respectively(we also investigatednorthward 200 BRANDESAND OMBALSKI VOL. 38, No. 3

PAH=0 PAH=30 RESULTS

Conductivity Fields. The mountain ridges create a network of high conductivitypathways relative to the surrounding terrain (Fig. 3). Although the deeply incised river valleysof the northern Appa- lachian Plateau also show high conductivity,these are generally not well aligned or continuous over large distances (Fig. 3). Note the similarity in the F•gure 2. Schematicof imposed migration used fbr tra- south/southeast and north/northwest fields, and versinglow-velocity zones of the model domain. The mi- the east/northeast and west/southwest fields; this gration track is deflected 200 m to the north for principal reflects the general longitudinal symmetry of the axis of migration (PAM) = 0ø, and 225 m to the north- ridges.There are important exceptionsto this sym- northeast for PAM = .BOø. metry, such as the Allegheny Front (Fig. 1) on south/southeast appearing as a long streak of high conductivity that all but disappears on north/ gradients of 100-0 and 10-0, but these had no effkct on the relative differences in flux values between locations northwest winds. The ridges in the southern por- or on the simulated tracks). tion of the studyarea are oriented at ca. 20-25ø , A 30ø (north/northeast) PAM was also simulated, be- and show high conductivityon east/northeast and causespring interthermal glide directionswere found to west/southwest winds (due to the east and west be ca. 20-30 ø in central New York where leading lines are components,respectively). Near the center of the absent (Kerlinger 1989). Furthermore, relative to the spnng counts in central Pennsylvania,few Golden Eagles studyarea the ridgesgenerally bend more easterly appear along the southern shore of Lake Ontario in to ca. 50-60 ø, and thus their conductivityis much March (Brandes 1998), which suggestsa northeastward reduced on east/northeast and west/southwest m•gration heading from central Pennsylvania.This was winds compared to south/southeast and north/ •mplemented by imposing an additional set of constant northwest winds. energy values to the north and south boundaries incor- porating the 30ø deflection. Simulated Migration Tracks. Basedon simulated Once the flow field was solved,particle tracking was trends there is a marked convergence of flight done from a seriesof equally spacedpoints along a por- paths acrossthe region, from 19 entering to 4 ex- t•on of the southern boundary of the model (column 200-1100 at 50 column [5 km] increments;Fig. 1). This iting (Figs. 4-7). The model clearly showsthe in- 90-km span encompassesthe region where hawk-watch fluence of the ridges in directing the migration data show that Golden Eagles enter Pennsylvaniaduring pattern, particularlyfor the PAM = 30ø case.In spnng migration (Brandes 1998). We note that the dis- many casesthe simulatedflight pathsfollow ridges tnbution of Golden Eagles entering Pennsylvaniais al- most certainly nonuniform; thus each starting point rep- for 10s of km (in some cases>100 km), including resents different numbers of migrants. The maximum ridges such as the Allegheny Front, TusseyMoun- velocitytracking algorithm describedpreviously was used tain, Sideling Hill, and JacksMountain (Fig. 1). At throughout. For each track, velocity data at each stepwas the termination of the ridgesin the northeastpart recorded so that travel times and mean velocities of dif- ferent tracks could be compared. of the study area for the PAM = 0ø case, flight In preliminary model runs, we found that in low-veloc- tracks bend northward acrossthe intervening val- ity regions of the model domain, such as fiat terrain, this leys,whereas for PAM = 30ø, the trackshead north- algorithm tends to produce unrealisticallycircuitous mi- northeast. gration tracks and dead-endsin terrain covesand dips. Su(h issuesare common in digital-elevationmodel-based Figure .5 showsthe simulated migration tracks analysiswhen the scaleof terrain variation is smallerthan for north/northwest wind directions. Overall, the the grid resolution, and are often solved by applying a particle tracksfor north/northwest winds (Fig. 5) p•t-filling routine to artificially smooth the terrain (e.g., are similar to those on south/southeast winds, with Jenson and Domingue 1988). To prevent such dead-end tracks and ensure continued migration acrosslow con- the flight even more confined to the ridge-and-val- ductivity regions, at each gridpoint where the maximum ley region. Convergenceof the flight to a few paths velocity from equation (2) dropped below a threshold through the central part of the studyarea is again velocity of 1 (typical velocities along ridges were 15 to apparent.For the PAM = 30ø case,the flight tends 150), a PAM-directed migration of two gridpointswas im- posed (Fig. 2). Our reasoning is that where sourcesof more toward the easternridges and awayfrom the hft are lacking, raptors will expend energy to continue Allegheny Plateau. The difference in PAM can be m•grating in the desired direction. influential in changing the flight pattern at a spe- SEPTEMBER2004 MODELING RAPTOR MIGRATION 201

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Figure 3. Relativeconductivity (i.e., updraftstrength) of centralPennsylvania for south/southeastwinds (top left), north/northwest winds (top right), west/southwestwinds (bottom left), and east/northeastwinds (bottom right). Regionsof high conductivityare dark and regionsof low conductivityare light.

cific location, such as the northern end of Brush The overall pattern for west/southwestwind di- Mountain (Fig. 1). For PAM = 0% the track heads rections (Fig. 6) trends more along the PAM under northward acrossthe l•-km wide Nittany Valley, these conditions than for the south/southeast and while for PAM = 30ø, it crossesthe 5-km wide gap north/northwest winds,with more trackscrossing northeastwardto TusseyMountain. Note that this the Allegheny Plateau, where conductivityis gen- effect did not occur on south/southeast winds, erally lower and the terrain is not as directionally showing the sensitivityto both wind direction and oriented. Although there is some ridge deflection PAM. in the southern portion of the study area where 202 BP,•Nr)•S AND OMBALSKI VOL. 38, NO. 3

Figure 4. Simulated migration tracks through central Pennsylvaniafor south/southeastwinds. Left image for prin- cipal axis of migration (PAM) = 0ø, right image for PAM = 30ø.

the ridges are oriented more northerly (20-25ø), The model results for east/northeast wind direc- the ridges are not as effective in deflecting the mi- tions (Fig. 7) are similar to those for west/south- gration as fbr the previouscases, particularly where west winds, again showing a more PAM-oriented the ridges bend eastwardnear the center of the pattern with less convergence than for south/ study area. As a result, the convergence of flight southeast or north/northwest winds. Several tracks paths is not as strong as for the south/southeast can be seen to crossthe ridges without deflection. and north/northwest winds. One dead-end track is shown in Fig. 7 (PAM =

Figure 5. Simulated migration tracks through central Pennsylvaniafor north/northwest winds. Left image for prin- cipal axis of migration (PAM) = 0ø, right image for PAM = 30ø. SEPTEMBER 2004 MODELING RAPTOR MIGRATION 203

Figure 6. Simulated migration tracks through central Pennsylvaniafor west/southwestwinds. Left image for prin- cipal axis of migration (PAM) = 0ø, right image for PAM = 30ø.

30ø); this is a result of local "pits" in the energy on west/southwest and east/northeast winds (Ta- field due to dips and southward-facingcoves in the ble 2). This is due to the flight being more con- terrain. fined to high-conductivity pathways extending For the two PAM values used, higher mean track acrossthe study area. A further point of interest is velocities through the study area are realized on that the tracks that enter west of the ridge-and-val- south/southeast and north/northwest winds than ley region (west of column 500) are significantly

Figure 7. Simulatedmigration tracks through central Pennsylvaniafor east/northeastwinds. Left imagefor principal axis of migration (PAM) = 0ø, right image for PAM = 30ø. 204 BRANDESAND OMBALSKI VOL. 38, NO. 3 slower than those that enter within the ridge-and- ity tracks (columns 500-700, columns 850-950, valleyregion. Three particular entry areasproduce and column 1100) are in qualitative agreement the highest velocity tracks:columns 500-700, col- with available count data. The first location in- umns 850-950, and column 1100. Each of these cludes two parallel ridges that converge to Tussey correspondsto the locationsof long parallel ridges Mountain, the second includes two parallel ridges (Fig. 1). that converge to Sideling Hill, and the third is near the end of Tuscarora Mountain. Tusseyand Side- DISCUSSION ling are both known for spring Golden Eagle mi- Simulated Migration Tracks. The model results gration (Table 1). Golden Eagles are uncommon indicated that migration patterns of raptors using migrants at Tuscarora Mountain, which is the east- terrain updrafts for lift can be simulated using dig- ernmost ridge that consistentlyrecords Golden Ea- ital-elevation model data and the fluid flow analo- gles in spring (Table 1). gy. The particular pathwaysare dependent on the In no casesdo simulatedmigration tracksfollow structure and orientation of the terrain, the wind the Kittatinny Ridge to the northeast. However, this direction, and choice of PAM. The convergenceof is a direct result of the location of the chosen entry pathwaysas the migration progressesis present to points, not a lack of updraftsalong that particular varying degrees in all simulations,and is the nat- ridge. Nonetheless, the simulations are consistent ural result of the requirement of minimum energy with field data: mean of one Golden Eagle per year consumptionin traversinga network of'conductive is seen during the spring count at Hawk Mountain pathways. This convergence effect, coupled with (L. Goodrich pers. comm.), and other part-time spatial differences in terrain conductivity,is at least counts that have been conducted along the Kitta- partially responsible for the diffbrence in migra- tinny Ridge have rarely reported Golden Eagles. tion counts between sites. Thus, the model provides indirect evidence that For the application to spring migration of Gold- Golden Eaglesare not entering Pennsylvaniato the en Eaglesthrough central Pennsylvania,the model east of Tuscarora Mountain. suggeststhat under south/southeast or north/ The lack of Golden Eagles in spring on the northwest winds, Golden Eagles migrate through southern shore of Lake Erie and the southwestern the ridge-and-valley region, and then north or shore of Lake Ontario (Table 1) is also predicted northeast acrossthe Allegheny Plateau, with con- by the model. Only two cases simulated (west/ vergence of pathways as migration progresses southwest winds with PAM = 0 and east/northeast northward. Under west/southwest and east/north- winds with PAM = 0) showedmigration tracks to- east winds, the orientation of the topographic fea- ward these areas, and these are low-velocitytracks, tures is such that high conductivity zones are less indicating poor lift conditions. well connected acrossthe region, and thus the pat- Although the simulated migration pattern is tern is less influenced by the ridge network and consistentwith availabledata, we suspectthat the lesssubject to pathwayconvergence. Furthermore, model tends to overpredict convergence of flight thesewinds result in poor lift conditionswith lower tracks due to the deterministic tracking algorithm. mean track velocities through the study area (Ta- Once two tracks converge,they cannot branch off ble 2). This is qualitativelyconsistent with our ex- because there is no stochasticor random compo- perience at Tussey Mountain, where 230 of 285 nent to the tracking algorithm. In reality,birds may Golden Eagles counted during full-time coverage leave a flight path for a variety of reasons during in spring 2001 and 2002 were on south/southeast migration (e.g., foraging, habitat preference, to in- or north/northwest winds, and all large Golden teract with other birds). Such behavior undoubt- Eagle flights (>10/d) have occurred on south/ edly occurs more than the model results indicate. southeast or north/northwest winds (D. Ombalski, We chose not to include wind drift effects, al- D Brandes,and M. Lanzone unpubl. data). At Tus- though these could easilybe incorporated into the sey Mountain, south/southeast winds in early tracking algorithm. Satellite tracking data across spring are usuallyassociated with rapidly warming the relatively fiat terrain of southern Quebec and temperatures, and east/northeast winds are often Ontario showedthat Golden Eaglescan maintain accompaniedby low pressureand rain, which may a consistentheading againstprevailing winds (Bro- account for some of these observed differences. deur et al. 1996). Our observations(pers. obs.) of The entry locationsproducing the highestveloc- Golden Eagles migrating along central Pennsylva- SEPTEMBER 2004 MODEIJNG RAgFOR MIGRATION 205

Table 2. Summary of mean velocitiesfor simulated migration tracks acrosscentral Pennsylvania.The values shown have been normalized by the mean velocity of all simulated tracks.

PAM = 0 PAM = 30 STARTING COLUMN SSE NNW WSW ENE MEAN a SSE NNW WSW ENE MEAN a

200 0.33 0.63 0.37 0.28 0.40 0.76 1.24 0.28 0.26 0.64 250 1.10 0.61 0.38 0.34 0.61 1.18 1.18 0.40 0.28 0.76 300 1.08 0.57 0.37 0.48 0.63 0.78 Dead-end 0.37 0.50 0.55 350 1.07 0.63 0.32 0.53 0.64 0.81 1.44 0.30 0.50 0.76 400 0.85 0.55 0.30 0.47 0.54 0.82 1.39 0.32 0.60 0.78 450 1.00 0.54 0.33 0.43 0.58 0.84 1.31 0.32 0.74 0.80 500 0.91 2.12 1.04 0.40 1.12 1.16 1.82 1.10 1.14 1.31 550 1.12 1.64 0.67 1.02 1.11 0.96 1.64 0.53 1.12 1.06 600 1.52 1.77 1.44 0.98 1.43 1.96 1.53 0.65 0.97 1.28 650 1.93 1.77 1.46 0.60 1.44 2.01 1.34 0.73 1.08 1.29 700 1.42 1.19 1.00 1.58 1.30 1.15 1.12 0.60 0.75 0.91 750 0.86 1.20 1.06 1.15 1.07 1.02 1.15 0.67 0.75 0.90 800 0.81 1.23 0.86 1.02 0.98 1.05 1.60 0.71 0.55 0.98 850 1.56 1.26 1.66 0.92 1.35 1.34 1.45 0.99 0.77 1.14 900 1.39 1.26 1.27 1.06 1.25 1.44 1.54 1.01 1.29 1.32 950 1.52 1.15 1.20 1.22 1.27 1.68 0.57 0.36 1.17 0.94 1000 1.59 1.11 1.03 1.07 1.20 1.57 0.72 0.35 0.50 0.79 1050 1.51 1.08 1.01 0.82 1.11 0.70 1.90 0.60 0.57 0.94 1100 1.28 1.95 1.03 1.48 1.44 1.20 2.57 0.35 1.09 1.30 Mean b 1.20 1.17 0.88 0.83 1.18 1.42 0.56 0.77

Mean velocityfbr a particular track acrossall four directions. Mean velocityfbr a parlicular direction acrossall tracks.

nia ridges under high-wind conditions (>50 kin/ With suchdata, one could use the model to predict hr) following passageof late fall cold fronts further numbers of migrants at different locations within argues againsta wind drift effect on Golden Eagle the region, which could be tested by field obser- migration. vation. Future simulations and model calibration Overall, the model results demonstrate that the will explore the effects of different raptor distri- fluid-flow analogy and digital-elevation-model- butions at the model boundary. based approach is useful for simulating raptor mi- It is clear that there are limitations to the fired- gration. The model yields quantitativeinsight into flow analogy. Choices of migration direction are observed migration patterns through a ridge sys- assumedto occur based on an energetic response tem, and helps explain why some count sitesyield to local conditions encountered during migration, greater numbersthan others. The model can also which does not reflect the behavioral flexibility of be used to predict sitesof concentratedraptor pas- migrating raptors. The model cannot account for sage,given known locationsfor the origin and des- the fact that a migrating eagle can see severalki- tination of the flight. lometers ahead and chooseits flight path based on Limitations. The ability to quantify the model re- distant landscape features; this is particularly evi- suits more precisely,or to test and calibrate the dent in simulationswhere tracks go up valleysde- model, is dependent on accurate boundary con- spite a nearby parallel ridge of high conductivity ditions, that is, data on the distribution of raptors (especiallyin the case of PAM = 30ø), or fail to entering the modeled region. In our application, crossa several-kilometergap in a ridge. Klem et al. we showedmigration tracks initiating from equally (1985) showed that >95% of migrating raptors spacedstarting points along a portion of the south- proceeded acrossa 1.3-km water gap (Lehigh Pav- ern boundary, but do not have the necessarydata er) in the Kittatinny Ridge without leaving the to assignnumbers of Golden Eaglesto each point. ridge, so it is clear that a raptor's decision process 206 BRANDESAND OMBALSKI VOL. 38, NO. 3 is not based strictly on local energy conditions. already exist, and could be coupled with our terrain- However, a modified tracking algorithm is under based updraft model and habitat data to create a developmentthat will searchbeyond adjacentgrid- raptor migration model capable of large-scaledy- points to choosethe direction toward the location namic simulations. Such a model would be a valu- of highest conductivitywithin a specified distance. able tool in identifyingconservation priorities at the Finally, the model also does not take into ac- continental scale,or planning field studiesin likely count "learned" behavior. Long-lived specieslike concentration areaswhere data are lacking. In ad- Golden Eaglesmay develop a preferred migration dition, this type of model for a local region could route over many seasonsof experience that is only be used as a predictive tool to estimate times, con- partially dependent on energy minimization. Oth- ditions, and locationswhen migratingbirds present er factors may determine migration route choices, a high risk of collisionwith aircraft. such as selection based on preferred or habitually- ACKNOWLEDGMENTS used habitat, prey availability, avoidance of hu- mans, or visual cues from other migrants. In the Conversations between the authors and Mike Lanzone caseof Golden Eagles,the Pennsylvaniaridges con- formed the genesisof the idea that digital terrain data stitute some of the most extensive and remote might be used to model raptor migration. We thank Lau- rie Goodrich, Steve Holtman, and Tim O'Connell woodland corridors in the region, so these high thoughtlhl commentson a draft of the paper. The review conductivitypathways may alsobe preferred migra- comments of Keith Bildstein and Jeff Smith also im- tion routes for other such reasons. One could con- proved the final manuscript. ceivablyuse habitat overlaysbased on geographical LITERATURE CITED information systemdatasets as weighting or adjust- merit factorsfor the conductivityfield, thus incor- BEAR,J. 1972. Dynamicsof fluidsin porousmedia. Amer- porating habitat considerationsinto the model. ican Elsevier, New York, NY U.S.A. Possible Applications and Extensions to the BRANDES,D. 1998. Spring Golden Eagle passagethrough Model. The model as described here is capable of the northeast U.S.--evidence for a geographically concentrated flight? Hawk Migrat. Assoc.No. Am• s•mulatingthe migration of a variety of diurnal rap- Hawk Migrat. Stud. 23:38-42. tors, so long as the basic premise of the model is BRODEUR, S., R. DE(:APaE, D.M. B•RD, AND M. FULLF•R. met--that updrafts resulting from horizontal sur- 1996. Complete migration cycle of Golden Eagles face winds deflecting off sloping terrain are the breeding in northern Quebec. Condor98:293-299. dominant source of lift. This would include other BROUN,M. 1935. The hawk migration during the lhll of late fall and early spring migrants besidesGolden 1934, along the Kittatinny Ridge in Pennsylvania.Auk Eagles, or migration during overcast conditions. 52:233-248. For smaller species,it may be necessaryto incor- H^UC,H, J.R. 1974. Local ephemeralweather conditions porate a wind-drift algorithm when crossing low and their eft•cts on hawkmigration routes. Pages 72- 84 in M. Harwood [ED.], Proceedingsof the North conductivity (flat) terrain. American hawk migration coni•rence 1974. Hawk Mi- Application of the model over larger spatial do- gration Association of North America, Washington, mains (e.g., the entire Appalachian Mountain CT U.S.A. range) is possible;however, several problems must HOffMAN, S.W. 1985. Raptor movementsin inland west- be overcome. First, computer memory is a signifi- ern North America: a synthesis.Pages 325-338 in M. cant limitation, becauseeven at much larger scales, Harwood [ED.], Proceedingsof hawk migration con- the digital-elevationmodel must be of sufficientres- ference IV. Hawk Migration Association of North olution to accuratelyrepresent the landscapefea- America, Rochester, NY U.S.A. tures that affect migration. Simulation of migration JENSON,S.K. ANDJ.O. DOMINGUE.1988. Extractingtopo- over a 2000 X 1000 km region using the 100-m res- graphic structuret?om digital elevationdata for geo- olution data would require the processingof ca. 1.5- graphical intbrmation systemanalysis. Photogram. Eng. liemote Sens. 54:1593-1600. gigabyte computer files. Secondly,the larger the KERL•NGEP,,P. 1989. Flight strategiesof migrating hawks. spatialscale, the more thne required for migration The Universityof ChicagoPress, Chicago, IL U.S.A. through the model domain. This means that a re- I•EM, D. Jp,.,B.S. HlkI•C,:Xs,D.A. PETrP,S, J.A. VIkL& AND alistic large-scalesimulation must take into account K. ILø,•N•C•.1985. Analysisof individual flight patterns changingwind conditions,and thus a time-varying of migrating raptors at a break in the Kittatinny conductivity field. However, dynamic models of Ridge: Lehigh Gap, Pennsylvania.Pages 1-11 in M. thermal uplift in the atmosphericboundary layer Harwood [ED.], Proceedingsof hawk migration con- SEPTEMBER2004 MODELING RAPTOR MIGRATION 207

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