REVIEW A polarimetric Doppler radar time-series simulator for biological applications Phillip M. Stepanian1,2, Djordje Mirkovic3 & Phillip B. Chilson4 1Radar Entomology Unit, Computational and Analytical Sciences Department, Rothamsted Research, Harpenden Hertfordshire AL5 2JQ, United Kingdom 2Corix Plains Institute, University of Oklahoma, Norman, Oklahoma 73019, USA 3Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma 73072, USA 4School of Meteorology, Advanced Radar Research Center, Center for Autonomous Sensing and Sampling, University of Oklahoma, Norman, Oklahoma 73072, USA
Keywords Abstract Aeroecology, agent-based modelling, individual-based modelling, polarimetry, The high mobility of airborne organisms makes them inherently difficult to simulation, weather surveillance radar study, motivating the use of radars and radar networks as biological surveil- lance tools. While the utility of radar for ecological studies has been demon- Correspondence strated, a number of challenges remain in expanding and optimizing their use Phillip M. Stepanian, Corix Plains Institute, for surveillance of birds, bats and insects. To explore these topics, a Lagran- University of Oklahoma, Norman, Oklahoma gian simulation scheme has been developed to synthesize realistic, polarimet- 73019. ric, pulsed Doppler radar baseband signals from modelled flocks of biological Tel: 405 325 4034; Fax: 405 325 7702; E-mail: [email protected] point scatterers. This radar simulation algorithm is described, and an applica- tion is presented using an agent-based model of the nocturnal emergence of a Funding Information cave-dwelling colony of Brazilian free-tailed bats (Tadarida brasiliensis). Dual- This work was supported by a Marshall polarization radar signals for an S-band weather surveillance radar are synthe- Sherfield Fellowship, the National Institute for sized and used to develop a new extension of the spectral velocity azimuth Food and Agriculture of the U.S. Department display for polarimetric roost-ring signature analysis, demonstrating one capa- of Agriculture under Award 2013-67009- bility of this simulation scheme. While these developments will have direct 20369 and the U.S. National Science Foundation under Grant EF-1340921. benefits for radar engineers and meteorologists, continuing investment in radar methods such as these will have cascading effects toward improving ecological Editor: Ned Horning models and developing new observational techniques for monitoring aerial Associate Editor: Clare Duncan wildlife.
Received: 13 November 2017; Revised: 19 February 2018; Accepted: 27 February 2018 doi: 10.1002/rse2.80
Remote Sensing in Ecology and Conservation 2018;4 (4):285–302
Introduction ecological measurement tool (Gauthreaux and Belser 2003), and potential use of existing networked weather The study of birds, bats and insects in their atmospheric radar infrastructure for real-time animal monitoring has habitat is an expansive area of research, making use of spurred research efforts across the US (Chilson et al. many measurement, modelling and analysis techniques 2012) and Europe (Shamoun-Baranes et al. 2014; Bauer (Kunz et al. 2008; Bridge et al. 2011). A need for long- et al. 2017). While ecological radar surveillance tech- term, large-scale and high-resolution surveillance of the niques continue to develop, parallel research programmes airspace has motivated application of radar as an are approaching the topic of animal movements from a
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 285 This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. A Radar Simulator for Biological Applications P. M. Stepanian et al. modelling perspective (Grimm et al. 2005). In an effort to known biological scatterers can enhance use of radar in understand interactions among airborne organisms and ecological applications. This can include the ability to test changes in their aerial and terrestrial ecosystems, ecologi- different scanning strategies on a static distribution of cal models have been developed to simulate animal abun- scatterers, or development of biological radar retrieval dance, behaviour, distribution and movement as a algorithms using known model state as truth (Zrni c function of their environment and surroundings (Erni 1975). Moreover, the capability of linking – and eventu- et al. 2005; Shamoun-Baranes et al. 2010; McLane et al. ally assimilating – radar measurements to a modelling 2011; Shamoun-Baranes and van Gasteren 2011; Bauer framework could represent a step toward real-time eco- and Klaassen 2013). These biological modelling tech- logical forecasting. niques have diagnostic value in identifying drivers of ani- The major difficulty in simulating biological radar sig- mal behaviour and movement, and also present future nals is that a parameterization framework (i.e. forward potential for prognostic applications in forecasting abun- operator) such as those used in meteorological applica- dance and distributions of organisms (Clark et al. 2001; tions does not exist for biological scatterers. For example, Shamoun-Baranes et al. 2010). rain is commonly parametrized using characteristic drop Although both ecological modelling and radar mea- size distributions, stochastic spatial arrangements and surements have been applied in biological studies, no canting angles, and the assumption of uniform beam fill- framework currently exists for generating realistic radar ing (e.g. Straka et al. 2000; Ryzhkov et al. 2011). These products from ecological models. The radar manifesta- rain characterizations can directly translate to Doppler tion of objects in the airspace is a complicated combina- moments at dual-polarizations using analytical or empiri- tion of physical effects, including propagation, refraction cal expressions (Straka et al. 2000). The parallel for and scattering of electromagnetic waves, as well as arte- parameterizing animal behaviour and scattering charac- facts of radar hardware and sampling scheme. The com- teristics directly into polarimetric radar products has only bination of these effects and their net influence on the been attempted for widespread, homogenous, single-spe- final radar observations is known generally as the ‘for- cies migration (Melnikov et al. 2015). The practical ward process’. The combination of mathematical compu- implication to radar simulation is that no general links tations that relate objects in the airspace to their radar exist between Eulerian animal movement models and manifestation is commonly termed the ‘forward opera- radio scattering characteristics, making Lagrangian tech- tor’ (Jung et al. 2008a). The task of synthesizing realistic niques the only available option for calculations. Further- radar observations from a defined set of aerial objects more, because animal flight behaviour can vary relies on defining a forward operator that emulates the erratically over small spatial scales, simplified Lagrangian forward process. The value of such a comparison tech- methods that use a small subset of scatterers to stochasti- nique has been demonstrated many times in meteorolog- cally represent the full collection (e.g. Vivekanandan ical applications in which atmospheric model output are et al. 1991) are not applicable. The only remaining related to remote-sensing measurements, providing method is a brute-force Lagrangian calculation in which model validation or physical interpretation of measure- all organisms within the radar sampling volume are trea- ments (e.g. Zrni c 1975; Muschinski et al. 1999; Cheong ted as individual point scatterers and contribute to the et al. 2008; Jung et al. 2008a,b, 2010; Scipion et al. 2008; final synthesized radar signals. As a first attempt toward Ryzhkov et al. 2011; Wainwright et al. 2014; Byrd et al. a forward operator that converts ecological models into 2016). radar measurements, a computational framework for syn- While the forward process converts aerial scatterers to thesizing polarimetric, pulsed-Doppler, baseband radar radar signals, the ‘backward’ or ‘retrieval’ process signals is developed. attempts the reverse – relating radar signals to the identity – of their underlying scatterers and is the ultimate goal in Notation and Coordinate most radar applications. Linking radar measurements to Transformations the taxonomic composition and behaviour of organisms aloft is still a major challenge, and often only possible For the following discussion, the term ‘agent’ will be used when geography, phenology, or other prior knowledge to describe a modelled biological point scatterer (i.e. bird, can be used to deduce the likely occupants of the airspace bat or insect) within a three-dimensional aerial domain. (e.g. Horn and Kunz 2008; Frick et al. 2012; Melnikov As such, the instantaneous state of an agent can be et al. 2015). Nonetheless, these specialized cases (e.g. described by its position, velocity and orientation within Leskinen et al. 2011) help illustrate capabilities of radar the modelled airspace. It is assumed that some technique in movement modelling. Beyond the value in validating (e.g. an ecological model) has produced a series of such ecological models, simulating radar signals from a set of information for a total of N agents across M time steps.
286 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications
The ultimate goal is to relate these native model output array is transformed onto this radar-centred coordinate fields to quantities that are more relevant to radar mea- system surements. Though conceptually simple, defining an Xcartði; tÞ¼hxði; tÞ; yði; tÞ; zði; tÞi (4) agent’s state with respect to a radar requires computations within and across several coordinate systems, often lead- through the geodetic relations ing to notational difficulties. In an effort to avoid ambi- p ð Þ guities, the following defines the notation of these ¼ð Þ a cos lat ½ x lon lonrad 1=2 m (5a) coordinate systems, and sequential transformations 180 ½1 e2 sin2ðlatÞ through them. A table of symbols and notation is pro- vided in Appendix 1. y ¼ 111 200ðlat latradÞ½m (5b) As a general starting point, it is assumed that the format of the ecological model output describes the z ¼ alt altrad ½m (5c) geographical position of the ith agent at the tth time step as in which a is the ellipsoidal Earth’s major axis radius in metres and e is eccentricity (Rapp 1991). In the 1984 X ði; tÞ¼hlonði; tÞ; latði; tÞ; altði; tÞi (1) geo World Geodetic System, these values are a = 6 378 137.0 = using degrees longitude (lon), degrees latitude (lat) and m and e 0.081819 (National Imagery and Mapping altitude in metres above mean sea level (alt). Similarly, Agency, 1997). the instantaneous motion of an agent is described as Following this coordinate transformation, the Cartesian agent location array X ði; tÞ implicitly assumes that the Vð ; Þ¼h ð ; Þ; ð ; Þ; ð ; Þi ½ 1 cart i t u i t v i t w i t m sec (2) Earth is flat. In other words, agent positions take the x-y where u, v and w represent the agent’s zonal, meridional plane as the Earth surface, with z representing height and vertical velocity components respectively (Fig. 1B). above the radar. In this system, the radar beam path is Thus, the ecological model output consists of two arrays subject to two distorting effects: perceived upward propa- – position and velocity – each with size (N9M93). Start- gation due to curvature of the Earth, and radio refraction ing from these native output arrays, it is first necessary to due to inhomogenieties in fields of pressure, temperature define the desired location of the simulated radar: and humidity (Doviak and Zrni c 1993). Within the simu- lation framework, it is more computationally efficient to Xgeo;rad ¼hlonrad; latrad; altradi (3) consider radar beams that follow ray geometry (i.e. Once this radar location has been designated, a Carte- straight-line propagation paths). Use of ray paths enables sian coordinate system is defined with the radar at the trigonometric calculations for describing the position of origin, the positive X^-axis pointing east, the positive Y^- the beam and resolution volumes. To allow this geometry, ^ axis pointing north and the positive Z-axis pointing the combined effect of these two sources of beam opposite the force of gravity (Fig. 1A). The agent position deformation are calculated and accounted for by
A BE
α CD
Figure 1. Coordinate system definitions: (A) The radar-centred cartesian coordinate system. (B) Blowup of agent location in (A) showing velocity components. (C) The radar-centred spherical coordinate system. (D) Blowup of agent location in (C) showing the projection of the velocity vector onto the ‘ray’ coordinate basis. (E) Details of the agent position in (D), showing orientation angle definitions.
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 287 A Radar Simulator for Biological Applications P. M. Stepanian et al.
‘pre-distorting’ the position of all agents in space with The resulting Cartesian agent location array Xcartði; tÞ is respect to the radar. In the original radar-centred coordi- converted into radar-centred spherical coordinates nates, agent location with respect to the surface is defined Xsphði; tÞ¼hrði; tÞ; /ði; tÞ; hði; tÞi (9) by thepffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi surface arc distance from the radar (s ¼ x2 þ y2) and height above ground level (z), while using the position with respect to the radar beam is defined by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ x2 þ y2 þ z2 ½m (10a) slant range (r) and distance from boresight vector (d). z These four values are identical for both round and flat / ¼ arcsin ½deg (10b) Earth models in which the beam travels in non-linear r paths (Fig. 2A and B, respectively). The radar measure- h ¼ arctan2 ðx; yÞ½deg (10c) ment of an agent depends on its position with respect to the beam (i.e. r and d), and since the simulated radar with / denoting elevation angle in degrees above the measurement must not be affected by our choice of coor- horizon, h denoting azimuth angle in degrees clockwise dinate system, beam-relative agent positions must be from north and arctan2( ) denoting the four-quadrant identical after transformation to ray geometry. To achieve inverse tangent. The result of these transformations is an these conditions, the surface-relative positions of agents array of three-dimensional agent positions in the radar- (i.e. x, y and z) are modified such that they create iden- relative spherical coordinates that are common in radar tical beam-relative positions for straight-line beam propa- applications (Fig. 1C). gation (Fig. 2C). If a specific altitudinal refractivity A similar procedure is needed to produce the final gradient is to be emulated, a so-called equivalent Earth two quantities relevant to polarimetric Doppler radar radius scaling parameter (ke) can be calculated using measurements, namely, radial velocity and radar-relative 1 orientation. Because both of these quantities are depen- ke ¼ (6) dent on the position and velocity of the agent with 1 þ aðdnÞ dz respect to the radar beam, it is convenient to introduce dn two additional coordinate bases to describe these quanti- with dz being change in refractive index with height (Schelleng et al. 1933). Under these refractive conditions ties. Following notation presented in Bringi and Chan- and for a given antenna elevation angle (/ ), beam drasekar (2001), the first system is centred on the agent pt ^ height above antenna level (h) as a function of surface arc with the positive K-axis pointing radially away from the ^ distance from the radar (s) can be computed for values of radar, the positive H-axis pointing to the left of the radial vector and parallel to the ground and the V^-axis ke using qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi completing the orthogonal, right-hand coordinate basis ¼ 2 þð Þ2 þ ð/ Þ (Fig. 1D). Describing this ‘ray’ system in terms of com- h r kea 2kearsin pt kea [m] (7a) mon polarimetric radar language, H^ is the horizontal ^ rcosð/ Þ polarization axis, V is the vertical polarization axis and ¼ pt ^ s keaarcsin [m] (7b) K is the radial axis of an incident beam directed at the kea þ h agent. as illustrated in Figure 2B (Doviak Zrni c 1993). Con- The second system is centred on the agent’s body, in versely, in simple ray geometry constant alignment with the agent’s orientation. In this case, orientation is defined based on the agent’s motion 0 ¼ ð/ Þ h rsin pt [m] (8a) under the assumption that each agent is oriented head- first along the horizontal component of its velocity vector 0 ¼ ð/ Þ s rcos pt [m] (8b) with the body and both wings parallel with the horizon. In other words, while an agent may climb or turn, as in Figure 2C. Using these relations, modified agent inflight orientation will not include pitch or roll – only locations hx0; y0; z0i are defined to account for ray depar- yaw. As a result, this Cartesian ‘body’ system is oriented ture due to refraction and surface curvature. In this dis- with the positive F^-axis pointing forward along the torted Cartesian system, the radar beam is subject to ray agent’s horizontal velocity vector, the positive L^-axis geometry across a flat Earth, while retaining the same rel- pointing to the agent’s left wing and parallel to the ative positions of scatterers with respect to the beam. ground, and the B^-axis emanating out of the agent’s back, Hereafter the Cartesian system Xcartði; tÞ will refer to completing the orthogonal, right-hand coordinate basis agent positions that have been pre-distorted to account (Fig. 1E). for Earth curvature and beam refraction, and the prime Following these definitions, an agent’s radial velocity, notation will be omitted (Fig. 1A). Vr, is the projection of the native velocity vector, V(i,t),
288 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications
r A d h z pt s
B r d h z pt
s = x2+y2
r C d h' pt z'
s' = x' 2 + y' 2
Figure 2. Relation between the Earth surface, agent position and beam geometry for (A) round Earth with beam refraction, (B) flat Earth with beam refraction and (C) flat Earth with ray beam geometry that maintains beam-relative agent positions.
onto the K^ axis, and can be calculated using the rotation assuming a value of zero. Following conventions shown relation in Figure 1E, these angles are calculated using
a ¼ sgnð ucosðhÞþvsinðhÞÞ... Vrði; tÞ¼ u sinðhÞ sinð/Þ v cosðhÞ sinð/Þ ! (11) þ ð/Þ xu þ yv (12a) w cos arccos pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi [deg] x2 þ y2 u2 þ v2 based on agent position angles found in (10b,c). Radar- relative orientation can be described in terms of angular b ¼ / [deg] (12b) differences between the ‘ray’ and ‘body’ coordinate sys- tems. This orientation with respect to the radar beam is with sgn( ) denoting the signum function. The result of found using three Euler angles that define three rotations these transformations are three new arrays that describe of the agent’s ‘body’ frame to final alignment with the the position 〈r,/,h〉, velocity hVri and orientation 〈a,b〉 radar ‘ray’ frame. In successive order, these rotations are: of agents in terms that are most relevant to polarimetric a rotation around the B^-axis (i.e. heading or yaw), Doppler radar. turning to the agent’s left, and yielding the new ‘prime body’ coordinates, F^0L^0B^0. b ^0 Radar Signal Synthesis for a Single rotation around the L -axis (i.e. elevation or pitch), Pulse with the head rising and tail dropping, and yielding the new ‘double-prime body’ coordinates, F^00L^00B^00. To simplify this initial formulation of the radar signal, c rotation around the F^00-axis (i.e. bank or roll), with only a single transmitted pulse will be considered. This the right wing dropping and left wing rising, and will eliminate the need to consider pulse-to-pulse motion resulting in the alignment with the ‘ray’ coordinates, of agents and mechanical scanning of the radar beam. K^H^ V^. Building upon these results, the following section formu- By imposing level inflight orientation, radar-relative lates the full algorithm that considers beam and agent orientation will only require a and b, with c always motions.
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 289 A Radar Simulator for Biological Applications P. M. Stepanian et al.
that the nth sample following the transmitted pulse corre- Defining the radar system sponds to a distance With only the position of the radar currently defined, cns it is necessary to specify the characteristics of the radar r ðnÞ¼ s [m] (16) o 2 system. For a single transmitted pulse, several specifica- k tions are required: radar wavelength ( , [m]), transmit with c representing the speed of light [m sec 1]. Com- s power (Pt, [W]), pulse width ( , [s]), receiver sample bined with the two boresight angles (/ ; h ), r ðnÞ pro- s pt pt o time ( s, [s]), antenna beam pattern (f), antenna gain vides the spatial coordinates for the centre of each (G), initial transmit phases at horizontal and vertical resolution volume for the n time-series samples following w w polarizations ( t;h and t;v, [deg]), and system phase the transmitted pulse. w w shifts on reception ( r;h and r;v, [deg]). Additionally, radar pointing direction (i.e. boresight) must be speci- / fied by the antenna elevation angle ( pt) and azimuth Organizing calculations for h ( pt). dual-polarizations When an existing radar system is to be emulated, it is often possible to obtain the precise specifications of the The defining characteristic of polarimetric radar is system (e.g. a measured antenna beam pattern). However, transmission and reception of radiation of diverse – when such information are not available, or when testing polarizations in this case, horizontal and vertical. hypothetical radar designs, generalized expressions may The method of sequestering these signals upon trans- be used. For example, Doviak and Zrni c (1993) provide a mission and reception can be conducted simultaneously functional expression for the one-way beam weighting or alternatingly. The following formulation will con- pattern for a circularly symmetric beam of a given beam- sider Simultaneous Transmission and Simultaneous Reception (STSR) because this mode of operation can width (#b)as ()produce polarimetric information with a single pulse. 2 8J ½ð1:27p sin #Þ=# This formulation can be extended to Alternating Trans- f 2ð#Þ¼ 2 b (13) 2 mission and Simultaneous Reception (ATSR) or Alter- ½ð1:27p sin #Þ=#b nating Transmission and Alternating Reception (ATAR) ϑ where is angular distance off of boresight in radians, modes by performing calculations for each polarization ð Þ and J2 denotes a second order Bessel function. Simi- separately. larly, the range weighting function (jWðr; roÞj) can be represented, assuming a Gaussian transfer function, as Determining scattering characteristics jWðr; roÞj ¼ ½erf ðx þ bÞ erf ðx bÞ =2 (14) Two factors are important for characterizing organismal in which radio scatter: radar cross section (rb) and backscatter pffiffiffiffiffiffiffi w b ¼ Bsp=4 ln 2 phase ( s). Both quantities vary with orientation of the animal with respect to the radar (a, b, c), as well as x ¼ 2aB=cðr rÞ (15) pffiffiffiffiffiffiffio polarization. As a result, a given animal can be defined at a ¼ p=2 ln 2 a specified wavelength by the incident and scattered polarization components of backscattered cross section with ro being location of the centre of the nominal and phase at each view angle relative to the radar: range gate [m], B representing receiver bandwidth and r ða; b; cÞ r ða; b; cÞ erf( ) denoting the error function (Doviak and Zrni c b;hh b;hv r ða; b; cÞ r ða; b; cÞ (17) 1993). b;vh b;vv The combination of beam and range weighting func- and tions defines the resolution (i.e. size) of the pulse sam- w ða; b; cÞ w ða; b; cÞ pling volumes, but their location in space is determined s;hh s;hv w ða; b; cÞ w ða; b; cÞ (18) by ranges corresponding with receiver sample times. In s;vh s;vv other words, immediately following the transmitted pulse, a sample will be taken every ss sec, placing the centre of a (Melnikov et al. 2015). resolution volume every css=2 m along the ray. This map- At present, studies of organismal radio-wave scattering ping between range and time provides the link between have rarely focused on dual-polarizations or phase contri- the time-series data stream that will be synthesized and butions, and generally only present radar cross section at the location of each nominal range gate in space, such the horizontal polarization (see Vaughn 1985 for a
290 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications review). Much of this work has focused on direct radio corresponding with the agent’s current orientation (as dis- measurements of specimens in a laboratory setting; how- cussed in the previous section (Skolnik 2001). The associ- ever, no work to date has presented such polarimetric ated echo phase contributions from the ith agent are measurements of both amplitude and phase from lateral defined as viewing angles. The most promising alternative source of p p these scattering data is from electromagnetic modelling w ¼ 4 ri þ 4 Ts þ w þ w þ w i;hh k k Vr;i s;hh;i t;h r;h (20a) efforts that use theoretical calculations to characterize the amplitude and phase of animal backscatter. In most exist- p p w ¼ 4 ri þ 4 Ts þ w þ w þ w ing studies, polarimetric power analysis has been con- i;hv k k Vr;i s;hv;i t;v r;h (20b) ducted to explain differential reflectivity observations (e.g. Mueller and Larkin 1985; Wilson et al. 1994; Lang et al. 4pri 4pTs w ; ¼ þ V ; þ w ; ; þ w ; þ w ; (20c) 2004; Hobbs and Aldhous 2006), but few have modelled i vh k k r i s vh i t h r v scattering phase (Zrni c and Ryzhkov 1998; Melnikov et al. 4pri 4pTs 2015; Mirkovic et al. 2016). These latter exceptions that w ¼ þ ; þ w þ w þ w i;vv k k Vr i s;vv;i t;v r;v (20d) present both scattered amplitude and phase fall into two categories. Studies by Melnikov et al. (2015) and Zrni c w ða; bÞ using radial velocity (Vr;i) and scatter phase ( s;i ) and Ryzhkov (1998) apply general scattering calculations, of the ith agent (Doviak and Zrni c 1993). Conceptually, modelling insects and birds as prolate spheroids, and thus each agent produces a contribution to the echo produce polarimetric scattering properties at a variety of power and phase for each sample. The complex echo viewing angles. Work by Mirkovic et al. (2016) uses the voltage contribution from the ith agent for the nth method of moments on a specialized anatomical model of sample is calculated using in-phase and quadrature- a bat to calculate the scattering amplitude and phase at phase components, dual-polarizations. Such modelling efforts represent the rffiffiffiffiffiffiffiffiffiffiffiffiffi ideal method for producing the scattering characteristics ð Þ ð Þ¼ Pr;i n w required for assimilation into this radar simulation Ii n cos i rffiffiffiffiffiffiffiffiffiffiffiffiffi2 framework. P ; ðnÞ (21) Q ðnÞ¼ r i sin w i 2 i Calculating echo amplitude and phase ViðnÞ¼IiðnÞþ|QiðnÞ Using the radar system and scattering characteristic pffiffiffiffiffiffiffi with j representing the imaginary unit (i.e. 1). definitions above, and assuming that half of the total Next, time-series components from each of the N transmit power is allocated to each polarization, the agents are coherently summed to obtain the final radar STSR power contributions from the ith agent for the time-series echo voltage for the given transmit and receive nth sample following a single transmitted pulse are polarizations: calculated using the radar range equation for point scatterers, XN VðnÞ¼ ViðnÞ: (22) 2 2 4 2 ¼ PtG k rb;hh;if ð#iÞjW ðri; roÞj i 1 P ; ; ðnÞ¼ (19a) r hh i ð pÞ3 4 2 4 ri In the case of ATAR operation, these calculations are only required for co-polar contributions, that is, V ðnÞ 2k2r 4ð# Þj 2ð ; Þj hh Pt G b;hv;if i W ri ro ð Þ P ; ; ðnÞ¼ (19b) and Vvv n . For STSR operation, the received signals are r hv i ð pÞ3 4 2 4 ri the coherent sums of co- and cross-polar contributions at each received polarization. As a result, these calculations 2 2 4 2 PtG k rb;vh;if ð#iÞjW ðri; roÞj P ; ; ðnÞ¼ (19c) must be computed for all four polarizations (Vhh, Vhv, r vh i ð pÞ3 4 2 4 ri Vvh and Vvv) and summed as,
2k2r 4ð# Þj 2ð ; Þj PtG b;vv;if i W ri ro VHðnÞ¼VhhðnÞþVhvðnÞ Pr;vv;iðnÞ¼ (19d) (23) ð pÞ3 4 ð Þ¼ ð Þþ ð Þ: 2 4 ri VV n Vvv n Vvh n in which #i is angular distance of the ith scatterer off the Finally, if desired, white noise can be added to the final centre of the beam axis and rb;iða; bÞ is radar cross section time-series at a level defined by the user. The resulting at the given transmission and reception polarizations, synthesized time-series segments represent the n range-
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 291 A Radar Simulator for Biological Applications P. M. Stepanian et al. time samples from a single STSR dual-polarized pulse Illustrative Example along a ray. Overview and simulation inputs Radar Signals for Realistic Sampling The US national network of weather surveillance radars The previous section describes synthesis of a single trans- (NEXRAD) is a proven tool for monitoring colonies of mitted pulse, but typical scanning strategies require Brazilian free-tailed bats (Tadarida brasiliensis) across the transmission and reception of many pulses, often direc- southwestern and south central US (e.g. Horn and Kunz ted at different regions of space. The process of synthe- 2008; Chilson et al. 2012; Frick et al. 2012), and Horn sizing realistic radar data within this framework is and Kunz (2008) provide a particularly good introduction primarily an exercise in bookkeeping – solving a rela- to the ecology, agricultural significance and radar surveil- tively simple set of equations for several hundred thou- lance of the bats of this region. As a brief demonstration sand agents at four unique polarization combinations of radar simulation capabilities in a realistic application, and coherently adding the results. It is also simple book- we synthesize S-band radar signals for the dusk emer- keeping to keep track of agent locations, velocities and gence and dispersion of a cave-dwelling Brazilian free- orientations with respect to the scanning beam boresight tailed bat colony. at every pulse. While conceptually easy, the process is computationally expensive, requiring large arrays to store Agent-based model the pertinent information. The first step before any radar simulation can be per- formed is producing a set of Lagrangian agents that will Defining the radar system and scan act as the scatterers and move through the radar domain. For the case of realistic sampling strategies, several more The behavioural simulator used in this example is based radar parameters must be specified that define the Vol- on the ‘boid’ model described by Reynolds (1987, 1999), ume Coverage Pattern (VCP). These parameters include and determines an agent’s flight velocity by the position the set of azimuth and elevation angles that the antenna of surrounding individuals. From this method, a relatively will cover, the Pulse Repetition Time (PRT, [sec]), and simple set of behavioural attributes, or ‘rules’, defines the 1 antenna scanning rate (xr, [deg sec ]). Given the VCP, decision-making process of each agent as it moves the antenna scanning rate dictates where the boresight is through space and time. Use of a rule-based technique located at a given time. Combined with the PRT, the enables dynamical interactions among agents to emerge / ; h antenna pointing direction ( pt pt) can be defined for across a wide range of spatial and temporal scales. Inputs each pulse. With this pointing direction continuously to the biological behavioural model were based on the updating in time, the set of equations from the previous BATOIDS agent-based model, which was designed specifi- section can be solved for each pulse, resulting in full vol- cally for emulating the emergence of Brazilian free-tailed ume coverage. Furthermore, by updating the antenna bat colonies, in which primary behavioural rules include pointing direction for each PRT, realistic sampling results velocity matching and collision avoidance (Hallam et al. such as beam smearing are created (see Appendix C in 2006). The total population of the colony was set to one Doviak and Zrni c 1993). hundred thousand agents. While this value is representa- tive of many maternity roosts of free-tailed bats in central Texas, some colonies may have populations on the order Temporal Interpolation of one million (Betke et al. 2008). Additionally, pulse-to-pulse motion of agents must be The model was initialized with all bats within the cave considered as the radar samples the airspace. For an (below ground level) and they were allowed to exit at a agent-based model with a temporal resolution on the set rate through a 10 m by 10 m hole at the surface, pro- order of 1 sec, the position, velocity and orientation of ducing the columnar group formation characteristic of each agent is linearly interpolated to result in unique these emergences (Wilkins 1989). Additional rules were information content at each PRT. Effects of agent set to mimic the transition from emergence to dispersion motions within the beam coupled with pulse-to-pulse flight modes at a set altitude of 1.5 km. The biological boresight motions result in samples that vary in time at behavioural simulation presented in this example spans a the PRT, yielding realistic Doppler spectra and correlation full emergence event, lasting 35 min and having updates coefficients. Following all calculations, the resulting ray every second. A video of the full emergence simulation is data can be organized into volume scans as a function of included in the supplemental file (Video S1). Figure 3 azimuth, elevation and range. shows four snapshots from the first 20 min of this
292 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications simulation, with time increasing from left to right. The shifting the centre of mass southward. This alternating top row of panels shows a projection of the location of preference for north-south flight trajectories is therefore a all 100 000 agents onto a horizontal plane. The bottom nuance of the specific behavioural rules, rather than any row shows the projection of the agents onto a vertically biologically meaningful behaviour. As the emergence col- oriented plane running west to east. Initially, bats exit the umn continues the transition, the horizontal projection cave and gain altitude in a dense, columnar formation, begins to develop a hole in the centre of the group as bats reducing individual risk of predation (Fig. 3, left column). diverge from the cave location. At the final stages of the Risk of encountering aerial predators decreases away from emergence, bats descend to the height at which they for- the cave mouth, allowing bats to transition to a disper- age for insects (Fig. 3, right column). While this visualiza- sion flight mode (beginning in Fig. 3, second column). tion only captures overall group motion, complex More specifically, upon reaching 1.5 km in altitude, each behavioural dynamics are also occurring on much smaller individual is programmed to move away from the group’s scales as individuals interact to avoid collisions and mod- collective centre of mass while slowly descending toward ify their position within the group. the ground. These rules were chosen to create the basic diverging flight directions observed in these emergence Scattering model events, and also resulted in the concentrations of individ- uals to the north and south of the cave. As the first indi- The complex scattering characteristics of each agent must viduals reach 1.5 km, they begin dispersing away from be defined to describe the desired organism – here, the the group’s centre of mass (i.e. flying primarily north- Brazilian free-tailed bat. We use the backscatter ampli- ward) and as a result, begin shifting the group’s centre of tudes and phases generated for a Brazilian free-tailed bat mass northward. The centre of mass eventually passes at S-band (10 cm) using a method of moments model north of the main emergence column, and individuals implemented in the WIPL-D software environment (Mir- reaching 1.5 km begin dispersing to the south, now kovic et al. 2016). Scattering values were calculated at
Figure 3. Biological behavioural model snapshots from 5, 10, 15 and 20 min into the simulation (left to right). The top row shows the horizontal projection of agent locations onto the ground. The bottom row shows the projection of agent locations onto a vertically oriented plane running west to east. Each point represents the location of a single agent (i.e. bat).
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 293 A Radar Simulator for Biological Applications P. M. Stepanian et al. horizontal and vertical polarizations across all 4p steradi- corresponding with the snapshots presented in Figure 3. ans of possible viewing angles at 1 by 1 resolution. For context, we can compare these simulated products to actual radar observations of a dusk emergence of cave- dwelling bats – in this case, the Frio Cave bat colony as Radar specifications and scanning strategy seen by the 0.5 elevation sweep of the Del Rio, Texas Simulated radar specifications were selected to emulate a NEXRAD radar (KDFX; Fig. 5). The 0.5 sweep was cho- NEXRAD system (Doviak et al. 2000) running a special- sen for comparison because Frio Cave is farther from the ized single-sweep, clear-air volume coverage pattern at a KDFX radar (61 km) than our modelled bat cave was 1.5-degree elevation angle. Radar system and scan specifi- from the simulated radar (28 km), and as a result, the cations are listed in Table 1. Use of a single elevation 1.5 sweep would likely overshoot much of the bat popu- sweep provides faster update times and avoids scanning lation at Frio Cave. Modelled products in Figure 4D altitudes above the expected flight ceiling for bats. The occur approximately at the same stage of the Frio Cave origin of the agent-based model was placed at emergence shown in Figure 5B. In both cases, a ring- (x = 20 km, y = 20 km) relative to the radar, such that shaped pattern is evident in the reflectivity factor product, the cave mouth was 28.28 km northeast of the radar site. with the corresponding divergence signature in the radial velocity product that is characteristic of outward flights from a shared roost. Similar patterns of reflectivity factor Simulation results and radial velocity can be seen for Purple Martin (Progne Using these radar specifications, the agent-based beha- subis) flights, and are presented in Van Den Broeke vioural model, and the bat scattering characteristics, the (2013) and Stepanian et al. (2016). The variability of simulation was run for the 35-min emergence event. The polarimetric products around the emergence ring indi- resulting dual-polarization baseband signals were pro- cates the variability of aspect viewing angles with respect cessed into three conventional Doppler moments – reflec- to the radar site as individual headings are oriented away tivity factor (ZH), mean radial velocity (Vr) and spectrum from the cave – a polarimetric signature common to width of radial velocity (rv) – using autocovariance pro- roost exodus flights of birds and bats (Van Den Broeke cessing (Doviak and Zrni c 1993, Section 6.4.1), as well as 2013; Stepanian et al. 2016; Mirkovic et al. 2016). While three standard NEXRAD polarimetric products – differen- many of these features of the real observations are emu- w tial reflectivity (ZDR), total differential phase ( DP) and lated in the simulated results, many details are clearly not q – copolar correlation coefficient ( HV ) following Doviak correct, indicating differences between our simulated bat and Zrni c (1993, Section 6.8). A video of the time-evolu- colony and the colony at Frio Cave or deficiencies in our tion of all six radar products through the full emergence underlying behavioural model. For example, despite cov- event is included in the supplemental file (Video S2). ering approximately the same spatial area, the simulated Figure 4 shows the radar products for four sweeps reflectivity factor (Fig. 4D) is much lower than observa- tions of Frio Cave (Fig. 5D), indicating that more bats were occupying the airspace over Frio Cave than our sim- Table 1. Radar specifications and scanning strategy for simulation ulated colony of 100 000 individuals. The radial velocity Radar Parameter Value product of real observations indicates inbound flights 1 k reaching 12 m sec (Fig. 5B), while our simulation has Radar wavelength ( ) 0.10 m 6 1 Transmit power (Pt )1 10 W maximum radial velocity values around 6 m sec . Simi- Pulse width (s)1:57 10 6 sec larly, the observed variance of radial velocity is higher in 6 Receiver sample time (ss)1:57 10 sec the observations than our simulations, with measured # ¼ : 1 Antenna beam pattern (f) eq. 13, b 0 96 spectrum width values around 4 m sec compared to Antenna gain (G)45dBour modelled values of approximately 2 m sec 1. The 3 Pulse repetition time (Ts)1 10 s 1 implication is that our behavioural model needs higher Antenna rotation rate(xr ) 6.02 deg s / flight speeds with greater spatial variability to yield results Elevation angle ( pt ) 1.5 Azimuth angles (hpt )1 360 that match observations. Azimuthal patterns in polarimet- Polarization mode STSR ric products are also different between modelled and w Horizontally polarized transmit phase ( t;h)45 observed fields, and have several possible sources of vari- w Vertically polarized transmit phase ( t;v )0 ability. As discussed in Melnikov et al. (2015), azimuthal w Horizontally polarized receive phase ( r;h)0 patterns of polarimetric products depend highly on the w Vertically polarized receive phase ( r;v )0 w radar system’s differential phase on transmission ( t;d) Pulses per Azimuth 166 w Volume update time 60 sec and reception ( r;d). Because these values are not known for NEXRAD sites such as KDFX, we chose arbitrary
294 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications
A
B
C
D
Figure 4. Synthesized radar products for the modelled bat emergence corresponding with the time steps shown in Figure 3. The red dotted boxes indicate the domain shown in the inset images. Colour scales in (A) are valid for all subplots. Range rings are spaced at 5-km increments. values for both parameters ( Table 1). Differences in these flight, such as variability in wing position. All of these values between our simulation and KDFX may yield dif- components – the behavioural model, scattering model ferences in the magnitude and morphology of polarimet- and system characterization – can be modified and tuned ric patterns. It is also possible that the scattering model until the simulated products approach those observed on does not capture some important characteristics of bat KDFX. For every resolution volume, the position, velocity
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 295 A Radar Simulator for Biological Applications P. M. Stepanian et al.
A
B
C
Figure 5. Radar products from the Del Rio, Texas radar (KDFX) showing the dusk emergence of Frio Cave at the 0.5 elevation sweep. The red dotted boxes indicate the domain shown in the inset images. Colour scales in (A) are valid for all subplots. Range rings are spaced at 5-km increments. and orientation of every scatterer is known, enabling alike, many other products and analysis techniques can be interpretation of the products with respect to animal dis- produced from the baseband data created in this simula- tributions and flight behaviour. For example, the variance tion. Perhaps the greatest benefit of generating signals at of agent velocities in each volume could be calculated and the baseband level is the capability of developing and test- related to the resulting spectrum width product, provid- ing signal processing techniques. For example, time-series ing a diagnostic link between this radar product and analysis has been used in biological applications of underlying bat flight behaviour. Such applications are an weather radar to identify scattering contributions of birds exciting future application of radar simulation schemes. and insects in mixtures (Bachmann and Zrni c 2007). This Furthermore, the simulation can be replicated with differ- unique application of power spectral density analysis uses ent radar specifications, scan configurations or locations azimuthal variability to characterize animal taxa within a relative to the cave to generate ensemble comparisons. An uniform flow field and demonstrates the additional bio- example of this utility is demonstrated in Stepanian and logical information contained within the baseband signals. Chilson (2012), which presents a single-polarization simu- Unfortunately, this Spectral Velocity Azimuth Display lation of a rapid-scanning mobile radar. (SVAD) analysis is not possible using routine NEXRAD Although the six radar products presented in Figure 5 data since the baseband (i.e. Level I) data are not retained are the most familiar to meteorologists and ecologists in the archive. Nonetheless, with increasing interest in
296 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications
AAB
C
D
E
F
Figure 6. Development of the roost-relative spectral velocity azimuth display using the simulated baseband data. (A) Agent positions at 1200 sec (as seen in Fig. 4d) with overlaid definition of roost-relative azimuth coordinates. (B) Radial velocity at 1200 sec (as seen in Fig. 4d) with overlaid definition of roost-relative azimuth coordinates. (C) Power spectral density of pixels within the emergence ring, displayed as a function of roost-relative azimuth. (D) Spectral density of differential reflectivity for pixels within the emergence ring, displayed as a function of roost-relative azimuth. (E) Spectral density of differential phase for pixels within the emergence ring, displayed as a function of roost-relative azimuth. (F) Spectral density of copolar correlation coefficient for pixels within the emergence ring, displayed as a function of roost-relative azimuth. The tails 1 1 of all spectral densities have been clipped to 10 msec to aid visualization (Va ¼ 25 msec ).
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 297 A Radar Simulator for Biological Applications P. M. Stepanian et al. radar for animal surveillance and dedicated deployment colony sizes may indicate population trends into the of specialized research radars to ecologically interesting autumn. Ultimately, we can only speculate the applica- sites (Mirkovic et al. 2016), one may wonder what types tions that may evolve from coupling radar observations of analyses could be possible if Level I data were available and modelling frameworks, but the prospects are expan- at sites overlooking bat caves. Investigating these theoreti- sive. Stakeholders in such radar research programmes are cal capabilities is an interesting application of this simu- diverse – whether they be agricultural departments (Leski- lated baseband data, and the focus of the following nen et al. 2011), civil and military aviation surveillance example. authorities (Dinevich and Leshem 2007), wind energy During an emergence event, the flight behaviour of bats developers (Huppop€ et al. 2006), environmental agencies is not well suited for SVAD analysis because their velocities (O’Shea and Bogan 2003; Ruth 2007) or public health are not horizontally homogenous around the radar site. officials (Bauer et al. 2017). In each application, an under- However, the SVAD principles can be modified to look at standing of the link between Eulerian radar measurements azimuthal velocity variability not around the radar site, and Lagrangian animal movements is important for a but rather around the emergence ring. To develop this clear picture of the underlying ecological processes. Fur- analysis technique, we define a polar coordinate system thermore, radar observations can serve as a basis by which centred on the cave location (i.e. the centre of the emer- to tune ecological models, helping to identify fundamental gence ring) with a roost-relative azimuth that increases behavioural rules on which animals act (Erni et al. 2005; clockwise from north (Fig. 6A). In this coordinate system, Shamoun-Baranes et al. 2010; McLane et al. 2011; Sha- radial velocity of divergence signatures approximates the moun-Baranes and van Gasteren 2011; Bauer and Klaassen azimuthal variability of the SVAD (Fig. 6B), and baseband 2013). Finally, the ability to simulate radar data from signals can be analysed as such. Following Bachmann and known distributions of scatterers will help ongoing efforts Zrni c (2007), we calculate power spectral density as well as in developing biological radar products. For example, spectral decomposition of polarimetric products for each methods for creating 2D composites from radar volume resolution volume (i.e. pixel) in the emergence ring, and scans or rastered mosaics from multiple radars within a plot the resulting spectra as a function of roost relative azi- network can be quantitatively assessed against the defined muth angle (Fig. 6C–F). Note that in this coordinate sys- animal positions. In the near-term, progress in radar sim- tem pixels are not evenly spaced in azimuth, resulting in ulation of animal movements will require close coopera- the nonuniform azimuthal resolution in Figure 6C–F. tion among ecologists, meteorologists and radar engineers, These polarimetric spectral densities plotted in roost-rela- with the ultimate goal of creating robust tools that can be tive azimuthal display highlight the divergence of bats applied by ecological modellers. away from the cave and highlight the dependence of polarimetric quantities on flight track, but also could Acknowledgments enable the identification of other scatterers mixed within these resolution volumes. For example, in this display The authors thank Boon Leng Cheong, Gary McCracken insects with zero-mean velocity would show up as a spec- and Jeff Kelly for their valuable conversations and insights 1 tral band at Vr ¼ 0 m sec , and their power contribu- at the onset of this project, as well as Judy Shamoun-Bar- tions could be quantified independently from the bats. anes and an anonymous reviewer for comments that Similarly, polarimetric variables could be sequestered by greatly improved the final paper. Rothamsted Research is animal taxa, allowing independent characterization of the a national institute of bioscience strategically funded by bats and the insects on which they are feeding. A full the UK Biotechnology and Biological Sciences Research description of spectral polarimetry and its prospects in Council. aeroecology is presented in Bachmann and Zrni c (2007). References Conclusion Bachmann, S. and D. Zrni c. 2007. Spectral density of polarimetric variables separating biological scatterers in the Standardized observations from weather radar networks VAD display. J. Atmos. Oceanic Technol. 24, 1186–1198. hold great potential as the foundation for automated anal- Bauer, S. and M. Klaassen. 2013. Mechanistic models of yses and forecasting of airborne animal movements. Just animal migration behaviour – their diversity, structure and as radar observations of weather are assimilated into mete- use. J. Animal Ecol.. 82, 498–508. orological models, similar frameworks are a future pro- Bauer, S., J. W. Chapman, D. R. Reynolds, J. A. Alves, A. M. spect in ecology. Real-time measurements of local insect Dokter, M. M. Menz, et al. 2017. From agricultural benefits pest abundance may be used to predict dispersal distribu- to aviation safety: Realizing the potential of continent-wide tions for the following day, or spring observations of bat radar networks. BioScience. 67, 912–918.
298 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications
Betke, M., D. E. Hirsh, N. C. Makris, G. F. McCracken, M. radar entomology. IEE Proc.-Radar, Sonar Navig.. 153, Procopio, N. I. Hristov, et al. 2008. Thermal imaging reveals 502–508. significantly smaller Brazilian free-tailed bat colonies than Horn, J. W., and T. H. Kunz. 2008. Analyzing NEXRAD previously estimated. J. Mammal.. 89,18–24. doppler radar images to assess nightly dispersal patterns and Bridge, E. S., K. Thorup, M. S. Bowlin, P. B. Chilson, R. H. population trends in Brazilian free-tailed bats (Tadarida Diehl, R. W. Fl eronet al.. 2011. Technology on the move: brasiliensis). Integr. Comp. Biol. 48,24–39. Recent and forthcoming innovations for tracking migratory Huppop,€ O., J. Dierschke, K.-M. Exo, E. Fredrich, and R. Hill. birds. BioScience. 61, 689–698. 2006. Bird migration studies and potential collision risk Bringi, V. N. and V. Chandrasekar. 2001. Polarimetric Doppler with offshore wind turbines. Ibis. 148,90–109. weather radar: principles and applications. 1st ed. Cambridge Jung, Y., M. Xue, G. Zhang, and J. M. Straka. 2008a. University Press, Cambridge. Assimilation of simulated polarimetric radar data for a Byrd, A. D., I. R. Ivic, R. D. Palmer, B. M. Isom, B. L. convective storm using the ensemble Kalman filter. Part II: Cheong, A. D. Schenkman, et al. 2016. A weather radar Impact of polarimetric data on storm analysis. Mon. simulator for the evaluation of polarimetric phased array Weather Rev. 136, 2246–2260. performance. IEEE Trans. Geosci. Remote Sens. 54, 4178– Jung, Y., G. Zhang, and M. Xue. 2008b. Assimilation of 4189. simulated polarimetric radar data for a convective storm Cheong, B. L., R. D. Palmer, and M. Xue. 2008. A time using the ensemble Kalman filter. Part I: observation series weather radar simulator based on high-resolution operators for reflectivity and polarimetric variables. Monthly atmospheric models. J. Atmos. Oceanic Technol. 25, Weather Rev. 136, 2228–2245. 230–243. Jung, Y., M. Xue, and G. Zhang. 2010. Simulations of Chilson, P. B., W. F. Frick, J. F. Kelly, K. W. Howard, R. P. polarimetric radar signatures of a supercell storm using a Larkin, R. H. Diehl, et al. 2012. Partly cloudy with a chance two-moment bulk microphysics scheme. J. Appl. Meteorol. of migration: Weather, radars, and aeroecology. Bull. Am. Climatol. 49, 146–163. Meteorol. Soc. 93, 669–686. Kunz, T. H., S. A. Gauthreaux, Jr., N. I. Hristov, J. W. Horn, Clark, J. S. and et al. 2001. Ecological forecasts: an emerging G. Jones, E. K. V. Kalko, et al. 2008. Aeroecology: probing imperative. Science. 293, 657–660. and modeling the aerosphere. Integr. Comp. Biol. 48,1–11. Dinevich, L., and Y. Leshem. 2007. Algorithmic system for Lang, T. J., S. A. Rutledge, and J. L. Stith. 2004. Observations identifying bird radio-echo and plotting radar ornithological of quasi-symmetric echo patterns in clear air with the CSU- charts. The Ring. 29,3–40. CHILL polarimetric radar. J. Atmos. Oceanic Technol. 21, Doviak, R. J. and D. S. Zrni c. 1993. Doppler radar and weather 182–1189. observations. 2nd ed. Academic Press, Cambridge, MA. Leskinen, M., I. Markkula, J. Koistinen, P. Pylkko, S. Ooperi, Doviak, R. J., V. Bringi, A. Ryzhkov, A. Zahrai, and D. Zrni c. P. Siljamo, et al.2011. Pest insect immigration warning by 2000. Considerations for polarimetric upgrades to an atmospheric dispersion model, weather radars and traps. operational WSR-88D radars. J. Atmos. Oceanic Technol. 17, J. Appl. Entomol. 135,55–67. 257–278. McLane, A. J., C. Semeniuk, G. J. McDermid, and D. J. Erni, B., F. Liechti, and B. Bruderer. 2005. The role of wind in Marceau. 2011. The role of agent-based models in wildlife passerine autumn migration between Europe and Africa. ecology and management. Ecol. Model. 222, 1544–1556. Behav. Ecol. 16, 732–740. Melnikov, V. M., M. J. Istok, and J. K. Westbrook. 2015. Frick, W. F., P. M. Stepanian, J. F. Kelly, K. W. Howard, C. Asymmetric radar echo patterns from insects. J. Atmos. M. Kuster, T. H. Kunz, et al. 2012. Climate and weather Oceanic Technol. 32, 659–674. impact timing of emergence of bats. Plos One. 7,1–8. 1997. Department of defense world geodetic system 1984, its Gauthreaux, S. A.Jr. and C. G. Belser. 2003. Radar ornithology definition and relationships with local geodetic systems. and biological conservation. The Auk. 120, 266–277. Technical Report NIMA TR8350.2. Grimm, V., E. Revilla, U. Berger, F. Jeltsch, W. M. Mooij, S. F. Mirkovic, D., P. M. Stepanian, J. F. Kelly, and P. B. Chilson. Railsback, et al. 2005. Pattern-oriented modeling of agent- 2016. Electromagnetic model reliably predicts radio-wave based complex systems: lessons from ecology. Science. 310, scatter from airborne organisms. Sci. Rep. 6, 35637. 987–991. Mueller, E. A. and R. P. Larkin. 1985. Insects observed using Hallam, T. G., A. Raghavan, D. T. Dimitrov, and P. Federico. dual-polarization radar. J. Atmos. Oceanic Technol. 2,49–54. 2006. Technology and simulation of bat population Muschinski, A., P. Sullivan, D. Wuertz, R. Hill, S. Cohn, D. dynamics. pp. 113–117 in Proceedings of the second IASTED Lenschow, and R. Doviak. 1999. First synthesis of wind- International Conference on Environmental Modelling and profiler signals on the basis of large-eddy simulation data. Simulation. St. Thomas, US Virgin Islands. Radio Sci. 34, 1437–1459. Hobbs, S. and A. C. Aldhous. 2006. Insect ventral radar O’Shea, T. and M. Bogan. 2003. Monitoring trends in bat cross-section polarisation dependence measurements for populations of the United States and territories: Problems
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 299 A Radar Simulator for Biological Applications P. M. Stepanian et al.
and prospects. U.S. Geological Survey, Information and Stepanian, P. M., K. G. Horton, V. M. Melnikov, D. S. Zrni c, Technology Report 0003. and S. A. Gauthreaux, Jr.. 2016. Dual-polarization radar Rapp, R. H. 1991. Geometric geodesy, Part I. Lecture Notes. products for biological applications. Ecosphere. 7, e01539. Department of Geodetic Science and Surveying, Ohio State Straka, J. M., D. S. Zrnic, and A. V. Ryzhkov. 2000. Bulk University, Columbus, OH. hydrometeor classification and quantification using Reynolds, C. W. 1987. Flocks, herds, and schools: A polarimetric radar data: Synthesis of relations. J. Appl. distributed behavioral model. Computer Graphics. 21, Meteorol. 39, 1341–1372. 25–34. Van Den Broeke, M. S. 2013. Polarimetric radar Reynolds, C. W. 1999. Steering behaviors for autonomous observations of biological scatterers in hurricanes Irene characters. pp. 763–782 in Proceeding of game developers (2011) and Sandy (2012). J. Atmos. Oceanic Technol. 30, conference, San Jose, California. Miller Freeman Game 2754–2767. Group, San Francisco, CA. Vaughn, C. R. 1985. Birds and insects as radar targets: a Ruth, J. M. 2007. Applying radar technology to migratory bird review. Proc. IEEE. 73, 205–227. conservation and management: Strengthening and Vivekanandan, J., W. Adams, and V. Bringi. 1991. Rigorous expanding a collaborative. U.S. Geological Survey, Fort approach to polarimetric radar modeling of hydrometeor Collins, Colo., Open-File Report 1361. orientation distributions. J. Appl. Meteorol. 30, 1053–1063. Ryzhkov, A. V., M. Pinsky, A. Pokrovsky, and A. Khain. 2011. Wainwright, C. E., P. M. Stepanian, P. B. Chilson, R. D. Polarimetric radar observation operator for a cloud model Palmer, E. Fedorovich, and J. A. Gibbs. 2014. A time series with spectral microphysics. J. Appl. Meteorol. Climatol. 50, sodar simulator based on large-eddy simulation. J. Atmos. 873–894. Oceanic Technol. 31, 876–889. Schelleng, J., C. Burrows, and E. Ferrell. 1933. Ultra-short- Wilkins, K. T. 1989. Tadarida brasiliensis. Mamm. Species. 331, wave propagation. Proc. Radio Inst. Eng.. 21, 427–463. 1–10. Scipion, D. E., P. B. Chilson, E. Fedorovich, and R. D. Wilson, J. W., T. M. Weckwerth, J. Vivekanandan, R. M. Palmer. 2008. Evaluation of an LES-based wind profiler Wakimoto, and R. W. Russell. 1994. Boundary layer clear- simulator for observations of a daytime atmospheric air radar echoes: Origin of echoes and accuracy of derived convective boundary layer. J. Atmos. Oceanic Technol. 25, winds. J. Atmos. Oceanic Technol. 11, 1184–1206. 1423–1436. Zrni c, D. S. 1975. Simulation of weatherlike doppler spectra Shamoun-Baranes, J. and H. van Gasteren. 2011. Atmospheric and signals. J. Appl. Meteorol. Climatol. 14, 619–620. conditions facilitate mass migration events across the north Zrni c, D. S. and A. V. Ryzhkov. 1998. Observations of insects sea. Animal Behav., 81, 691–704. and birds with a polarimetric radar. IEEE Trans. Geosci. Shamoun-Baranes, J., W. Bouten, and E. E. van Loon. 2010. Remote Sens.. 36, 661–668. Integrating meteorology into research on migration. Integr. 50 – Comp. Biol. , 280 292. Supporting Information Shamoun-Baranes, J., J. A. Alves, S. Bauer, A. M. Dokter, O. Huppop,€ J. Koistinen, et al.2014. Continental-scale radar Additional supporting information may be found online monitoring of the aerial movements of animals. Mov. Ecol. in the supporting information tab for this article. 2,1–6. Video S1. Skolnik, M. 2001. Introduction to radar systems. 3rd ed. Video of the full agent-based behavioral model McGraw-Hill Education, New York, NY. of the dusk emergence of a cave-dwelling colony of Stepanian, P. M., and P. B. Chilson. 2012. A time-series radar 100,000 Brazilian free-tailed bats. Video S2. simulator for biological applications. pp. 25–29 in The Animated GIF of the synthesized radar pro- Seventh European Conference on Radar in Meteorology and ducts corresponding with the simulated bat emergence Hydrology. Toulouse, France. event.
Appendix 1. List of Symbols and Notation
Symbol Definition a Euler rotation angle for agent flight yaw b Euler rotation angle for agent flight pitch c Euler rotation angle for agent flight roll q HV Copolar correlation coefficient product
(Continued)
300 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. P. M. Stepanian et al. A Radar Simulator for Biological Applications
Appendix 1. Continued.
Symbol Definition h Azimuth angle of an agent hpt Azimuth angle of the radar pointing direction ϑ Angular distance off of radar boresight
#b One-way radar beamwidth k Radar wavelength rb Radar cross section rv Spectrum width of radial velocity product s Transmit pulse width ss Receiver sample time / Elevation angle of an agent / pt Elevation angle of the radar pointing direction w s Backscatter phase w t;d Initial system differential phase on transmission w r;d System differential phase shift on reception w t;h Initial system phase in the horizontal polarization on transmission w t;v Initial system phase in the vertical polarization on transmission w r;h System phase shift in the horizontal polarization on reception w r;v System phase shift in the vertical polarization on reception w i;vh The received vertically polarized echo phase contribution from the ithagent from a horizontally polarized transmission w DP Total measured differential phase product xr Antenna rotation rate a Earth radius c Speed of light d Distance of an agent from the radar beam boresight axis e Earth eccentricity f Antenna beam pattern h Height of the beam above the level of the radar i Index or subscript denoting a specific single agent ke Equivalent Earth radius scaling parameter n Index or subscript denoting a specific receiver sample r Slant range of an agent from the radar r0 Centre location of a given range gate s Arc distance of an agent from the radar t Index or subscript denoting a specific single time step x Longitudinal distance of an agent from the radar y Latitudinal distance of an agent from the radar z Altitudinal distance of an agent above ground level B Receiver bandwidth G Antenna gain M Total number of time steps in the ecological model N Total number of agents in the ecological model
Ii ðnÞ Received in-phase echo voltage component contribution from the ith agent at the nth time sample Qi ðnÞ Received quadrature-phase echo voltage component contribution from the ith agent at the nth time sample
Pr;vh;i ðnÞ The received vertically polarized power contribution from the ith agent for the nth sample from a horizontally polarized transmission Pt Radar transmit power Ts Pulse repetition time (inverse of the pulse repetition frequency) W Range weighting function
Xcartði; tÞ Location vector of the ith agent at the tth time step in radar-centred Cartesian coordinates 〈x,y,z〉
Xgeoði; tÞ Location vector of the ith agent at the tthtime step in geographic coordinates 〈lat,lon,alt〉
Xgeo;rad Location vector of the radar site in geographic coordinates hlatrad; lonrad; altradi
Xsphði; tÞ Location vector of the ith agent at the tthtime step in radar-centred spherical coordinates 〈r,/,h〉 V(i,t) Velocity vector of the ith agent at the tthtime step in Cartesian coordinates 〈u,v,w〉
Vr ði; tÞ Radial velocity of the ith agent at the tth time step
Vi ðnÞ Received complex echo voltage contribution from the ith agent at the nth time sample V(n) Total received complex echo voltage at the nth time sample
(Continued)
ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd. 301 A Radar Simulator for Biological Applications P. M. Stepanian et al.
Appendix 1. Continued.
Symbol Definition
Vr Radial velocity radar product VHðnÞ Total received horizontally polarized complex echo voltage at the nth time sample
VV ðnÞ Total received vertically polarized complex echo voltage at the nth time sample ZH Radar reflectivity factor product for the horizontal polarization
ZDR Differential reflectivity factor product
302 ª 2018 The Authors. Remote Sensing in Ecology and Conservation published by John Wiley & Sons Ltd.