Horizontal Aspect Research Articles

Evaluation of cephalometric points in midface bone lengthening with the use of a rigid external device in syndromic craniosynostosis patients

SummaryDistraction osteogenesis has been extensively used to correct severe midface hypoplasia in syndromic craniosynostosis patients. However few studies have reported midface distraction outcomes through cephalometric evaluation.AimThe purpose of the present study was to evaluate outcomes with midface distraction rigid external device (RED) in patients with syndromic craniosynostosis, in terms of quantity of bone lengthening, skeletal stability and facial growth.Materials and methodsEleven patients were retrospectively evaluated in this study. Cephalometrics was carried out through three teleradiographies from each patient (T1 -before surgery; T2- immediate postop, rigth after distractor removal; T3 - late postop, obtained with a minimal interval of 12 months after surgery).ResultsSignificant midface advancement was achieved with the procedure. The rate of horizontal relapse was minimal. We noticed a clear vertical facial growth, contrary to what was seen in the horizontal aspect, when there was a mild posterior relapse and no growth evidence.ConclusionCephalometric evaluation showed adequate results in midface bone lengthening with rigid external distractor.

The average three-dimensional target strength of fish by spheroid model for sonar surveys

Abstract Tang, Y., Nishimori, Y., and Furusawa, M. 2009. The average three-dimensional target strength of fish by spheroid model for sonar surveys. – ICES Journal of Marine Science, 66: 1176–1183. When surveying fish schools by sonar, the fish are insonified from various directions. Because the fish target strength (TS) has three-dimensional directivity, according to its orientation relative to the sonar beam, the TS must be appropriately averaged. By connecting the geometries of the sonar beam and the fish body, the relationship between the apparent orientation of fish, as viewed by the sonar, and the actual orientation in space is derived. Using this relationship, equations for calculating the three-dimensional-averaged TS (<TS>3D) are presented. A prolate-spheroid, modal-series, scattering model is then used to determine the characteristics of <TS>3D against various parameters, such as fish attitudes, fish length, sonar frequency, and method of beam scanning. The model is evaluated with two boundary conditions at the spheroid surface: a gas-fluid boundary relevant to fish with a swimbladder, and a fluid-fluid boundary relevant to fish without a swimbladder. The results reveal that <TS>3D varies greatly with the horizontal aspect (yaw angle), but only slightly with the vertical aspect (pitch angle) of the fish. The difference in <TS>3D between the side-on aspect and the end-on (head or tail) aspect increases with the ratio of the fish length to the acoustic wavelength.

CONVECTION SUPPRESSION IN A TRIANGULAR-SHAPED ENCLOSURE

The use of convection suppression devices has been widely discussed in the literature as a means of reducing natural convection heat loss from the front surface of glazed solar collectors. In this study, the use of baffles in an attic-shaped enclosure was examined as a possible low-cost means of suppressing heat loss by natural convection from the rear surface of a roof-integrated solar collector. To determine the effect of baffles in the attic-shaped enclosure, a three-dimensional triangular cross-sectioned enclosure with a vertical aspect ratio of 0.5 and a horizontal aspect ratio of 3.3 was modeled. The flow patterns and heat transfer in the enclosure were determined for Grashof Numbers in the range of 106−107 using a commercially available finite volume CFD solver. It was found that the use of a single adiabatic baffle mounted vertically downward from the apex, and extending the length of the enclosure, would alter the flow such that the heat transfer due to natural convection was reduced as the length of the baffle was increased.

A simplified analytical method for estimating the productivity of a horizontal well producing at constant rate or constant pressure

In this work, we present an analytical method for estimating the productivity of an infinite-conductivity horizontal well in a closed, box-shaped reservoir producing at either a constant rate or a constant pressure. It is based on approximate analytical solutions for the 2D inflow performance of an infinite-conductivity fracture in a rectangular drainage area and the near-well pressure drop for flow to a circular well in a vertical cross-section of the reservoir. The method can accommodate reservoirs with arbitrary horizontal and vertical aspect ratios, off-center wells, permeability anisotropy and skin factors. Being simple and straightforward, the method can be readily implemented in a standard spreadsheet program. Well productivities for depletion at constant rate are always higher than at constant pressure. The difference can be as much as 22% for a fully penetrating well in a thin, isotropic reservoir.

Orographic Clouds in Terrain-Blocked Flows: An Idealized Modeling Study

Abstract Idealized numerical simulations of moist strongly stratified flow over topography are used to study the processes that control orographic clouds in terrain-blocked flows as a joint function of the nondimensional flow parameter Nh/U, the horizontal topographic aspect ratio β, and the Rossby radius of deformation Nh/f. The simulations show the competition between enhanced upstream condensation in the secondary vertically propagating gravity wave and the reduction of condensation owing to enhanced low-level flow deflection. As Nh/U increases above about 1.5, the tendency for flow to be deflected around the barrier reduces cloud formation in the primary gravity wave over the ridge, while increasing β expands low-level clouds over a broader upstream area. Ice clouds may form aloft in the secondary vertically propagating gravity wave and extend upstream for several hundred kilometers. In terrain-blocked flows, more than half of the condensate mass develops upstream of the barrier in the secondary gravity wave, while in unblocked flows most of the condensate is downstream of the barrier in the primary lee wave. In 2D, none of the flow can be diverted around the barrier, and it therefore produces a much more vigorous hydrologic cycle than over long (β = 8) 3D ridges, increasing upstream lifting and cloud water content by at least a factor of 2, and generating primary wave clouds that are not produced in the 3D case. Rotation reduces the upstream extent of condensation in blocked flows to a region on the order of the radius of deformation and in 3D induces a marked asymmetry in the lifting and condensation upstream of the terrain.

On Shape and Spaciousness

Theory suggests that having enough space is a fundamental human need and so research on how environments can be modified to increase perceived spaciousness is important. Two experiments, covering 109 participants and 30 stimuli, investigated possible effects of horizontal area and aspect ratios of recesses on judged spaciousness of streets. One experiment simulated the streets with dynamic virtual reality models in which participants could move around. The other experiment simulated the streets with three static colored images. Both simulation protocols generated the same conclusions. The most important factor in judged spaciousness was horizontal area. Larger areas were judged as being more spacious. Streets with setbacks that were shallower but longer were judged as being more spacious than streets with setbacks that were deeper but shorter. The results suggest that even if the actual size of a space is fixed, it is possible to increase perceived spaciousness by modifying the shape of the space.

Fish orientation along the longitudinal profile of the Římov reservoir during daytime: Consequences for horizontal acoustic surveys

The orientation of fish in a horizontal plane has important consequences for estimating their true size from horizontal acoustic records. The aim of this work was to verify the assumption that during the daytime fish are randomly orientated in the lacustrine zone of the canyon-shaped Římov reservoir and to compare distributions of fish orientation between the lacustrine and tributary (riverine) zones. Fish orientation was acoustically surveyed at fixed locations using the SIMRAD EK 60 split-beam echo sounder (elliptical beam, 120 kHz) with a horizontally aligned transducer. The horizontal aspect (angle between the fish body and the transducer axis) was used to describe their orientation. The conventional single-echo detector (SED) and the cross-filter detector (CFD) were applied. No trend was found along the reservoir when comparing records from four sites processed with the conventional SED. At all sites, most fish appeared to move predominantly in directions perpendicular to the central axis of the acoustic beam, i.e. the side-aspects (90°) of fish prevailed over other aspects. The CFD registered tracked fish several times more often than the SED. In the lacustrine zone the frequency distribution of fish aspect appears very similar when recorded by sonar beams oriented parallel to and across the longitudinal axis of the reservoir (criss-cross-beaming experiment). In the tributary zone, beaming perpendicular to the longitudinal axis of the reservoir revealed a significantly higher proportion of fish moving along the longitudinal axis. Therefore, the assumption of random fish orientation is not applicable in the tributary zones of such reservoirs.

Mesoplodon densirostris transmission beam pattern estimated from passive acoustic bottom mounted hydrophones and a DTag recording

The transmission beam pattern of a female Mesoplodon densirostris tagged on October 23, 2006 in the Tongue of the Ocean, Bahamas is estimated using data from a Woods Hole Oceanographic Institution DTag and simultaneous recordings from broadband, bottom mounted hydrophones at the Atlantic Undersea Test and Evaluation Center, Andros Island, Bahamas. The bottom mounted hydrophones are used to localize the tagged animal and measure the received level of each click. Pitch, roll and heading from the DTag are used to determine the horizontal and vertical aspect angles relative to the hydrophone. An estimate of the M. densirostris horizontal and vertical transmission beam pattern based on four dives will be presented.

Subtitles: On the Foreignness of Film

Translating the experience of film: filmmakers, writers, and artists explore the elements of that make us and inside at the same time. Every is a film, Atom Egoyan and Ian Balfour tell us in their introduction to Subtitles. How, then, to translate the experience of film-which, as Egoyan says, makes us feel outside and inside at the same time? Taking subtitles as their point of departure, the thirty-two contributors to this unique collection consider translation, foreignness, and otherness in culture. Their discussions range from the mechanics and aesthetics of subtitles themselves to the xenophobic reaction to translation to subtitles as a metaphor for the distance and intimacy of film. The essays, interviews, and visuals include a collaboration by Russell Banks and Atom Egoyan, which uses quotations from Banks's novel The Sweet Hereafter as subtitles for publicity stills from Egoyan's of the book; three early reviews by Jorge Luis Borges; an interview with filmmaker Claire Denis about a scene in her Friday Night that should not have been subtitled; and Eric Cazdyn's reading of the running subtitles on CNN's post-9/11 newscasts as a representation of new global realities. Several writers deal with translating cultural experience for an international audience, including Frederic Jameson on Balkan cinema, John Mowitt on the history of the foreign film category in the Academy Awards, and Ruby Rich on the marketing of films and their languages-Somehow, I'd like to think it's harder to kill people when you hear their voices, she writes. And Slavoj Zizek considers the foreign gaze (seen in films by Hitchcock, Lynch, and others), the misperception that sees too much. Designed by Egoyan and award-winning graphic designer Gilbert Li, the book includes many color images and ten visual projects by artists and filmmakers. The pages are horizontal, suggesting a movie screen; they use the cinematic horizontal aspect ratio of 1.66:1. Subtitles gives us not only a new way to think about but also a singular design object.Subtitles is being copublished by The MIT Press and Alphabet City Media (John Knechtel, Director). Subtitles has been funded in part by grants from The Canada Council for the Arts, The Henry N.R. Jackman Foundation, and the Toronto Arts Council, and the Ontario Arts Council.

Microtensile bond strength between crown and root dentin and two adhesive systems

Since bonding agent effectiveness is usually evaluated on coronal substrates, available knowledge for judging the effectiveness of bonds to root dentin is insufficient. The objective of this study was to evaluate the bond strength of 2 adhesive systems to crown, cervical finish line, and post space dentin. Twenty bovine maxillary incisors were used in this study. Teeth were sectioned along the cemento-enamel junction using a low-speed diamond blade to separate the crowns and roots. Then the crowns and roots were each divided into 2 groups, according to the 2 adhesive systems tested (n=10). The facial enamel surfaces of the crowns were abraded with 600-grit silicon carbide paper to expose flat, midcoronal dentin surfaces. Drills and a diamond rotary cutting instrument were used in a low-speed handpiece to prepare post spaces in the root canals. The same diamond rotary instrument was used to prepare horizontally flat surfaces in the cervical areas, similar to the horizontal aspect of a shoulder finish line. Composite resin was placed incrementally into the post spaces, over the flat cervical shoulder areas, and on the coronal dentin. Bonded beam specimens (0.5 mm(2) of cross-sectional area) derived from crown, cervical finish line, and post space dentin, were prepared for microtensile bond testing and tested in tension. Data were analyzed using 2-way ANOVA and Tukey post hoc test (alpha=.05). Failure patterns of tested specimens were analyzed using scanning electron microscopy. The mean tensile bond strength values (SD) (MPa) were: Single Bond-crown: 29.8 (4.0); Single Bond-finish line: 18.7 (4.3); Single Bond-post space: 17.0 (4.8); Clearfil SE Bond-crown: 30.1 (6.4); Clearfil SE Bond-finish line: 30.4 (5.3); and Clearfil SE Bond-post space: 17.0 (4.2). Bond strengths to post space dentin were lower than those to coronal dentin for both adhesives (P<.001). However, no significant difference was observed between coronal and finish line dentin for Clearfil SE Bond. Bond strength was reduced when adhesives were used in bonding to post space dentin. Cervical finish line sites bonded using Clearfil SE Bond adhesive yielded bond strength similar to that of coronal dentin sites.

Numerical Simulation of Natural Convection in Three-dimensional Cavities with a High Vertical Aspect Ratio and a Low Horizontal Aspect Ratio

In this article a commercial computational fluid dynamic program is used to study the effect of the horizontal aspect ratio on heat flow through cavities with a high vertical aspect ratio (cavities typically found in vertical window frames with internal cavities). The cavities studied have two opposite isothermal vertical walls separated by four adiabatic walls. The vertical aspect ratios are 20, 40, and 80 and the horizontal aspect ratios range from 0.2 to 5. Simulations of two-dimensional cavities are also included. The simulations show that three-dimensional cavities with a horizontal aspect ratio larger than five can be considered as being two-dimensional cavities to within 4% when considering heat transfer rates. Nusselt number correlations for the different horizontal aspect ratios are included. Complex multicellular flow is presented for one of the three-dimensional cavities.

Traitement arthroscopique des conflits ulnolunaires

The ulnar impaction syndrome is due to hyperpressure in the ulnocarpal joint. It occurs most frequently following distal radial fractures with shortening, but can also be secondary to a primitive length discrepancy between a short radius and a long ulna (positive ulnar variance). Symptoms and clinical findings, even though characteristic, are not specific. Standard X rays show a positive ulnar variance, and sometimes a hyperpressure cyst in the lunate. CT arthroscan and MRI studies demonstrate indirect signs of hyperpressure. If medical treatment fails to improve the condition, the choice surgical technique is arthroscopic, allowing debridement of the TFCC central tear, and shortening of the horizontal aspect of the ulnar head.

The stability of quasi-geostrophic ellipsoidal vortices

A vertically standing freely-rotating ellipsoidal vortex of uniform anomalous potential vorticity in a rotating stratified fluid under quasi-geostrophic conditions of small Rossby and Froude numbers steadily rotates without change of form. The vortex can have arbitrary axis lengths, but must have one axis parallel to the vertical $z$ -axis along the direction of gravity. The rotation rate is proportional to the potential vorticity anomaly but otherwise depends on only two independent aspect ratios characterizing the shape of the vortex. The linear stability of this class of vortex equilibria was first determined semi-analytically more than a decade ago. It was found that vortices are unstable over a wide range of the parameter space and are stable only when strongly oblate and of nearly circular cross-section. New results, presented here, using a complementary approach and backed by nonlinear simulations of the full quasi-geostrophic equations indicate that these ellipsoidal vortices are in fact stable over a much wider range of parameter space. In particular, a mode previously thought to be unstable over much of the parameter space is evidently stable. Moreover, we have determined that this mode is just the difference between two neighbouring equilibrium states having slightly different horizontal aspect ratios; hence, this mode must be neutrally stable. Agreement is found for all other modes. However, by an independent analysis considering only ellipsoidal (though time-varying) disturbances, we have identified one unstable mode as purely ellipsoidal, i.e. it does not change the form of the ellipsoid, only its shape. Under this instability, the vortex quasi-periodically tilts over while undergoing mild changes in shape. The range of parameters leading to non-ellipsoidal instabilities turns out to be narrow, with instability principally occurring for highly eccentric (horizontally squashed, prolate) vortices. The long-term fate of these instabilities is examined by nonlinear contour-dynamical simulations. These reveal a wealth of complex phenomena such as the production of a sea of small-scale vortices, yet, remarkably, the dominant vortex often tends to relax to a stable rotating ellipsoid.

Elliptical-inertial instability of rotating Karman vortex streets

Clouds often reveal a small-scale vortex shedding in the wake of mountainous islands. Unlike the classical bidimensional Karman street, these observed vortex streets are affected by the earth’s rotation and vertical stratification of the atmosphere. These effects induce a selective destabilization of anticyclonic vorticity regions. It is well known that inertial instability, also called centrifugal instability, induces a three-dimensional destabilization of anticyclonic vortices when the absolute vorticity is larger than the local Coriolis parameter. However, we have shown by means of laboratory experiments, that it is a different type of instability which is mainly responsible for the secondary destabilization of rotating Karman streets. A series of experiments were performed to study the wake of a cylinder in a rotating deep water layer, at a medium Reynolds number and an order one Rossby number. We have shown that the unstable mode is a core-centered perturbation and its vertical wavelength strongly depends on the Rossby number. These dynamical characteristics are the signature of an elliptical instability in rotating flows. We have also checked that an asymptotic instability criterion, valid around an elliptical stagnation point, was satisfied in the early stage of shedding when the anticyclonic boundary layer detaches and rolls up in elliptical structures. Similar asymmetric Karman streets were also found in the shallow-water configuration when the vertical to horizontal aspect ratio is close to unity.

A numerical study of the run‐up generated by three‐dimensional landslides

A large set of numerical experiments are designed to examine the maximum run‐up generated by three‐dimensional (3‐D) submerged and subaerial, solid body landslides. A depth‐integrated numerical model is utilized, allowing for the efficient simulation of landslides in shallow and intermediate water. Six dimensionless parameters are introduced: the slide thickness, the slide wave number, a slide shape parameter, the horizontal aspect ratio of the slide, the specific gravity of the slide mass, and the slope of the beach. Six sets of simulations are first presented, wherein one of the six dimensionless parameters are singularly varied. This allows for the identification of parameter dependence on maximum run‐up. After combining the dependencies a number of relationships appear. Most notably, a very clear division between the near and far field is observed, where here the far field is defined as the region displaced from the projection of the landslide, on the nearby beach, where edge waves may dominate the wave pattern. For submerged slides a nondimensional estimation of the maximum run‐up just landward of the slide is found as well as the location and magnitude of the secondary run‐up peak. This secondary peak is due to the propagation of edge waves and is in some cases larger than the peak immediately landward of the slide. The results presented in this paper may be useful for preliminary hazard assessment, where a simple and quick estimation of the maximum run‐up height and locations are required. Additionally, the formulas developed will be particularly beneficial to those developing 3‐D landslide experiments.

Topographic amplitude dependence of internal wave generation by tidal forcing over idealized three‐dimensional topography

This numerical study using the Princeton Ocean Model investigates the conversion of energy from an eastward propagating surface tide to the internal wave field as an oscillating tidal current flows over and around idealized three‐dimensional Gaussian seamounts. In particular, the relationship between the energy flux in the internal wave field and the height of the topography is explored using a range of horizontal aspect ratios. In agreement with theory, the energy flux is found to increase as the square of the topographic amplitude ho for subcritical topography. For supercritical topographies the functional relationship is more complex aspect ratio dependent. It increases more rapidly than ho2 for near‐critical topography. For larger circular seamounts the energy flux increases much more slowly, with the rate of increase dropping with amplitude. As the seamounts are elongated in the cross‐tidal wave (north‐south) direction the energy flux increases more rapidly with height and, for a two‐dimensional ridge, increases as approximately ho2.2. The directional dependence of the energy flux also depends on the aspect ratio and amplitude of the seamount. For circular seamounts, energy flux has its maximum in directions between 20° and 45° counterclockwise from the east‐west axis (Northern Hemisphere). For elongated seamounts the energy flux is directed in the east‐west direction.

Oscillatory Marangoni convection in binary mixtures in square and nearly square containers

Three-dimensional simulations of oscillatory convection in binary mixtures driven by the Marangoni effect have been performed. The upper surface of the fluid is heated by a constant heat flux while the bottom is maintained at a constant temperature. Surface deflection is ignored. Oscillations are the result of concentration-induced changes in the surface tension due to the presence of an anomalous Soret effect. In domains with a square horizontal cross section and aspect ratio Γ=1.5 these take the form of either a standing wave with left–right reflection symmetry or a discrete rotating wave, depending on the separation ratio and the Schmidt number. Standing oscillations with reflection symmetry in a diagonal are unstable. When the cross section is slightly rectangular only the former bifurcate from the conduction state, and the transition to stable rotating waves with increasing Marangoni number proceeds via a sequence of secondary local and global bifurcations. The results are interpreted in terms of predictions from equivariant bifurcation theory.

On the amphidromic structure of inertial waves in a rectangular parallelepiped

Enclosed rotating homogeneous fluids support waves that are restored by Coriolis forces. These waves propagate obliquely through the fluid under a fixed angle with respect to the rotation axis which is set by the ratio of the frequency of the wave and the inertial frequency (twice the angular frequency of the tank). In the particular case that boundaries are either parallel, or perpendicular to the rotation axis, eigenmodes may be expected. An example is Kelvin's (1880) axial can. However, the spatial structure of these waves can still be quite complicated, as shown here for waves in a ‘horizontal’ rectangular parallelepiped. The container's rigid horizontal top and bottom surfaces allow for modal expansion in the vertical, each mode being governed by the ‘inertial’ analogs of surface Poincaré and Kelvin waves. Combining these, as in the Taylor problem of reflecting surface Kelvin waves, one finds both the eigenfrequencies as well as the typical amphidromic structure (phase lines circling around nodal points) of the resulting inertial wave pattern in dependence of the remaining two parameters: the horizontal and vertical aspect ratios. This entails the approximative determination of eigenvalues of an infinite matrix equation, obtained with the Proudman–Rao method. It appears that certain specific frequencies persist as eigenfrequency for different aspect ratios, albeit belonging to different eigenmodes. Surprisingly, these correspond to the eigenfrequencies of an infinitely long channel of waves lacking along-channel structure. Inertial wave patterns are presented by means of the amplitude and phase of the internal elevation field (related to the axial velocity component) and of the two horizontal velocity components. These reveal predominant anticyclonic turning of phase and currents; maximum elevation and current amplitudes detached from the solid walls; and, occasionally, a nearly sloshing type of response (nodal lines, instead of points).

Inference of geometrical and behavioural parameters of individual fish from echo-trace-analysis

The volume scattering strength of swim-bladdered fish is very sensitive to fish size, shape, and orientation. However, the appropriate geometrical and behavioral parameters necessary to determine these parameters are not always available. Inadequate knowledge of these parameters limits our ability to correctly estimate lengths and abundances of fish with acoustic technology. A method for extracting geometrical and behavioral parameters of individual fish using a scattering model-based echo-trace-analysis (ETA) is presented. The scattering model used in the ETA is based on the Kirchhoff approximation and a prolate spheroid is used to approximate the shape of the swimbladder. The geometric shape of a resolved echo from an individual fish is used in a least-squares algorithm to infer information about the swimming speed, direction, and orientation of the fish. The acoustic intensity distribution of an individual fish along a resolved echo trace is used in a least-squares algorithm to infer information about the size, aspect ratio, and orientation of the swimbladder. Results from the ETA were more sensitive to variations in vertical swimming speed and orientation of the swimbladder than to variations in horizontal swimming speed and aspect ratio of the swimbladder. The proposed ETA was applied to field data, a 38 kHz echogram of a school of Atlantic cod recorded with a Simrad EK500 echo sounder. The inferred sizes and orientations of a number of the resolved echo traces for individual fish were consistent with available observation data. One of the advantages of the ETA method presented here is that it can be easily extended to a dual beam, a split-beam, or a multi-beam acoustic system.

Simultaneous MST radar and radiosonde measurements at Gadanki (13.5°N, 79.2°E) 1. Causative mechanism and characteristics of radar backscatterers at VHF

Simultaneous MST radar and radiosonde observations have been carried out from Gadanki (13.5°N, 79.2°E), a tropical station in India. The radar measurements are used to obtain winds, vertical shear of horizontal winds (S), reflectivity (η), aspect sensitivity and horizontal correlation length (ζ) of the radar backscatterers. The radiosonde measurements of pressure, temperature and humidity are utilized for the computations of Brunt Vaisala frequency (N) and potential refractive index gradient (M). These measurements are used to understand the characteristics of the radar backscatterers in terms of prevailing background atmospheric conditions. Observations show strong vertical shears of horizontal winds in the height range of 16–18 km, at the upper edge of the tropical easterly jet (TEJ) associated winds. Results show that these shears and N2 both contribute to enhance the echo power in oblique directions (χ = 10°). The oblique beam observed enhancement of echo power, due to enhanced wind shears, is noticed to be confined to a narrow height range and associated backscatterers are more or less isotropic. At the height where N2 (or MD2) contribution to oblique echo power is significant, the radar backscatterers appear to be relatively more anisotropic with the horizontal correlation length (ζ) of 16–20 m. Present observations thus bring out clearly that even at oblique beam with zenith angle χ = 10° contribution of enhanced N2 to radar reflectivity (η) from refractivity structure with correlation length of ∼10–20 m can be very significant especially at the height above 17.5 km. These results have to be necessarily taken into account while interpreting the observed radar reflectivity observations.