Earth Geometry Research Articles

Utilizing Euler poles for the evaluation of plate rigidity in numerical mantle convection models

SUMMARY Evidence that the Earth’s surface is divided into a tessellation of piece-wise rigidly translating plates is the primary observation supporting the solid-state creep-enabled convection paradigm, utilized to investigate evolution of the Earth’s mantle. Accordingly, identifying the system properties that allow for obtaining dynamically generated plates remains a primary objective in numerical global mantle convection simulations. The first challenge for analysing fluid dynamic model output for the generation of rigid plates is to identify candidate plate boundaries. Here, we utilize a previously introduced numerical tool for plate boundary detection which uses a user specified threshold (tolerance) to automatically detect candidate plate boundaries. The numerical tool is applied with different sensitivities, to investigate the nature of the surface velocity fields generated in three calculations described in earlier work. The cases examined differ by the values that they specify for the model yield stress, a parameter that can allow the formation of tightly focussed bands of surface deformation. The three calculations we examine include zones comprising possible plate boundaries that are characterized by convergence, divergence and strike-slip behaviour. Importance of the potential plate boundaries is assessed by examining the rigidity of the inferred model generated plates. The rigidity is measured by comparing the model velocities to the rigid rotation velocities implied by the statistically determined Euler poles for each candidate plate. We quantify a lack in rigidity by calculating a deformity field based on disagreement of actual surface velocity with rotation about the Euler pole. For intermediate yield stress and boundary detection threshold value, we find that the majority of the model surface can translate almost rigidly about distinct plate Euler poles. Regions that conform poorly to large-scale region rigid translation are also obtained but we find that generally these regions can be decomposed into subsets of smaller plates with a lower tolerance value. Alternatively, these regions may represent diffuse boundary zones. To clarify the degree to which the mantle convection model behaviour shows analogues with Earth’s current-day surface motion, we apply the plate boundary detection and Euler pole calculation methods to previously published terrestrial strain-rate data. Strong parallels are found in the response of the terrestrial data and mantle convection calculations to the threshold value, such that appropriate choice of that parameter results in very good agreement between observations and convection model character. We conclude that plates generated by fluid dynamic convection models can exhibit motion that is markedly rigid, and define statistics (plateness) and fields (deformity) by which the generation of self-consistently determined plate rigidity can be quantified, as well as describing how plate recognition might be optimized. We also note that in agreement with the Earth’s current state, we obtain a dozen dominant plates in the case exhibiting the most plate-like (rigid) surface, suggesting that this approximate number of plates is perhaps intrinsic to the geometry, surface area and physical properties of Earth’s mantle.

Re-evaluating falls through skylights in the USA: has anything changed?

Purpose With proper design and work planning, falls through fragile skylights are preventable. Skylights pose a hazard to workers when their work tasks for operations, maintenance and repair require them to be on roofs. The National Institute of Occupational Health and Safety produced guidelines and special alerts to address the dangers that are present around skylights, and the Occupational Safety and Health Administration regulations have prescriptive requirements for work performed around skylights, and yet incidents still occur. The purpose of this study is to investigate and raise awareness for the causality of the incidents involving skylights in the USA. Design/methodology/approach The authors investigated and analyzed 204 incidents involving skylights recorded by the Bureau of Labor Statistics to characterize their nature and to determine any correlation with the roof environment or the nature of the work performed. Using Google Earth and Google Maps roof geometry, proximity of skylights to roof edge and rooftop mechanical equipment was determined. Findings The majority of falls through skylights occur during roof maintenance and repair activities. Falls through skylights are underreported. Because of a general lack of good design to reduce or eliminate the risk of falling through skylights, facility managers carry the burden to properly assess work and access on roofs where fragile skylights are present. Originality/value The phenomenon of falling through skylights was made aware on a national level in the USA in 1989; however, little has been done from a design and planning perspective to reduce these incidents. This paper presents a unique perspective on the role of facility managers in understanding the hazards associated with roof maintenance near skylights.

Reconstructing the Paleoproterozoic Heart of Nuna, from Fennoscandia to Northeastern Laurentia

Abstract Accurate palaeogeographical reconstructions of past supercontinents are necessary to test models of supercontinent cyclicity, secular variation in plate tectonics and mantle geodynamics. However, numerous factors limit our ability to reconstruct past supercontinents as is evident in the ongoing debates regarding the construction phase and geometry of Earth's most recent supercontinent, late Paleozoic to early Mesozoic Pangaea. An important factor in these debates, and a focus of our study is how best to palinspastically restore, in section and in plan-view, the orogenic belts along which supercontinents were stitched together. We utilize the orogenic belts spanning Baffin Island, Greenland and Fennoscandia that are inferred to record the assembly of the Paleoproterozoic supercontinent Columbia to test the accepted reconstruction of the Nuna core of Columbia. We show that as reconstructed in the Nuna model, each of Baffin Island, Greenland (with some complications) and Fennoscandia are characterized by an older cratonic backstop that gives way to younger accretionary complexes toward the inferred oceanic domain that lay to the south and which is inferred to have closed by subduction beneath northeastern Laurentia–Fennoscandia during Columbia assembly. This southward transition from cratonic backstop to accretionary orogen is a hallmark of upper plates in modern convergent plate margins and is consistent with the construction of the Columbia supercontinent, including its Nuna core, through plate tectonic processes, and provides a broad validation of the Nuna reconstruction and hence for Columbia as a whole. Map view curvature of the cratonic backstops is restricted to long wavelength, open bends consistent with the Archean crust having been characterized by significant lithospheric strength. The more accretionary southern portions of Nuna are, however, characterized by sinuous orogens that developed by oroclinal bending of formerly more linear belts, significantly complicating their palinspastic restoration and rendering detailed correlation of juvenile orogenic belts across Nuna problematic.

Viscoelastic Response of a Self‐Gravitational Spherical Earth to Shear Dislocation Obtained Using the Fixed‐Talbot Method

AbstractViscoelastic dislocation theory is important to understanding fundamental geodynamics and validating numerical models in the study of earthquake deformation. Available mathematical solutions differ in assumed Earth geometry and formulation of gravity terms, but the main challenge they commonly face is Inverse Laplace Transform (ILT). Limitations in previously used ILT methods tend to degrade the performance and/or accuracy of the solutions. To overcome these limitations, we have derived new Green's functions for a layered spherical Earth based on the Fixed‐Talbot ILT method. The new solution uses a precise density‐gravity relation, includes pre‐stress advection, buoyancy, and self‐gravitation, invokes the bi‐viscous Burgers rheology, and yields deformational and gravitational changes both at the surface and in the interior of the Earth. The Fixed‐Talbot ILT method, which involves a left‐open parabolic integration path in the complex plane, greatly improves computing efficiency and allows convenient use of a large number of Earth layers. Comparison with other existing solutions demonstrates the excellent performance of the new solution. Taking the postseismic deformation of the 2004 Sumatra Mw 9.2 earthquake as an example, we illustrate how to integrate numerically our Green's functions to represent realistic slip distribution over a three‐dimensionally curved fault. The combination of computational efficiency, mathematical completeness in modeling gravitational effects, adaptability to any radial structure of the Earth, and ability to provide results at any depth including the surface enables a powerful tool for forward and inverse modeling of viscoelastic earthquake cycles in a self‐gravitating spherical Earth.

Parametric nonstationary covariance functions on spheres

Gaussian Processes are powerful tools for modelling spatial data. In this context, a significant amount of modelling focus is placed on specifying the covariance function, which is required to be symmetric and positive definite. Covariance functions have classically been defined and used in Euclidean space. However, as data collected from the globe becomes more prevalent, accounting for Earth's geometry becomes increasingly important. Using Euclidean distance can be suboptimal for these data. We survey the literature for recent developments related to construction of nonstationary covariance functions on spheres, which historically has been a challenging area. We present contributions in this effort by providing three general forms for families of parametric nonstationary covariance functions.

Unique NISTAR-Based Climate GCM Diagnostics of the Earth’s Planetary Albedo and Spectral Absorption Through Longitudinal Data Slicing

Deep Space Climate Observatory (DSCOVR) measurements of Earth’s reflected solar and emitted thermal radiation permit a unique model/data comparison perspective that is not readily available from other satellite data. The key factor is the unique Lissajous orbital viewing geometry from the Lagrangian L1 point, which enables a continuous view of Earth’s sunlit hemisphere. The National Institute of Standards and Technology Advanced Radiometer (NISTAR) is the DSCOVR Mission energy budget instrument, which views the reflected and emitted radiation of the Earth’s sunlit hemisphere by means of single pixel active cavity full-spectrum (Band-A, 0.2–100 μm) and filtered solar wavelength (Band-B, 0.2–4.0 μm; and Band-C, 0.7–4.0 μm) radiometer measurements. An additional solar wavelength photodiode channel (0.3–1.1 μm) provides a calibration reference. The objective of this study is the assessment of climate GCM performance via direct model/data comparisons. Such comparisons are difficult due to quasi-chaotic natural variability present in real-world observational data and in climate GCM simulations. This is where the unique DSCOVR viewing geometry makes possible the longitudinal data slicing methodology for more direct model/data comparison. The key point of the longitudinal slicing approach is that data integration over the entire sunlit hemisphere eliminates the quasi-chaotic meteorological weather-scale noise, while preserving intra-seasonal and planetary-scale variability. The rotation of the Earth that retrieves this climate-style, large-scale longitudinal and seasonal variability. The hemispheric averaging is accomplished automatically in NISTAR measurements with its single-pixel view of the Earth. For climate GCMs, this requires implementing the Sunlit Hemisphere Sampling (SHS) scheme to operate on the GCM run-time output data, utilizing the DSCOVR Satellite Ephemeris data to assure precise viewing geometry between NISTAR measurements and GCM output data, while averaging out the meteorological weather noise. However, GCM generated data are radiative fluxes, while NISTAR (and EPIC) measurements are near-backscattered radiances. Conversing NISTSR measurements into radiative fluxes cannot be accomplished using NISTAR data alone, even with detailed support from conventional satellite data. But the identical viewing geometry of Earth’s sunlit hemisphere, and synergistic analyses of EPIC data make it feasible for this conversion of NISTAR near-backscatter radiances into radiative fluxes.

Forward modeling of magnetotellurics using Comsol Multiphysics

Magnetotellurics is an electromagnetic geophysical method that has been widely used to study structures in Earth's subsurface. Numerical modeling of magnetotellurics is important for survey design, inversion, geological interpretation and many other aspects of geophysical studies. For example, modeling a subsurface conductive body in terms of its conductivity, geometry and dipping angle would yield substantial information on the phase response and sensitivity in an MT survey. While there are many different modeling techniques, the finite element method is most commonly used. In this effort, we present magnetotelluric models of layered Earth, uplift structures, auroral electrojets, and geomagnetically induced currents in power-line skywires using the commercial finite-element package Comsol Multiphysics. The AC/DC module in Comsol can be used to solve Maxwell's equations in the quasi-static limit for modeling the magnetotelluric response. One of the advantages of Comsol modeling is its Graphical User Interface (GUI), which allows users to solve complex single or multi-physics problems in a meshed domain. The use of Comsol also reduces the need for sophisticated computer coding when solving partial differential equations such as Maxwell's equations. In the effort presented here, we first discuss model validation for layered Earth geometries. We then present two examples of magnetotellurics modeling in impact crater and geomagnetically induced current studies. Numerical results were compared with analytical solutions or benchmark results whenever possible.

Channel Modeling and Performance Analysis of Airplane-Satellite Terahertz Band Communications

Wireless connectivity in airplanes is becoming more important, demanded, and common. One of the largest bottlenecks with the in-flight Internet is that the airplane is far away from both the satellites and the ground base stations during most of the flight time. Maintaining a reliable and high-rate wireless connection with the airplane over such a long-range link thus becomes a challenge. Microwave frequencies allow for long link distances but lack the data rate to serve up to several hundreds of potential onboard customers. Higher bands in the millimeter-wave spectrum (30 GHz–300 GHz) have, therefore, been utilized to overcome the bandwidth limitations. Still, the per-user throughput with state-of-the-art millimeter-wave systems is an order of magnitude lower than the one available with terrestrial wireless networks. In this paper, we take a step further and study the channel characteristics for the terahertz band (THz, 0.3 THz–10 THz) in order to map the feasibility of this band for aviation. We first propose a detailed channel model for aerial THz communications taking into account both the non-flat Earth geometry and the main features of the frequency-selective THz channel. We then apply this model to estimate the characteristics of aerial THz links in different conditions. We finally determine the altitudes where the use of airplane-to-satellite THz connection becomes preferable over the airplane-to-ground THz link. Our results reveal that the capacity of the airborne THz link may reach speeds ranging from 50–150 Gbps, thus enabling cellular-equivalent data rates to the passengers and staff during the entire flight.

Comparison of the Lunar Models Using the Hyper-Spectral Imager Observations in Lijiang, China

A lunar observation campaign was conducted using a hyper-spectral imaging spectrometer in Lijiang, China from December 2015 to February 2016. The lunar hyper-spectral images in the visible to near-infrared region (VNIR) have been obtained in different lunar phases with absolute scale established by the National Institute of Metrology (NIM), China using the lamp–plate calibration system. At the same time, the aerosol optical depth (AOD) is measured regularly by a lidar and a lunar CE318U for atmospheric characterization to provide nightly atmosphere extinction correction of lunar observations. This paper addressed the complicated data processing procedure in detail from raw images of the spectrometer into the spectral lunar irradiance in different lunar phases. The result of measurement shows that the imaging spectrometer can provide lunar irradiance with uncertainties less than 3.30% except for absorption bands. Except for strong atmosphere absorption region, the mean spectral irradiance difference between the measured irradiance and the ROLO (Robotic Lunar Observatory) model is 8.6 ± 2% over the course of the lunar observation mission. The ROLO model performs more reliable to clarify absolute and relative accuracy of lunar irradiance than that of the MT2009 model in different Sun–Moon–Earth geometry. The spectral ratio analysis of lunar irradiance shows that band-to-band variability in the ROLO model is consistent within 2%, and the consistency of the models in the lunar phase and spectrum is well analyzed and evaluated from phase dependence and phase reddening analysis respectively.

Seasonal Variations of Impedance in the Ionospheric Plasma

The ionosphere is an ionized layer that extends between 50 km and 1000 km altitudes in the atmosphere. It plays an important role in atmospheric electricity. The ionosphere has the number of electrically charged particles and thus, it affects the propagation of the radio waves. In this study, magnitudes of impedance for different seasons and different geomagnetic activity periods in the ionospheric plasma are calculated using the real geometry of Earth. It is observed that the impedance of the ionospheric plasma in all directions generally has high values for all seasons. The diagonal components of the tensor of the impedance are greater than the other components. It is also observed that the ionospheric plasma, generally, has weak conductivity in all directions and seasons. Impedance varies inversely with electron density. Hence, geomagnetic activity periods which lead to an increase in electron density decreases the impedance. It is observed that the ionospheric plasma has a reactive character in the geographic coordinates where the study was performed. The ionosphere displays a dielectric structure.

Controlling the Chirping of Chorus Waves via Magnetic Field Inhomogeneity

AbstractWhistler mode chorus waves are coherent electromagnetic emissions in planetary magnetospheres, characterized by rising‐tone or falling‐tone chirping elements. Understanding the cause of different chirping directions and their properties is an important step in resolving the long‐standing problem of nonlinear chorus generation. We report here, for the first time, particle‐in‐cell simulations of bidirectional chirping of whistler waves in a uniform magnetic field and falling‐tone‐only chirping in an inhomogeneous field. Combined with previous simulations of rising‐tone‐only emissions, we demonstrate that the background magnetic field inhomogeneity is not required for chirping of chorus, but it plays a key role in determining the chirping direction. The findings of the present work also unveil the critical role of the dipole geometry of Earth's magnetic field in causing the statistical predominance of rising‐tone chorus and the oblique propagation of falling‐tone chorus.

Coseismic and post-seismic gravity disturbance induced by seismic sources using a 2.5-D spectral element method

SUMMARYI present a prescription for computing free-air coseismic and post-seismic gravity changes induced by seismic sources in a viscoelastic earth model. I assume a spherical earth geometry and a 2.5-D calculation, that is, 3-D motions that satisfy the equations of quasi-static equilibrium on a 2-D viscoelastic structure. The prescription permits application to regional gravity computations where a 2-D structure adequately represents the structural heterogeneity. I use a hybrid approach where deformation is computed on a discretized domain and the resulting density perturbations are expanded with spherical harmonics to produce the free-air gravity field. Starting with a solution to the equations of quasi-static displacements in the Laplace transform domain for a given dislocation source, I solve Poisson’s equation using Lagrangian interpolation on spectral element nodes to compute the required deformation quantities that contribute to free-air gravity. A numerical inverse Laplace transform then yields time domain results. This methodology is tested with analytic solutions on a spherically stratified viscoelastic structure, then applied to evaluate the effect of a descending slab of relatively high viscosity on post-seismic gravity in a megathrust faulting setting.

Effects of Temporal Sampling Interval on the Moon-Based Earth Observation Geometry

The effects of temporal sampling interval on the moon-based earth observation geometry are analyzed in this study based on three observation angles, namely viewing zenith angle, solar zenith angle, and relative azimuth angle. According to the definitions of these three angles, the calculation method for these angles and their variations between adjacent temporal samplings are deduced. Furthermore, the effects of the different positions of the lunar surface on the observation angles are derived. The results show that the variations of the nadir point and subsolar point determine the variations of the viewing zenith angle and solar zenith angle, respectively, whereas the relative azimuth angle needs to consider the relative variations of the moon-based platform's nadir point and the subsolar point. By evaluating the variations of these three observation angles, it is found that the effects of the temporal sampling interval will have significant impacts on the relative azimuth angle of the observed points at mid-low latitude regions, especially near the regions of the moon-based platform's nadir point and the subsolar point. In conclusion, the observation angles can characterize the moon-based earth observation geometry, and enlarging the temporal sampling interval will lead to the obvious impacts on the observation geometry in the mid-low latitude regions, especially the loss of the sampling of the relative azimuth angle.

Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates

We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are of paramount importance for the modeling of realistic flows, that is, flows that are observed in some averaged sense in the ocean. Owing to the employment of spherical coordinates we do not need to resort to approximations (e.g., of f- and β-plane type) that simplify the geometry in the governing equations. Our explicit solution represents a steady purely azimuthal stratified flow with a free surface that—thanks to the inclusion of forcing terms and the consideration of the Earth’s geometry via spherical coordinates—makes it suitable for describing the Antarctic Circumpolar Current and enables an in-depth analysis of the structure of this flow. In line with the latter aspect, we employ functional analytical techniques to prove that the free surface distortion is defined in a unique and implicit way by means of the pressure applied at the free surface. We conclude our discussion by setting out relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations.

Расчет скорости ионизации вещества атмосферы Земли протонами галактических и солнечных космических лучей

This paper explores the applied use of the RUSCOSMICS software package [http://ruscosmics.ru] designed to simulate propagation of primary cosmic ray (CR) particles through Earth’s atmosphere and collect information about characteristics of their secondary component. We report the results obtained for proton fluxes with energy distributions corresponding to the differential spectra of galactic CR (GCR) and solar CR (SCR) during ground level enhancement (GLE) events GLE65 and GLE67. We examine features of the geometry of Earth’s atmosphere, parametrization methods, and describe a primary particle generator. The typical energy spectra of electrons obtained both for GCR and for GLE65 provide information that allows us to quantitatively estimate the SCR contribution to the enhancement of secondary CR fluxes. We also present altitude dependences of ionization rate for GCR and both the GLE events for several geomagnetic cutoff rigidity values. The conclusion summarizes and discusses the prospects for future research.

Calculating the ionization rate induced by GCR and SCR protons in Earth’s atmosphere

This paper explores the applied use of the RUSCOSMICS software package [http://ruscosmics.ru] designed to simulate propagation of primary cosmic ray (CR) particles through Earth’s atmosphere and collect information about characteristics of their secondary component. We report the results obtained for proton fluxes with energy distributions corresponding to the differential spectra of galactic CR (GCR) and solar CR (SCR) during ground level enhancement (GLE) events GLE65 and GLE67. We examine features of the geometry of Earth’s atmosphere, parametrization methods, and describe a primary particle generator. The typical energy spectra of electrons obtained both for GCR and for GLE65 provide information that allows us to quantitatively estimate the SCR contribution to the enhancement of secondary CR fluxes. We also present altitude dependences of ionization rate for GCR and both the GLE events for several geomagnetic cutoff rigidity values. The conclusion summarizes and discusses the prospects for future research.

Design of Solar Power LED Lighting System using Horizontal Two-Axis Arduino Based Solar Tracking System

The project deals with design of solar power LED lighting system using Horizontal Two-Axis Arduino based Solar Tracking System. The main goal of this project is to design a very precise solar tracker. The project is divided into two parts; hardware and software. Hardware part generally composed of solar panel, two-DC motors with gearbox, LDR sensor module and electronic circuit. Software part represents the thinking behavior of the system, that is how the system acting under several weather conditions. In this work sensing of the sun position carried out in two stages primary and secondary. Primary stage or indirect sensing performed via sun-earth relationship as a coarse adjustment and second stage or direct sensing performed via set of LDR sensors as output tuning to trims the azimuth and altitude angles. If the weather is cloudy or dusty, the tracking system uses primary stage or sun-earth geometrical relationships only to identify the location of the sun; so the system tracks the position of the sun regardless the weather condition. The energy extracted from photovoltaic (PV) or any solar collector depends on solar irradiance. For maximum extraction of energy from the sun, the solar collector panel should always be normal to the incident radiation Solar trackers moves the solar collector to follow the sun path and keeps the orientation of the solar collector at an optimal tilt angle. Solar tracking system improves substantially the energy efficiency of photovoltaic (PV) panel. In this paper, an automatic dual axis solar tracking system is designed and developed using Light Dependent Resistor (LDR) and DC motors on a mechanical structure with gear arrangement. Two axis solar tracking (azimuth angle as well as altitude angle) is implemented through Arduino UNO controller based on Sun Earth Geometry. The results indicated that the automatic solar tracking system is more reliable and efficient than fixed one.

Diffusivity-Factor Approximation for Spectral Outgoing Longwave Radiation

Abstract Accurate integration of directional radiance shows that the conventional diffusivity-factor approximation with a constant diffusivity angle results in an overestimation of the outgoing longwave radiation (OLR) in the window band and an underestimation in the absorption band. We propose an analytical estimation of a spectrally dependent diffusivity angle for clear-sky spectral OLR, considering actual atmospheric conditions and realistic optical path geometry. Beginning with the plane-parallel geometry, we present a new, physical explanation of the conventional diffusivity angle that applies to the gas absorption bands and derives an alternative solution for the window bands. Then a correction scheme is developed to account for the impact of the spherical Earth geometry on the diffusivity angle. The proposed method achieves higher accuracy, reducing biases to generally less than 2% in all spectral regions.

100 Years of Progress on Mountain Meteorology Research

ABSTRACTMountains significantly influence weather and climate on Earth, including disturbed surface winds; altered distribution of precipitation; gravity waves reaching the upper atmosphere; and modified global patterns of storms, fronts, jet streams, and climate. All of these impacts arise because Earth’s mountains penetrate deeply into the atmosphere. This penetration can be quantified by comparing mountain heights to several atmospheric reference heights such as density scale height, water vapor scale height, airflow blocking height, and the height of natural atmospheric layers. The geometry of Earth’s terrain can be analyzed quantitatively using statistical, matrix, and spectral methods. In this review, we summarize how our understanding of orographic effects has progressed over 100 years using the equations for atmospheric dynamics and thermodynamics, numerical modeling, and many clever in situ and remote sensing methods. We explore how mountains disturb the surface winds on our planet, including mountaintop winds, severe downslope winds, barrier jets, gap jets, wakes, thermally generated winds, and cold pools. We consider the variety of physical mechanisms by which mountains modify precipitation patterns in different climate zones. We discuss the vertical propagation of mountain waves through the troposphere into the stratosphere, mesosphere, and thermosphere. Finally, we look at how mountains distort the global-scale westerly winds that circle the poles and how varying ice sheets and mountain uplift and erosion over geologic time may have contributed to climate change.

Projection Techniques for Altitude Estimation Over Complex Multipath Condition-Based VHF Radar

In very high-frequency (VHF) radar, the performance of low-angle target tracking is strongly affected by multipath phenomenon, especially in the case of complex terrain where exact information of reflection paths is unknown. To deal with this problem, a practical multipath signal model for VHF radar in complex terrain is presented, where both curved earth geometry and actual ground surface reflection coefficient are considered. Then, a novel altitude estimation technique based on alternating projection is proposed, where the motion or Doppler shift of a target is neglected during the observation time of one coherent processing interval. The technique applies to vertical antenna arrays which perform an interferometric estimation of the target elevation angle. Simulation results and real data analysis show that the target tracking accuracy can be efficiently improved by using the proposed algorithm under both simple and complex multipath scenarios.