Numerical modeling of the thermal state of Earth after the Moon-forming impact event

Planetary collisions play an important role in the compositional and thermal evolution of planetary systems and such collisions are caracteristics of the final stage of planetary formation. The Moon-forming impact event is thought to (re)set the conditions for the subsequent thermochemical evolution of Earth and Moon. Large parts of proto-Earth are thought to melt as a consequence of the impact [e.g.1] and the extent of melting affects the evolution of the Earth&#8217;s interior and atmosphere. It is then critical to address the initial conditions of the proto-Earth and the volume and shape of a possible magma ocean after the impact. Previously, the Moon-forming giant impact was modeled with mesh-free so-called smoothed particle hydrodynamics (SPH [1, 2, 3]). In this study, we, in contrast, carried out numerical simulations of the Moon-forming impact event considering different impact scenarios with the three-dimensional (3D) iSALE code [4, 5], that tends to be more accurate in the description of thermodynamics and shock waves than SPH simulations. We also compare simulation results from our iSALE code with SPH models for benchmarking ([1]) because SPH uses self-gravity, whereas iSALE uses central gravity. We vary the impact angle (15&#176; to 90&#176;) and impact velocities (12 to 20 km/s). In order to quantify the volume of impact-induced melt, we use the so-called peak-shock pressure approach (&#8216;Tracer method&#8217;) that has been used in several modeling studies [6,7] and is described in more detail by [8]. The benchmark study shows a good agreement of the two different numerical approaches with respect to pressure evolution. However the production of a magma ocean show some differences that need to be further explored, with notably the effects of considering central gravity instead of self-gravity into iSALE 3D simulations. &#160; Acknowledgments: We gratefully thank the iSALE developers, including Gareth Collins, Kai W&#252;nnemann, Dirk Elbeshausen, Boris Ivanov and Jay Melosh and Thomas Davison for the development of the pysaleplot tool. We also thank the Deutsche Forschungsgemeinschaft (SFB-TRR 170, subproject C2 and C4) for funding. &#160; References:[1] Nakajima M. and Stevenson D. J. (2015) EPSL, 427, 286-295. [2] Canup R. M. et al. (2013) ICARUS 222, 200-219. [3] Canup R, M. (2004) Science 338, 1052-1054. [4] Collins G. S. et al. (2004) Meteoritics & Planet. Sci., 39, 217-231. [5] W&#252;nnemann K. (2006) ICARUS 180, 514-527. [6] W&#252;nnemann K. et al. (2008) EPSL 269, 529-538. [7] Pierazzo et al. (1997) ICARUS 127, 408-423. [8] Manske L. et al. (2018) 49th LPSC, abstract# 2269.[11] Pierazzo and Melosh (1999) EPSL 165, 163-176

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Fixed-time three-dimensional guidance law with input constraint and actuator faults

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410020971973 ◽

2020 ◽

pp. 095441002097197

Author(s):

Peng Li ◽

Qi Liu ◽

Chen-Yu He ◽

Xiao-Qing Liu

Keyword(s):

Fault Tolerant ◽

Sliding Mode ◽

Input Saturation ◽

Three Dimensional ◽

Impact Angle ◽

Actuator Faults ◽

Input Constraint ◽

Guidance Law ◽

The Impact ◽

Impact Angle Constraint

This paper investigates the three-dimensional guidance with the impact angle constraint, actuator faults and input constraint. Firstly, an adaptive three-dimensional guidance law with impact angle constraint is designed by using the terminal sliding mode control and nonhomogeneous disturbance observer. Then, in order to solve the problem of the input saturation and actuator faults, an adaptive anti-saturation fault-tolerant three-dimensional law is proposed by using the hyperbolic tangent function based on the passive fault-tolerant control. Finally, the effectiveness of the designed guidance laws is verified by using the Lyapunov function and simulation.

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Linking the core heat content to Earth's accretion history

10.5194/egusphere-egu2020-10540 ◽

2020 ◽

Author(s):

Renaud Deguen ◽

Vincent Clési

Keyword(s):

Thermal State ◽

Thermal Evolution ◽

Heat Content ◽

Magma Ocean ◽

The Core ◽

Current State ◽

Partitioning Coefficients ◽

The Mean ◽

Mantle Diapirism ◽

Do So

The composition of Earth's mantle, when compared to experimentally determined partitioning coefficients, can be used to constrain the conditions of equilibration - pressure P, temperature T, and oxygen fugacity fO2 - of the metal and silicates during core-mantle differentiation. This places constraints on the thermal state of the planet during its accretion, and it is tempting to try to use these data to estimate the heat content of the core at the end of accretion. To do so, we develop an analytical model of the thermal evolution of the metal phase during its descent through the solid mantle toward the growing core, taking into account compression heating, &#160; viscous dissipation heating, and heat exchange with the surrounding silicates. For each impact, the model takes as initial condition the pressure and temperature at the base of the magma ocean, and gives the temperature of the metal when it reaches the core. The growth of the planet results in additional pressure increase and compression heating of the core. The thermal model is coupled to a Monte-Carlo inversion of the metal/silicates equilibration conditions (P, T, fO2) in the course of accretion from the abundance of Ni, Co, V and Cr in the mantle, and provides an estimate of the core heat content at the end of accretion for each geochemically successful accretion. The core heat content depends on the mean degree of metal-silicates equilibration, on the mode of metal/silicates separation in the mantle (diapirism, percolation, or dyking), but also very significantly on the shape of the equilibration conditions curve (equilibration P and T vs. fraction of Earth accreted). We find that many accretion histories which are successful in reproducing the mantle composition yield a core that is colder than its current state. Imposing that the temperature of the core at the end of accretion is higher than its current values therefore provides strong constraints on the accretion history. In particular, we find that the core heat content depends significantly on the last stages of accretion.&#160;

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CIRA/CSU Four-Dimensional Variational Data Assimilation System

Monthly Weather Review ◽

10.1175/mwr2891.1 ◽

2005 ◽

Vol 133 (4) ◽

pp. 829-843 ◽

Cited By ~ 39

Author(s):

Milija Zupanski ◽

Dusanka Zupanski ◽

Tomislava Vukicevic ◽

Kenneth Eis ◽

Thomas Vonder Haar

Keyword(s):

Data Assimilation ◽

Initial Conditions ◽

Control Variable ◽

Three Dimensional ◽

Atmospheric Modeling ◽

Variational Data Assimilation ◽

Regional Atmospheric Modeling ◽

The Impact ◽

Data Assimilation System ◽

Assimilation System

A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Prediction (NCEP) Eta 4DVAR system, however with added improvements addressing its use in a research environment. Preliminary results with RAMDAS are presented, focusing on the minimization performance and the impact of vertical correlations in error covariance modeling. A three-dimensional formulation of the background error correlation is introduced and evaluated. The Hessian preconditioning is revisited, and an alternate algebraic formulation is presented. The results indicate a robust minimization performance.

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Analysis and Forecast of a Tornadic Thunderstorm Using Multiple Doppler Radar Data, 3DVAR, and ARPS Model

Advances in Meteorology ◽

10.1155/2013/281695 ◽

2013 ◽

Vol 2013 ◽

pp. 1-18

Author(s):

Edward Natenberg ◽

Jidong Gao ◽

Ming Xue ◽

Frederick H. Carr

Keyword(s):

Doppler Radar ◽

Initial Conditions ◽

Three Dimensional ◽

Radar Data ◽

Advanced Regional Prediction System ◽

Regional Prediction ◽

Upper Level ◽

Using Data ◽

Nwp Model ◽

The Impact

A three-dimensional variational (3DVAR) assimilation technique developed for a convective-scale NWP model—advanced regional prediction system (ARPS)—is used to analyze the 8 May 2003, Moore/Midwest City, Oklahoma tornadic supercell thunderstorm. Previous studies on this case used only one or two radars that are very close to this storm. However, three other radars observed the upper-level part of the storm. Because these three radars are located far away from the targeted storm, they were overlooked by previous studies. High-frequency intermittent 3DVAR analyses are performed using the data from five radars that together provide a more complete picture of this storm. The analyses capture a well-defined mesocyclone in the midlevels and the wind circulation associated with a hook-shaped echo. The analyses produced through this technique are used as initial conditions for a 40-minute storm-scale forecast. The impact of multiple radars on a short-term NWP forecast is most evident when compared to forecasts using data from only one and two radars. The use of all radars provides the best forecast in which a strong low-level mesocyclone develops and tracks in close proximity to the actual tornado damage path.

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How sensitive are modeled contemporary subsea permafrost thaw and thickness of the methane clathrates stability zone in Eurasian Arctic to assumptions on Pleistocene glacial cycles?

10.5194/cp-2016-66 ◽

2016 ◽

Author(s):

Valentina V. Malakhova ◽

Alexey V. Eliseev

Keyword(s):

Time Scales ◽

Thermal State ◽

Initial Conditions ◽

Single Point ◽

Ice Core ◽

Oceanic Water ◽

Stability Zone ◽

Glacial Cycles ◽

The Impact ◽

Subsea Permafrost

Abstract. Single-point simulations with a model for thermal state of subsea sediments driven by the forcing constructed from the ice core data show that the impact of initial conditions is lost after ~ 100 kyr. The time scales of temperature propagation in sediments and respective permafrost response are ~ 10–20 kyr which is longer than the present interglacial. The timings of shelf exposure during oceanic regressions and flooding during transgressions are important for representation of sediment thermal state and hydrates stability zone (HSZ). These timings should depend on the contemporary shelf depth (SD). During glacial cycles temperature at the top of sediments is a major driver of HSZ vertical boundaries change for SD of few tens of meters, while the pressure exerted by oceanic water becomes more important for larger SD. Thus, even the existence of HSZ and its disappearance might not be easily tied to oceanic transgressions and regressions.

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The Impact of Airborne Doppler Aerosol Wind (DAWN) Lidar Wind Profiles on Numerical Simulations of Tropical Convective Systems during the NASA Convective Processes Experiment (CPEX)

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-19-0123.1 ◽

2020 ◽

Vol 37 (4) ◽

pp. 705-722 ◽

Cited By ~ 1

Author(s):

Zhiqiang Cui ◽

Zhaoxia Pu ◽

G. David Emmitt ◽

Steven Greco

Keyword(s):

Data Assimilation ◽

Initial Conditions ◽

Three Dimensional ◽

Tropical Storm ◽

Convective System ◽

Spatiotemporal Resolution ◽

Convective Systems ◽

Convective Processes ◽

Wind Profiles ◽

The Impact

AbstractHigh-spatiotemporal-resolution airborne Doppler Aerosol Wind (DAWN) lidar profiles over the Caribbean Sea and Gulf of Mexico region were collected during the NASA Convective Processes Experiment (CPEX) field campaign from 27 May to 24 June 2017. This study examines the impact of assimilating these wind profiles on the numerical simulation of moist convective systems using an Advanced Research version of the Weather Research and Forecasting (WRF) Model (WRF-ARW). A mesoscale convective system and a tropical storm (Cindy) that occurred on 16 June 2017 in a strong shear environment and on 21 June 2017 in a weak shear environment, respectively, are selected as case studies. The DAWN wind profiles are assimilated with the NCEP Gridpoint Statistical Interpolation analysis system using a three-dimensional variational (3DVar) and a hybrid three-dimensional ensemble-variational (3DEnVar) data assimilation systems to provide the initial conditions for a short-range forecast. Results show that the assimilation of DAWN wind profiles has significant positive impacts on convective simulations with the two assimilation approaches. The assimilation of DAWN wind profiles creates notable adjustments in the analysis of the divergence field for WRF simulations with a good agreement of wind forecasts with radiosonde observations. The quantitative precipitation forecasting is also improved. In general, the 3DEnVar data assimilation method is deemed more promising for DAWN data assimilation. There are cases with Tropical Storm Cindy in which DAWN data have slight to neutral impact on rainfall forecasts with 3DVAR, implying complicated interactions between errors of retrieved wind data and background error covariance in the lower and upper troposphere.

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Fracture Behavior of the Hot Rolled Strip’s Surface Scale Layer from Different Impacts Angles

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.905.67 ◽

2022 ◽

Vol 905 ◽

pp. 67-72

Author(s):

Shang Wang ◽

Rui Can Hao ◽

Hua Gang Liu ◽

Xiao Chen Wang ◽

Quan Yang

Keyword(s):

Finite Element ◽

Three Dimensional ◽

Element Model ◽

Impact Angle ◽

Rolled Strip ◽

Shot Blasting ◽

Cracking Behavior ◽

Scale Layer ◽

Hot Rolled ◽

The Impact

In order to improve the energy efficiency of shot blasting impact descaling, a three-dimensional finite element impact descaling model was established. Based on the finite element model, the cracking behavior of the scale layer on hot rolled strip from different impacts angles was simulated. The results of finite element calculation and theoretical analysis show that: (1)Under the premise of constant velocity, the descaling area increases with the increase of impact angle, but the increasing rate tends to be moderate. (2)The depth of the impact tunnel and the residual compressive stress surface (-200 MPa) increase as the impact angle goes bigger. The ideal range of impact angle for shot blasting descaling should be 60°-75°.

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Modeling of the impact of rigid ellipsoidal blocks by means of an elastic-visco-plastic constitutive model

10.5194/egusphere-egu21-12604 ◽

2021 ◽

Author(s):

Giuseppe Dattola ◽

Giovanni Battista Crosta ◽

Claudio Giulio di Prisco

Keyword(s):

Constitutive Model ◽

Three Dimensional ◽

Impact Angle ◽

Material Point ◽

Lumped Mass ◽

Mountain Areas ◽

Block Motion ◽

The Impact ◽

Constitutive Parameters

Rockfall is one of the most common hazards in mountain areas causing severe damages to structures/infrastructures and, human lives. For this reason, numerous are the papers published in the last decades on this subject, both introducing reliable approaches to simulate the boulder trajectory and defining design methods for sheltering structures. As is well known, the most popular strategy to simulate the block trajectory and velocity is based on the lumped mass material point approach. This is capable of describing the block trajectory, before either its natural arrest or impact against an artificial/natural obstacle, by suitably considering its interaction with soil/rock materials, interaction always dynamic, very often highly dissipative and defined, according to its nature, as sliding, rolling or impact.In this framework, this study focusses on impacts and, in particular, on the role of block geometry in affecting the block kinematic response. The problem is approached numerically; by modifying a previously conceived elastic-viscoplastic constitutive model, based on the macro-element concept. and capable of satisfactorily simulating impacts of spherical blocks.The modified constitutive model relaxes the assumption of spherical block by assuming an ellipsoidal shape and by allowing for the boulder rotation. These two changes make the problem more complex but allow to model more realistically the impact. For the sake of simplicity, the results shown in this work consider the block motion to be planar, but the model already allows to include general three dimensional conditions.In this work, the model is briefly outlined and the procedure for calibrating the model constitutive parameters described. Then, the results of an extensive parametric analysis, employing constitutive parameters calibrated on experimental data taken from the literature, are discussed. In particular, the role of (i) the inner block orientation, and (ii) the inner impact angle is considered in terms of both kinematic variables and restitution coefficients. Finally, interpolation functions to compute restitution coefficients, once both block shape and inner impact block orientation are known, are provided.

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Analytical thermochronometric models of Earth’s crust during the late accretionary bombardment epoch (4.5-3.5 Ga)

10.5194/egusphere-egu2020-3675 ◽

2020 ◽

Author(s):

Stephen J. Mojzsis ◽

Oleg Abramov

Keyword(s):

Age Distribution ◽

Three Dimensional ◽

Plate Boundary ◽

Impact Angle ◽

Asteroid Belt ◽

Size Frequency Distribution ◽

Frequency Distributions ◽

The Earth ◽

Size Frequency ◽

The Impact

Late accretionary bombardments in the first billion years of solar system history strongly affected the initial physical and chemical states of the Earth. Evidence of ancient impacts can be preserved in the oldest known terrestrial zircons with ages up to ca. 4.4 Ga. Here, we use the Hadean zircon record to directly assess the thermal effects of impact bombardment on the early Earth&#8217;s crust, couple the results to models of closure temperature-dependent diffusive loss and U-Pb age-resetting in zircon, derive zircon ages, and compare them to published ages.The impact bombardment model consists of (i) a stochastic cratering model which populates the surface with craters within constraints derived from the lunar cratering record, the size/frequency distribution of the asteroid belt, and dynamical models; (ii) analytical expressions that calculate a temperature field for each crater; and (iii) a three-dimensional thermal model of the terrestrial lithosphere, where craters are allowed to cool by conduction and radiation. Equations for diffusion in zircon are coupled to these thermal models to estimate the amount of age-resetting.We present modeling results for the Earth between 4.5 Ga and 3.5 Ga based new mass-production functions. Mean surface temperatures and geothermal gradients were assumed as 20 &#176;C and 70 &#176;C/km. Total delivered mass was estimated at 0.0013(Mplanet), or 7.8 &#215; 1021 kg. The size-frequency distributions of the impacts were derived from dynamical modeling. We begin model runs with a global magma ocean, which would have been formed by the Moon-forming impact. Mean impactor density of 3000 kg/m3 and impactor velocity distribution from [1,2] was used, and impact angle of each impactor was stochastically generated from a gaussian centered at 45 degrees. The typical impact velocity of the Earth is ~21 km s-1.It is important to note that the model age outputs we report omit normal processes of generation of zircon-saturated magmas that were operative in the Hadean. We find that as the impact flux decreases with time and becomes negligible for the purposes of thermal modeling by ca. 3.5 Ga. We find that the probability of randomly selecting a zircon of a given age increases with increasing age, predicting a large number of very old zircons. This contrasts with the actual age distribution of Hadean zircons, which, for >4 Ga, indicates the opposite case: the probability of selecting a zircon of a given age decreases with increasing age. We interpret this discrepancy to mean that impacts were not the dominant process in determining the ages of Hadean zircons. This is consistent with observations that the majority of Hadean zircons had formation temperature significantly lower than those expected for melt sheets and thermobarometry measurements suggesting formation of some Hadean zircons in a plate boundary environment.[1] Mojzsis, S.J. et al. (2019). Astrophys. J., 881, 44. [2] Brasser, R. et al. (2020) Icarus 338, 113514.&#160;

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Impact of radar data assimilation using WRF three-dimensional variational system, for the simulation of a heavy rainfall case in Central Italy

Atmospheric Measurement Techniques Discussions ◽

10.5194/amtd-6-7315-2013 ◽

2013 ◽

Vol 6 (4) ◽

pp. 7315-7353

Author(s):

I. Maiello ◽

R. Ferretti ◽

S. Gentile ◽

M. Montopoli ◽

E. Picciotti ◽

...

Keyword(s):

Data Assimilation ◽

Radial Velocity ◽

Heavy Rainfall ◽

Initial Conditions ◽

Positive Impact ◽

Central Italy ◽

Three Dimensional ◽

Warm Start ◽

The Impact ◽

Dwr Data

Abstract. This work is a first assessment of the role of Doppler Weather radar (DWR) data in a mesoscale model for the prediction of a heavy rainfall. The study analyzes the event occurred during 19–22 May 2008 in the urban area of Rome. The impact of the radar reflectivity and radial velocity acquired from Monte Midia Doppler radar, on the assimilation into the Weather Research Forecasting (WRF) model version 3.2, is discussed. The goal is to improve the WRF high resolution initial condition by assimilating DWR data and using ECMWF analyses as First Guess thus improving the forecast of surface rainfall. Several experiments are performed using different set of Initial Conditions (ECMWF analyses and warm start or cycling) and a different assimilation strategy (3 h-data assimilation cycle). In addition, 3DVAR (three-dimensional variational) sensitivity tests to outer loops are performed for each of the previous experiment to include the non-linearity in the observation operators. In order to identify the best ICs, statistical indicators such as forecast accuracy, frequency bias, false alarm rate and equitable threat score for the accumulated precipitation are used. The results show that the assimilation of DWR data has a positive impact on the prediction of the heavy rainfall of this event, both assimilating reflectivity and radial velocity, together with conventional observations. Finally, warm start results in more accurate experiments as well as the outer loops strategy.

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