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At least 811 records · Page 45

Reply to “Comments on ‘MSE minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel’”

A standard convention in moist thermodynamics, adopted by D. M. Romps and others, is to set the specific energy and entropy of dry air and liquid water to zero at the triple-point temperature and pressure. P. Marquet claims that this convention leads to physically incorrect results. To support this claim, Marquet presents numerical calculations of a lifted parcel. It is shown here that the claim is false and that the numerical calculations of Marquet are in error. In the context of a simple two-phase thermodynamic system, an analysis is presented here of the freedoms one has to choose additive constants in the definitions of energy and entropy. Many other misconceptions are corrected as well.

54 ENVIRONMENTAL SCIENCES↗

Physics-Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress

Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: a) Subgrid processes which the model cannot (yet) resolve, due to its discrete resolution, and b) sources in the equation, due to radiation for example. Hence coupling between these physics parameterizations and the resolved fluid dynamics and also between the dynamics of the different fluids in the system (air and water) is necessary. This coupling is an important aspect of geophysical models. However, often model development is strictly segregated into either physics or dynamics. Hence, this area has many more unanswered questions than in-depth understanding. Furthermore, recent developments in the design of dynamical cores (significant increase of resolution, move to non-hydrostatic equation sets etc), extended process physics (prognostic micro physics, 3D turbulence, non-vertical radiation etc) and predicted future changes of the computational infrastructure (Exascale with its need for task parallelism, data locality and asynchronous time stepping for example) is adding even more complexity and new questions.

Gross, Markus↗

Assimilation of Satellite-Derived Soil Moisture for Improved Forecasts of the Great Plains Low-Level Jet

In the context of forecasting societally impactful Great Plains low-level jets (GPLLJs), the potential added value of satellite soil moisture (SM) data assimilation (DA) is high. GPLLJs are both sensitive to regional soil moisture gradients and frequent drivers of severe weather, including mesoscale convective systems. An untested hypothesis is that SM DA is more effective in forecasts of weakly synoptically forced, or uncoupled GPLLJs, than in forecasts of cyclone-induced coupled GPLLJs. Using the NASA Unified Weather Research and Forecasting (NU-WRF) Model, 75 GPLLJs are simulated at 9-km resolution both with and without NASA Soil Moisture Active Passive SM DA. Differences in modeled SM, surface sensible (SH) and latent heat (LH) fluxes, 2-m temperature (T2), 2-m humidity (Q2), PBL height (PBLH), and 850-hPa wind speed (W850) are quantified for individual jets and jet-type event subsets over the south-central Great Plains, as well as separately for each GPLLJ sector (entrance, core, and exit). At the GPLLJ core, DA-related changes of up to 5.4 kg m–2 in SM can result in T2, Q2, LH, SH, PBLH, and W850 differences of 0.68°C, 0.71 g kg –2 , 59.9 W m –2 , 52.4 W m –2 , 240 m, and 4 m s –1 , respectively. W850 differences focus along the jet axis and tend to increase from south to north. Further, jet-type differences are most evident at the GPLLJ exit where DA increases and decreases W850 in uncoupled and coupled GPLLJs, respectively. Data assimilation marginally reduces negative wind speed bias for all jets, but the correction is greater for uncoupled GPLLJs, as hypothesized.

54 ENVIRONMENTAL SCIENCES↗

A Second-Order Time-Stepping Scheme for Simulating Ensembles of Parameterized Flow Problems

Abstract We consider settings for which one needs to perform multiple flow simulations based on the Navier–Stokes equations, each having different initial condition data, boundary condition data, forcing functions, and/or coefficients such as the viscosity. For such settings, we propose a second-order time accurate ensemble-based method that to simulate the whole set of solutions, requires, at each time step, the solution of only a single linear system with multiple right-hand-side vectors. Rigorous analyses are given proving the conditional stability and establishing error estimates for the proposed algorithm. Numerical experiments are provided that illustrate the analyses.

Mathematics↗

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗

Surrogate Modeling For Efficiently Accurately and Conservatively Estimating Measures of Risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. We adopt a probabilistic description of risk that assigns probabilities to consequences associated with an event and use risk measures, which combine objective evidence with the subjective values of decision makers, to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical estimates obtained from the training data. These surrogate models not only limit over-confidence in reliability and safety assessments, but produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to the specific risk preferences of the stakeholder and then present an approach, based upon stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. The surrogate models introduce a bias that allows them to conservatively estimate the target risk measures. We provide theoretical results that show that this bias decays at the same rate as the L 2 error in the surrogate model. Our numerical examples confirm that risk-aware surrogate models do indeed over-estimate the target risk measures while converging at the expected rate.

97 MATHEMATICS AND COMPUTING↗

Monte-Carlo Neutrino Transport in Neutron Star Merger Simulations

Gravitational waves and electromagnetic signals from merging neutron star binaries provide valuable information about the the properties of dense matter, the formation of heavy elements, and high-energy astrophysics. To fully leverage observations of these systems, we need numerical simulations that provide reliable predictions for the properties of the matter unbound in these mergers. An important limitation of current simulations is the use of approximate methods for neutrino transport that do not converge to a solution of the transport equations as numerical resolution increases, and thus have errors that are impossible to quantify. Here, we report on a first simulation of a binary neutron star merger that directly solves the transport equations using Monte-Carlo techniques. We demonstrate that a computationally cheap Monte-Carlo transport can be implemented without ill effects from sampling noise. We apply Monte-Carlo transport to an unequal mass neutron star binary merger up to 5ms past merger, and report on the properties of the matter and neutrino outflows. Finally, we compare our results to the output of our best approximate `M1' transport scheme, demonstrating that an M1 scheme that carefully approximates the neutrino energy spectrum only leads to ~10% uncertainty in the composition and velocity of the ejecta, and ~20% uncertainty in the electron (anti)neutrino luminosities and energies. Here, the most significant disagreement found between M1 and Monte-Carlo results is a factor of ~2 difference in the luminosity of heavy-lepton neutrinos.

79 ASTRONOMY AND ASTROPHYSICS↗

Modeling the small-scale deposition of snow onto structured Arctic sea ice during a MOSAiC storm using snowBedFoam 1.0.

The remoteness and extreme conditions of the Arctic make it a very difficult environment to investigate. In these polar regions covered by sea ice, the wind is relatively strong due to the absence of obstructions and redistributes a large part of the deposited snow mass, which complicates estimates for precipitation hardly distinguishable from blowing or drifting snow. Moreover, the snow mass balance in the sea ice system is still poorly understood, notably due to the complex structure of its surface. Quantitatively assessing the snow distribution on sea ice and its connection to the sea ice surface features is an important step to remove the snow mass balance uncertainties (i.e., snow transport contribution) in the Arctic environment. In this work we introduce snowBedFoam 1.0., a physics-based snow transport model implemented in the open-source fluid dynamics software OpenFOAM. We combine the numerical simulations with terrestrial laser scan observations of surface dynamics to simulate snow deposition in a MOSAiC (Multidisciplinary Drifting Observatory for the Study of Arctic Climate) sea ice domain with a complicated structure typical for pressure ridges. The results demonstrate that a large fraction of snow accumulates in their vicinity, which compares favorably against scanner measurements. However, the approximations imposed by the numerical framework, together with potential measurement errors (precipitation), give rise to quantitative inaccuracies, which should be addressed in future work. The modeling of snow distribution on sea ice should help to better constrain precipitation estimates and more generally assess and predict snow and ice dynamics in the Arctic.

54 ENVIRONMENTAL SCIENCES↗

Two-way coherent tracking systems.

Review of some results pertinent to the development of nonlinear theory on two-way coherent tracking systems. In particular, the model of cascaded systems is presented, and approximations to steady state probability density functions of the two-way system phase and Doppler error are developed. From these, certain numerical results required in the design and planning of these systems are derived.

Lindsey, W. C.↗

SSME structural computer program development. Volume 2: BOPACE users manual

A computer program for use with a thermal-elastic-plastic-creep structural analyzer is presented. The following functions of the computer program are discussed: (1) analysis of very high temperature and large plastic-creep effects, (2) treatment of cyclic thermal and mechanical loads, (3) development of constitutive theory which closely follows actual behavior under variable temperature conditions, (4) stable numerical solution approach which avoids cumulative errors, and (5) capability of handling up to 1000 degrees of freedom. The computer program is written in FORTRAN IV and has been run on the IBM 360 and UNIVAC 1108 computer systems.

Vos, R. G.↗

First-order corrections to approximate solutions to two-point boundary-condition problems

A method, applicable to real time guidance, is developed for accurate solution to exo-atmospheric space flight optimization problems. In principle the method is applicable to many other two-point boundary-condition (TPBC) problems. The first step of the method is the iterative solution (using a shooting method) of a TPBC problem with differential equations simplified so that they may be solved analytically by means of a single closed-form solution over each stage of the flight. The second step is the addition of a closed-form correction to the solution to the TPBC problem obtained in the first step. The correction accounts (to first-order accuracy) for the errors due to the aforementioned simplifications. Numerical results are given for several orbital injection problems.

Andrus, J. F.↗

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Liu, J. J. F.↗

On minimal surfaces, membranes and compressible flows

The theory, variational formulation and finite element analysis of a class of nonlinear problems arising in optimization, thin membrane deflection and compressible flows are developed. Error estimates are summarized, and representative numerical results are presented. Particular theoretical questions pertaining to the existence and uniqueness of solutions are addressed, and their implications for such applications of finite element analysis as the study of compressible flows indicated.

Carey, G. F.↗

Solar particle propagation and modulation theory

Developments related to solar flare particle propagation theory are considered, taking into account the transport equation currently employed to describe the propagation of solar flare particles. This equation does not take into consideration convection with the solar wind, drifts, and changes in particle energy. The equation was solved numerically to generate typical solar flare particle time profiles at 1 AU. The results, however, were not satisfactory. It was found that the numerical method used was apparently in error. New advances which provide approximate analytical solutions to the equation are reported. Questions of galactic cosmic ray propagation in interplanetary space are also discussed.

Lee, M. A.↗

Development of the functional simulator for the Galileo attitude and articulation control system

A simulation program for verifying and checking the performance of the Galileo Spacecraft's Attitude and Articulation Control Subsystem's (AACS) flight software is discussed. The program, which is called Functional Simulator (FUNSIM), provides a simple method of interfacing user-supplied mathematical models coded in FORTRAN which describes spacecraft dynamics, sensors, and actuators; this is done with the AACS flight software, coded in HAL/S (High-level Advanced Language/Shuttle). It is thus able to simulate the AACS flight software accurately to the HAL/S statement level in the environment of a mainframe computer system. FUNSIM also has a command and data subsystem (CDS) simulator. It is noted that the input/output data and timing are simulated with the same precision as the flight microprocessor. FUNSIM uses a variable stepsize numerical integration algorithm complete with individual error bound control on the state variable to solve the equations of motion. The program has been designed to provide both line printer and matrix dot plotting of the variables requested in the run section and to provide error diagnostics.

Namiri, M. K.↗

Gas filter radiometer for carbon monoxide measurements during the 1979 Summer Monsoon Experiment (MONEX)

The instrumental and data-reduction techniques used in obtaining remote measurements of carbon monoxide during the 1979 Summer Monsoon Experiment are described. The form of the signal function (the variation of signal with altitude) and the impact of variations in the vertical distribution of carbon monoxide are discussed. Estimates of the experimental accuracy are made both by assessment of error sources through the use of numerical simulations and by comparison with concurrent measurements made by means of gas chromatography. It is found that the radiometric measurements tend to be about 9 percent lower than the direct measurements and to have a precision of about 8 percent.

Reichle, H. G., Jr.↗

Hydrostatic temperature calculations

Comparisons are made between hydrostatically computed temperatures and ambient temperatures associated with nine different data sources, including analyses, forecasts and conventional observations. Five-day averages and the day-to-day variations in the root-mean-square temperature differences are presented. Several different numerical and interpolation procedures are examined. Error correction and a constrained optimum procedure that minimizes ambient minus calculated hydrostatic temperature differences are introduced. Systematic differences between ambient and hydrostatic temperatures are found to be associated with the sinoptic situation. When compared with ambient temperatures, hydrostatic temperatures at 500 mb tend to be too warm at or in front of a trough and too cold behind the trough. In the vertical direction, for the eight-level configuration tested, the average hydrostatic temperatures are too cold at low levels (850, 700 mb) and too warm at upper levels, (300, 250 mb).

Raymond, William H.↗