scholarly journals Uncertainty in Scatterometer-Derived Vorticity

2010 ◽  
Vol 27 (3) ◽  
pp. 594-603 ◽  
Author(s):  
Mark A. Bourassa ◽  
Kelly McBeth Ford
Keyword(s):  
Spatial Organization ◽  
Truncation Error ◽  
Random Errors ◽  
Observational Error ◽  
Worst Case ◽  
Truncation Errors ◽  
The Third ◽  
Representation Error ◽  
Observational Uncertainty ◽  
Observational Errors

Abstract A more versatile and robust technique is developed for determining area-averaged surface vorticity based on vector winds from swaths of remotely sensed wind vectors. This technique could also be applied to determine the curl of stress, and it could be applied to any gridded dataset of winds or stresses. The technique is discussed in detail and compared to two previous studies that focused on early development of tropical systems. Error characteristics of the technique are examined in detail. Specifically, three independent sources of error are explored: random observational error, truncation error, and representation error. Observational errors are due to random errors in the wind observations and determined as a worst-case estimate as a function of averaging spatial scale. The observational uncertainty in the Quick Scatterometer (QuikSCAT)-derived vorticity averaged for a roughly circular shape with a 100-km diameter, expressed as one standard deviation, is approximately 0.5 × 10−5 s−1 for the methodology described herein. Truncation error is associated with the assumption of linear changes between wind vectors. Uncertainty related to truncation has more spatial organization in QuikSCAT data than observational uncertainty. On 25- and 50-km scales, the truncation errors are very large. The third type of error, representation error, is due to the size of the area being averaged compared to values with 25-km length scales. This type of error is analogous to oversmoothing. Tropical and subtropical low pressure systems from three months of QuikSCAT observations are used to examine truncation and representation errors. Representation error results in a bias of approximately −1.5 × 10−5 s−1 for area-averaged vorticity calculated on a 100-km scale compared to vorticity calculated on a 25-km scale. The discussion of these errors will benefit future projects of this nature as well as future satellite missions.

scholarly journals On uncertainty of Jupiter's core mass due to observational errors

2007 ◽  
Vol 3 (S249) ◽  
pp. 163-166
Author(s):  
Yasunori Hori ◽  
Takayoshi Sano ◽  
Masahiro Ikoma ◽  
Shigeru Ida
Keyword(s):  
Narrow Range ◽  
Giant Planets ◽  
Observational Error ◽  
Core Mass ◽  
The Core ◽  
Observational Uncertainty ◽  
Observational Errors ◽  
Gas Giant ◽  
Accurate Observation ◽  
Juno Mission

AbstractThe origins of extrasolar gas giant planets have been discussed, based on our understanding of the gas giant planets in the solar system, Jupiter and Saturn. However, how Jupiter and Saturn formed is still uncertain because of the uncertainty in their interiors, especially the core mass (Mc). The uncertainty in Mc is partly due to those in observational data such as gravitational moments (J2n), equatorial radius (Req) and 1-bar temperatures (T1bar). New frontiers mission to Jupiter by NASA (JUNO) launched in 2011 is expected to reduce the observational errors. However, it is not necessarily clear yet which observational uncertainty dominates and how accurate observation is needed to constrain Mc enough to know the origin of Jupiter. Thus, modeling the interior of Jupiter, we evaluate each effect on Mc and required precision. We have found that the observational error of 5% in T1bar yields an error of several M⊕ in Mc. We have also found that the values of J6 of our successful models are confined in a narrow range compared to its observational error. This implies that comparison between the values of J6 of our successful models and the J6 value obtained from JUNO mission helps us to know whether the present theoretical model is valid.

Optimal Third-Order Symplectic Integration Modeling of Seismic Acoustic Wave Propagation

2020 ◽  
Vol 110 (2) ◽  
pp. 754-762 ◽  
Author(s):  
Chuan Li ◽  
Jianxin Liu ◽  
Bo Chen ◽  
Ya Sun
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Wave ◽  
Truncation Error ◽  
Seismic Wave Propagation ◽  
Symplectic Integrator ◽  
Third Order ◽  
The Third ◽  
2D And 3D

ABSTRACT Seismic wavefield modeling based on the wave equation is widely used in understanding and predicting the dynamic and kinematic characteristics of seismic wave propagation through media. This article presents an optimal numerical solution for the seismic acoustic wave equation in a Hamiltonian system based on the third-order symplectic integrator method. The least absolute truncation error analysis method is used to determine the optimal coefficients. The analysis of the third-order symplectic integrator shows that the proposed scheme exhibits high stability and minimal truncation error. To illustrate the accuracy of the algorithm, we compare the numerical solutions generated by the proposed method with the theoretical analysis solution for 2D and 3D seismic wave propagation tests. The results show that the proposed method reduced the phase error to the eighth-order magnitude accuracy relative to the exact solution. These simulations also demonstrated that the proposed third-order symplectic method can minimize numerical dispersion and preserve the waveforms during the simulation. In addition, comparing different central frequencies of the source and grid spaces (90, 60, and 20 m) for simulation of seismic wave propagation in 2D and 3D models using symplectic and nearly analytic discretization methods, we deduce that the suitable grid spaces are roughly equivalent to between one-fourth and one-fifth of the wavelength, which can provide a good compromise between accuracy and computational cost.

An Error Compensation Method for Structural Responses and Sensitivities

2011 ◽  
Vol 421 ◽  
pp. 743-749
Author(s):  
Xiao Ming Wu ◽  
Chun Liu
Keyword(s):  
Error Compensation ◽  
Truncation Error ◽  
Compensation Method ◽  
Superposition Method ◽  
Truncation Errors ◽  
Modal Superposition ◽  
Modal Superposition Method ◽  
Structural Responses ◽  
Epsilon Algorithm ◽  
Modal Method

Abstract. The computation of the responses and their design sensitivities play an essential role in structural analysis and optimization. Significant works have been done in this area. Modal method is one of the classical methods. In this study, a new error compensation method is constructed, in which the modal superposition method is hybrid with Epsilon algorithm for responses and their sensitivities analysis of undamped system. In this study the truncation error of modal superposition is expressed by the first L orders eigenvalues and its eigenvectors explicitly. The epsilon algorithm is used to accelerate the convergence of the truncation errors. Numerical examples show that the present method is validity and effectiveness.

Role of Observational Errors in Optimum Interpolation Analysis

1978 ◽  
Vol 59 (12) ◽  
pp. 1603-1611 ◽  
Author(s):  
Kenneth H. Bergman
Keyword(s):  
Observational Data ◽  
Root Mean Square ◽  
Mean Square ◽  
Observational Error ◽  
Optimum Interpolation ◽  
Analysis Scheme ◽  
Data Statistics ◽  
Observational Errors ◽  
Interpolation Analysis

The theory of optimum interpolation analysis is presented, with emphasis on the role that observational errors have in the analysis scheme. It is shown that an estimate of the root-mean-square observational error is required and also that the correlations between errors of observations, if nonzero, must be specified. Methods of determining these quantities from observational data statistics are discussed and examples shown. Finally, error-checking routines that either accept or reject data are described. It is pointed out that care should be exercised when checking for errors so that good and useful data are not inadvertently rejected.

The Impact of Synoptic Observing and Analysis Systems on Flow Pattern Forecasts

1976 ◽  
Vol 57 (10) ◽  
pp. 1225-1240 ◽  
Author(s):  
Norman A. Phillips
Keyword(s):  
Negative Impact ◽  
Positive Impact ◽  
Interpolation Method ◽  
Forecast Error ◽  
Observational Error ◽  
Optimum Interpolation ◽  
Error Covariance ◽  
Analysis Scheme ◽  
Observational Errors ◽  
The Impact

A linear dynamical prediction model is combined with a linear analysis scheme to give a formula for the expected squared forecast error, as a function of space and time, given a knowledge of observational error covariance and spectrum of the true field. The formula is applied with a two-layer geostrophic model to estimate the maximum impact of tropospheric temperatures derived from satellite radiances over oceanic areas on the accuracy of 500 mb forecasts over North America. The results show a positive impact if the observations are analyzed by an unrealistically efficient optimum interpolation method, but they show a negative impact at all but the smallest satellite error values if the observations are analyzed by a method that ignores observational errors. Eight conclusions are reached concerning routine numerical forecasts and the First GARP Global Experiment.

Toxicity and persistence of sodium fluoroacetate (1080) in the land crab (Gecarcinus lagostoma) on Ascension Island

2008 ◽  
Vol 35 (1) ◽  
pp. 86 ◽  
Author(s):  
D. J. Pain ◽  
R. White ◽  
J. Stevenson ◽  
M. Bell ◽  
K. K. Williams ◽  
...  
Keyword(s):  
Toxic Effects ◽  
Human Consumption ◽  
Withdrawal Period ◽  
Worst Case ◽  
Feral Cats ◽  
Eradication Program ◽  
Land Crab ◽  
Secondary Exposure ◽  
The Third ◽  
Ascension Island

An eradication program for introduced feral cats, using sodium fluoroacetate (1080) bait, was planned on Ascension Island to help breeding seabird populations to recover. We investigated the likelihood of mortality and the occurrence of residual 1080 in the ‘non-target’ Ascension land crab (Gecarcinus lagostoma) through simulating ‘realistic’ and ‘worst case’ exposure to 1080 bait. Crabs feeding on 1080 baits ingested an estimated maximum of 9–56 mg 1080 (kg bodyweight)–1 and although two of 32 treatment crabs died, this mortality was not attributed to 1080 poisoning but to other, unknown, causes. Our results suggest that G. lagostoma has relatively low susceptibility to acute toxic effects of 1080. Most residual 1080 was eliminated rapidly from crab tissue, with concentrations of 0.006–0.070 mg (kg bodyweight)–1 measured in crab claw/leg tissue 9–11 days after exposure. Concentrations of 0.200 and 0.650 mg (kg bodyweight)–1 were measured in the claw tissue of two crabs that died from other causes on the third day of exposure to 1080, indicating potential for secondary exposure of sensitive scavengers or predators of 1080-exposed crabs. We recommend a moratorium on human consumption of all crabmeat for a withholding period following the eradication program. The withdrawal period should be defined by further research on the longevity of 1080 in crab tissues, and be confirmed by monitoring of residues in crabs after baiting.

scholarly journals Accuracy analysis and improvement for the cell-centered scheme with the quasi-one-dimensional reconstriction

2021 ◽  
pp. 1-32 ◽  
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Transport Equation ◽  
Finite Volume ◽  
Constant Velocity ◽  
Truncation Error ◽  
Finite Volume Scheme ◽  
Accuracy Analysis ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Reconstruction

We study the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction. For the model transport equation with a constant velocity, we prove that on translationally-invariant (TI) triangular meshes it possesses the second order of the truncation error and, if the solution is steady, the third order of the solution error. We offer the modification possessing the third order of the solution error on TI-meshes for unsteady solutions also and verify its accuracy on unstructured meshes.

Peace keeping in a model of conflict with foreign investments

2019 ◽  
Vol 13 (2) ◽  
pp. 391-413
Author(s):  
Sajal Lahiri ◽  
Valerica Vlad
Keyword(s):  
Dual Role ◽  
Third Party ◽  
Foreign Investments ◽  
Worst Case ◽  
Economic Implications ◽  
Content Type ◽  
The Third ◽  
Multilateral Agreement ◽  
First Case ◽  
Peacekeeping Forces

Purpose This paper aims to examine the role of outside peacekeepers in a bilateral conflict. Design/methodology/approach The authors build upon a trade theoretic framework by incorporating disruptions due to war, which could affect directly the return to investment, both domestic and foreign, and by introducing explicitly peacekeeping forces into the model. Two countries are engaged in a war, with the purpose of capturing capital. A third country plays a dual role: it is the source of investments in the warring countries, and it deploys soldiers on ground for peacekeeping purposes. The authors consider the cases where the levels of foreign investments are exogenous and when they are endogenously determined by free mobility conditions. In the worst case, they find that foreign investment reduces conflict. In the case of endogenous foreign investments, they examine the effect of multilateral agreements where the two warring countries reduce their number of soldiers and the third increases the number of peacekeepers. Findings The authors find that the reform benefits all three countries and increases the level of foreign investments. They consider the cases of exogenous and endogenous foreign direct investment (FDI). In the first case, the authors examine the effect of an exogenous increase in FDI on the war equilibrium and find that it reduces the employment of soldiers in the warring countries and increases the size of the peacekeeping force. They also find that the first-best level of peacekeeping is larger than the equilibrium level. When FDI is endogenous, starting from the initial war equilibrium, they also examine the effect of a multilateral agreement in which the size of the peacekeeping force is increased by the third country and the two warring countries agree to reduce their war efforts. The authors find that the reform makes all three countries better off and increases the level of FDI. Originality/value The paper uses a theoretical model with third-party interventions in a bilateral war. It intends to shed light on some of the missing economic implications of peacekeeping. The paper introduces explicitly peacekeeping forces into the analysis and introduces a factor that represents a disruption to return on investment in both warring countries. The third country has a dual role; it provides investments in the warring countries and deploys soldiers for peacekeeping. Peacekeeping reduces the disruption mentioned above and affects the employment of soldiers by the warring countries. The authors find that a multilateral agreement in which the two warring countries reduce their war efforts and the third party increases its peacekeeping force can increase welfare in all three countries.

Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Direct Methods ◽  
Historical Background ◽  
Random Errors ◽  
Practical Application ◽  
Fourth Degree ◽  
Numerical Errors ◽  
The Third ◽  
Numeral Systems ◽  
The Given

Textbook, established at several universities. Second edition. *** Written primarily for students at technical studies. Valuable handbook for engineers, PhD students and scientists. *** Published in several variants. *** Seven chapters. In the first chapter, a historical background and basic properties of various numeral systems, as well as conversion of numbers from one system to another are briefly explained. In the second chapter, numbers in digital computers, namely integers and floating point numbers are described. This helps the reader to choose precision and range limits of stored numbers. The third chapter explains constant variables and related numerical errors, including error propagation and algorithm instability. The fourth and fifth chapters explain random variables and related random errors, uncertainty, confidence level, as well as propagation of random errors. Various types of regression analyses of experimental data are described in the sixth chapter. Direct methods for finding roots of the third and fourth degree polynomials are described in the seventh chapter, followed by general iterative methods for polynomials of any degree. *** Why the presented topics are so important? Simply, they are common to all numerical methods. *** Practical application is supported by 84 examples and 17 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be implemented in any computer program. Finally, the given text with 98 figures and 52 tables represents a valuable background for understanding, applying and developing various numerical analyses.

scholarly journals Toward Estimating Climatic Trends in SST. Part II: Random Errors

2006 ◽  
Vol 23 (3) ◽  
pp. 476-486 ◽  
Author(s):  
Elizabeth C. Kent ◽  
Peter G. Challenor
Keyword(s):  
Spatial Variability ◽  
Error Estimates ◽  
Statistical Technique ◽  
Random Errors ◽  
Observational Error ◽  
Data Set ◽  
Spatial Error ◽  
Semivariogram Analysis ◽  
Merchant Ship ◽  
Method Of Measurement

Abstract Random observational errors for sea surface temperature (SST) are estimated using merchant ship reports from the International Comprehensive Ocean–Atmosphere Data Set (ICOADS) for the period of 1970–97. A statistical technique, semivariogram analysis, is used to isolate the variance resulting from the observational error from that resulting from the spatial variability in a dataset of the differences of paired SST reports. The method is largely successful, although there is some evidence that in high-variability regions the separation of random and spatial error is not complete, which may have led to an overestimate of the random observational error in these regions. The error estimates are robust to changes in the details of the regression method used to estimate the spatial variability. The resulting error estimates are shown to vary with region, time, the quality control applied, the method of measurement, the recruiting country, and the source of the data. SST data measured using buckets typically contain smaller random errors than those measured using an engine-intake thermometer. Errors are larger in the 1970s, probably because of problems with data transmission in the early days of the Global Telecommunications System. The best estimate of the global average random error in ICOADS ship SST for the period of 1970–97 is 1.2°C if the estimates are weighted by ocean area and 1.3°C if the estimates are weighted by the number of observations.

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