A Comparative Study to Quantify Sensitive Dependence in Numerical Models for a Developing Low in the Southern Plains

2010 ◽  
Vol 44-45 (2010-2011) ◽  
pp. 29-40
Author(s):  
Amy E. Schnetzler ◽  
Justin M. Glisan ◽  
H. Athar ◽  
Patrick S. Market ◽  
Anthony R. Lupo
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
Numerical Models ◽  
Wrf Model ◽  
Convective Precipitation ◽  
Southern Plains ◽  
Southeast United States ◽  
Sensitive Dependence ◽  
Trajectory Divergence

Abstract Studies have shown that numerical models display the characteristics of chaotic systems, and that the solutions can be sensitive to the initial conditions, the model used, or the parameterizations used. Using the Kain-Fritsch, Grell, and modified Kuo convective parameterizations in the MASS and the WRF model, the results from a case study show that 48-h forecasts were not identical. Lyapunov exponents were calculated by plotting forecast trajectories in a phase diagram and estimating the rate of trajectory divergence for two time periods outside the study of the main cyclone. These calculations did show divergence at a rate which was consistent with differences in model height in 48-h forecasts from other studies. Additionally, the integrated enstrophy can be used to estimate the Lyapunov value. Finally, a qualitative analysis comparing various model runs (pseudo-ensemble) was performed to determine if there were regions or areas where consistent differences in the runs existed between the indexes used for forecasting convective precipitation. Results demonstrated that the region of the southeast United States associated with the developing cyclone showed the most significant differences in these indexes and for heights and temperatures. The differences in the model forecasts between convective parameterizations (intramodel forecasts) in this case were not as great as the model-to-model forecast differences (intermodel forecasts).

CLARIFYING CHAOS: EXAMPLES AND COUNTEREXAMPLES

1996 ◽  
Vol 06 (02) ◽  
pp. 219-249 ◽  
Author(s):  
RAY BROWN ◽  
LEON O. CHUA
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Closed Form Solutions ◽  
Power Spectral ◽  
Sensitive Dependence ◽  
Universal Definition ◽  
Definition Of ◽  
One Dimensional Maps ◽  
Continuous Power

Over the past fifteen years there have been various attempts to define chaos. In an effort to find a universally acceptable definition we began constructing new examples of chaotic systems in the hope that the salient features of chaos could be captured. Our efforts to date have failed and the examples we have constructed seem to suggest that no such definition exists. However, these examples have proved to be valuable in spite of our inability to hone a universal definition of chaos from them. Consequently, we present this list of examples and their significance. Some interesting conclusions that we can draw from them are: It is possible to construct simple closed form solutions of chaotic one-dimensional maps; sensitive dependence on initial conditions, the most widely used definition of chaos, has many counterexamples; there are invertible chaotic dynamical systems defined by simple differential equations that do not have horseshoes; three important properties that are thought to characterize chaos, continuous power spectral density, exponentially sensitive dependence on initial conditions, and exponential loss of information (Chaitin’s concept of algorithmic complexity), are independent. Chaos seems to be tied to our notion of rates of divergence of orbits or degradation of information such as is found in systems with positive Lyapunov exponents. The reliance on rates seems to open the door to a pandora’s box of rates, both higher and lower than exponential. The intuitive notion of pseudo-randomness, a practical feature of chaos, is present in examples that do not have positive Lyapunov exponents. And in general, nonlinear polynomial rates of degradation of information are also quite “unpredictable”. We conclude that it appears that for any given definition of chaos, there may always be some “clearly” chaotic systems which do not fall under that definition, thus making chaos a cousin to Gödel’s undecidability.

REAL LIFE

1996 ◽  
Vol 06 (11) ◽  
pp. 2077-2086 ◽  
Author(s):  
GARY MAR ◽  
PAUL ST. DENIS
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
Real Life ◽  
Game Of Life ◽  
Life And Death ◽  
Sensitive Dependence ◽  
Conway’S Game Of Life ◽  
Special Case

In Conway’s Game of Life every cell is either fully alive (has the value of 1) or completely dead (has the value 0). In Real Life this restriction to bivalence is lifted to countenance “real-valued” degrees of life and death. Real Life contains Conway’s Game of Life as a special case; however, Real Life, in contrast to Conway’s Game of Life, exhibits sensitive dependence on initial conditions which is characteristic of chaotic systems.

scholarly journals Vertical Temperature Structure Associated with Evaporation of Stratiform Precipitation in Idealized WRF Simulations

2020 ◽  
Vol 77 (5) ◽  
pp. 1851-1864
Author(s):  
M. Virman ◽  
M. Bister ◽  
V. A. Sinclair ◽  
J. Räisänen ◽  
H. Järvinen
Keyword(s):  
Initial Conditions ◽  
Numerical Models ◽  
Wrf Model ◽  
Lower Troposphere ◽  
Horizontal Distribution ◽  
Temperature Structure ◽  
Maximum Magnitude ◽  
Vertical Temperature ◽  
Warm Anomaly ◽  
Stratiform Precipitation

Abstract A recent study based on observations has shown that after precipitation over tropical oceans rather shallow temperature structures occur in the lower troposphere and that their magnitude depends on climatological low- to midtropospheric humidity. As any process that produces temperature perturbations in the lower troposphere can be of great significance for the formation of atmospheric deep convection, the vertical temperature structure associated with evaporation of stratiform precipitation and its sensitivity to low- to midtropospheric humidity are studied by conducting three-dimensional, high-resolution, idealized simulations with the Advanced Research version of the Weather Research and Forecasting (WRF) Model. In the simulations, rainwater with mixing ratio and number concentration characteristic of stratiform precipitation associated with mesoscale convective systems is added in a large round area at roughly 560 hPa. Evaporative cooling and subsidence warming below result in a cold anomaly at roughly 560–750 hPa and, especially, a warm anomaly at roughly 750–900 hPa. The cold-over-warm anomalies are stronger with smaller low- to midtropospheric relative humidity in the initial conditions, with the maximum magnitude of the warm anomaly ranging between 0.7 and 1.2 K. The temperature anomalies propagate to the environment and still remain present after precipitation stops. The results show that evaporation of stratiform precipitation alone can lead to temperature structures, which are on the same order of magnitude as the observed ones, that potentially inhibit subsequent convection by increasing convective inhibition. Therefore, the representation of microphysical processes affecting the location, amount, and vertical and horizontal distribution of stratiform precipitation and its evaporation in numerical models requires special attention.

scholarly journals Changes in the simulation of instability indices over the Iberian Peninsula due to the use of 3DVAR data assimilation

2020 ◽  
Author(s):  
Santos J. González-Rojí ◽  
Sheila Carreno-Madinabeitia ◽  
Jon Sáenz ◽  
Gabriel Ibarra-Berastegi
Keyword(s):  
Data Assimilation ◽  
Iberian Peninsula ◽  
Initial Conditions ◽  
Atlantic Coast ◽  
Wrf Model ◽  
R Package ◽  
Mediterranean Coast ◽  
Convective Precipitation ◽  
Seasonal Analysis ◽  
Instability Indices

Abstract. The ability of two downscaling experiments to correctly simulate the instability conditions that can trigger thunderstorms over the Iberian Peninsula is compared in this paper. To do so, three instability indices are evaluated: TT index, CAPE and CIN. The WRF model is used for the simulations. The N experiment is driven by ERA-Interim’s initial and boundary conditions; The D experiment has the same configuration as N, but the 3DVAR data assimilation step is additionally run at 00, 06, 12 and 18 UTC. Eight radiosondes are available over the IP, and the values for these indices calculated from the University of Wyoming were chosen as reference in the validation of both simulations. Additionally, measured variables at different pressure levels from the radiosondes provided byWyoming were used to calculate the three instability indices by our own methodology using the R package aiRthermo. According to the validation, the correlation, SD and RMSE obtained by the experiment D for all the indices in most of the stations are better than those for N. The different methodologies produce small discrepancies between the values for TT, but these are larger for CAPE and CIN due to the dependency of these indices on the initial conditions assumed for the calculation of an air parcel’s vertical evolution. Similar results arise from the seasonal analysis concerning both WRF experiments: N tends to overestimate or underestimate (depending on the index) the variability of the reference values, but D is able to capture it in most of the seasons. The heterogeneity of the indices is highlighted in the mean maps over the Iberian Peninsula. According to those from D, the ingredients for the development of convective precipitation during winter are found along the entire Atlantic coast, but in summer they are located particularly in the Mediterranean coast. The chances of developing thunderstorms in those areas at 12 UTC is much higher than at 00 UTC; The convective inhibition is more extended towards inland at 00 UTC in those areas, which prevents storms from developing. However, high values are observed near Murcia also at 12 UTC.

scholarly journals Using and Evaluating the Efficiency of GRIMs Model in Making Some Simulations of Weather Variables in Three Countries in Middle East: A Snowfall Case Study

2021 ◽  
pp. 4489-4502
Author(s):  
Vian Almusawi ◽  
Thaer O. Roomi ◽  
Alaa M. Al-Lami
Keyword(s):  
Middle East ◽  
Initial Conditions ◽  
Numerical Models ◽  
Rare Event ◽  
Dust Storms ◽  
Reanalysis Dataset ◽  
Snowfall Event ◽  
Snow Precipitation ◽  
First Time

    Predicting weather by numerical models have been used extensively in research works for Middle East, mostly for dust storms, rain showers, and flash floods with a less deal of interest on snow precipitation. In this study, the Global/Regional Integrated Model System (GRIMs) that was developed in South Korea was used to predict a rare snowfall event occurred in three countries in Middle East (Syria, Jordan and Iraq) located between (25-65 oE; 12-42 oN) in year 2008. The main aim of this study was to test GRIMs efficiency, which would be used for the first time in Middle East, to make predictions of weather parameters such as pressure, temperature, and relative humidity especially in the selected area. In addition, the study would investigate the conditions that caused the snowfall event. GRIMs model was installed, compiled, and run on a Linux platform by using NCEP-NCAR reanalysis dataset as initial conditions on 0.5 × 0.5 grid resolution to make simulations for three days at intervals of three hours. The output of the model was evaluated by making comparisons with actual data obtained from the GFS Agency dataset and the model showed its efficiency. The snowfall event was synoptically discussed in details. It was found that the snowfall event was a result of fast succession systems of a strong cold high pressure and then a deep warm low pressure. The high instability in the region had led to form large cumuliform clouds with snow precipitation as a rare event in very long period.

scholarly journals Comparison of Modeled and Observed Accumulated Convective Precipitation in Mountainous and Flat Land Areas

2011 ◽  
Vol 12 (2) ◽  
pp. 245-261 ◽  
Author(s):  
Mladjen Ćurić ◽  
Dejan Janc
Keyword(s):  
Size Distribution ◽  
Correlation Coefficient ◽  
Initial Conditions ◽  
Numerical Models ◽  
Cloud Model ◽  
Rain Gauge ◽  
Convective Precipitation ◽  
Spatial And Temporal Variability ◽  
Mountainous Area ◽  
Alternative Scheme

Abstract Convective precipitation is the main cause of extreme rainfall events in small areas. Its primary characteristics are both large spatial and temporal variability. For this reason, the monitoring of accumulated precipitation fields (liquid and solid components) at the surface is difficult to carry out through the use of rain gauge networks or remote sensing observations. Alternatively, numerical models may be a useful tool to simulate convective precipitation for various analyses and predictions. This paper focuses on improving quantitative convective precipitation estimates that are obtained with a cloud-resolving model. This aim is attained by using the appropriate cloud drop size distribution and modified single sounding data. The authors perform comparisons between observations and three model samples of the areal-accumulated convective precipitation for a 15-yr period over mountainous and flat land areas with 45 and 29 convective events, respectively. They compare the results from a numerical cloud model that uses 2 different microphysical schemes—the unified Khrgian–Mazin size distribution of cloud drops—and an alternative scheme that is a combination of a monodispersed cloud droplet spectrum and the Marshall–Palmer size distribution for raindrops. The authors’ statistical analysis shows that the model version with the Khrgian–Mazin size distribution and the new initial conditions better simulates the observed areal-accumulated convective precipitation than the alternative microphysical approach for both study areas. The model simulations with the Khrgian–Mazin size distribution most closely match observations for the flat land area with a correlation coefficient of 0.94, while it is somewhat lower (0.89) for the mountainous area. Use of the alternative microphysical approach, on the other hand, underestimates the observed precipitation, and has the lowest correlation coefficient among the methods, 0.82 for the mountainous area and 0.85 for the flat land.

SEISMIC RISK AND RESILIENCE ASSESSMENT OF INDUSTRIAL FACILITIES: CASE STUDY ON A BLACK CARBON PLANT

2020 ◽  
Author(s):  
George Karagiannakis
Keyword(s):  
Seismic Risk ◽  
Numerical Models ◽  
Fragility Curves ◽  
Human Life ◽  
Mitigation Strategies ◽  
Economic Losses ◽  
Risk And Resilience ◽  
Industrial Plants ◽  
Plant Equipment

This paper deals with state of the art risk and resilience calculations for industrial plants. Resilience is a top priority issue on the agenda of societies due to climate change and the all-time demand for human life safety and financial robustness. Industrial plants are highly complex systems containing a considerable number of equipment such as steel storage tanks, pipe rack-piping systems, and other installations. Loss Of Containment (LOC) scenarios triggered by past earthquakes due to failure on critical components were followed by severe repercussions on the community, long recovery times and great economic losses. Hence, facility planners and emergency managers should be aware of possible seismic damages and should have already established recovery plans to maximize the resilience and minimize the losses. Seismic risk assessment is the first step of resilience calculations, as it establishes possible damage scenarios. In order to have an accurate risk analysis, the plant equipment vulnerability must be assessed; this is made feasible either from fragility databases in the literature that refer to customized equipment or through numerical calculations. Two different approaches to fragility assessment will be discussed in this paper: (i) code-based Fragility Curves (FCs); and (ii) fragility curves based on numerical models. A carbon black process plant is used as a case study in order to display the influence of various fragility curve realizations taking their effects on risk and resilience calculations into account. Additionally, a new way of representing the total resilience of industrial installations is proposed. More precisely, all possible scenarios will be endowed with their weighted recovery curves (according to their probability of occurrence) and summed together. The result is a concise graph that can help stakeholders to identify critical plant equipment and make decisions on seismic mitigation strategies for plant safety and efficiency. Finally, possible mitigation strategies, like structural health monitoring and metamaterial-based seismic shields are addressed, in order to show how future developments may enhance plant resilience. The work presented hereafter represents a highly condensed application of the research done during the XP-RESILIENCE project, while more detailed information is available on the project website https://r.unitn.it/en/dicam/xp-resilience.

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

2020 ◽  
Vol 18 (1) ◽  
Keyword(s):  
Image Encryption ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Chaotic Map ◽  
Security Applications ◽  
The Common ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Sensitivity To Initial Conditions ◽  
Diffusion Properties

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

scholarly journals A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear

2021 ◽  
Vol 11 (9) ◽  
pp. 4136
Author(s):  
Rosario Pecora
Keyword(s):  
Numerical Method ◽  
Initial Conditions ◽  
Impact Load ◽  
Numerical Models ◽  
Landing Gear ◽  
Design Stage ◽  
Impact Dynamics ◽  
State Variables ◽  
Adopted Model ◽  
The Impact

Oleo-pneumatic landing gear is a complex mechanical system conceived to efficiently absorb and dissipate an aircraft’s kinetic energy at touchdown, thus reducing the impact load and acceleration transmitted to the airframe. Due to its significant influence on ground loads, this system is generally designed in parallel with the main structural components of the aircraft, such as the fuselage and wings. Robust numerical models for simulating landing gear impact dynamics are essential from the preliminary design stage in order to properly assess aircraft configuration and structural arrangements. Finite element (FE) analysis is a viable solution for supporting the design. However, regarding the oleo-pneumatic struts, FE-based simulation may become unpractical, since detailed models are required to obtain reliable results. Moreover, FE models could not be very versatile for accommodating the many design updates that usually occur at the beginning of the landing gear project or during the layout optimization process. In this work, a numerical method for simulating oleo-pneumatic landing gear drop dynamics is presented. To effectively support both the preliminary and advanced design of landing gear units, the proposed simulation approach rationally balances the level of sophistication of the adopted model with the need for accurate results. Although based on a formulation assuming only four state variables for the description of landing gear dynamics, the approach successfully accounts for all the relevant forces that arise during the drop and their influence on landing gear motion. A set of intercommunicating routines was implemented in MATLAB® environment to integrate the dynamic impact equations, starting from user-defined initial conditions and general parameters related to the geometric and structural configuration of the landing gear. The tool was then used to simulate a drop test of a reference landing gear, and the obtained results were successfully validated against available experimental data.

scholarly journals Estimation of Damage Induced by Single-Hole Rock Blasting: A Review on Analytical, Numerical, and Experimental Solutions

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 29
Author(s):  
Mahdi Shadabfar ◽  
Cagri Gokdemir ◽  
Mingliang Zhou ◽  
Hadi Kordestani ◽  
Edmond V. Muho
Keyword(s):  
Structural Reliability ◽  
Numerical Models ◽  
Experimental Models ◽  
Rock Blasting ◽  
Discussion Section ◽  
Reliability Models ◽  
Fine Grain ◽  
Experimental Approaches ◽  
Engineering Projects

This paper presents a review of the existing models for the estimation of explosion-induced crushed and cracked zones. The control of these zones is of utmost importance in the rock explosion design, since it aims at optimizing the fragmentation and, as a result, minimizing the fine grain production and recovery cycle. Moreover, this optimization can reduce the damage beyond the set border and align the excavation plan with the geometric design. The models are categorized into three groups based on the approach, i.e., analytical, numerical, and experimental approaches, and for each group, the relevant studies are classified and presented in a comprehensive manner. More specifically, in the analytical methods, the assumptions and results are described and discussed in order to provide a useful reference to judge the applicability of each model. Considering the numerical models, all commonly-used algorithms along with the simulation details and the influential parameters are reported and discussed. Finally, considering the experimental models, the emphasis is given here on presenting the most practical and widely employed laboratory models. The empirical equations derived from the models and their applications are examined in detail. In the Discussion section, the most common methods are selected and used to estimate the damage size of 13 case study problems. The results are then utilized to compare the accuracy and applicability of each selected method. Furthermore, the probabilistic analysis of the explosion-induced failure is reviewed using several structural reliability models. The selection, classification, and discussion of the models presented in this paper can be used as a reference in real engineering projects.

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