Storm Sandy first appeared as a tropical storm in the southern Caribbean Sea on Oct. 22, 2012, mo... more Storm Sandy first appeared as a tropical storm in the southern Caribbean Sea on Oct. 22, 2012, moved northeastward, turned northwestward, and made landfall near Brigantine, New Jersey in late October. Sandy devastated surrounding areas, caused an estimated damage of $50 billion, and became the second costliest tropical cyclone (TC) in U.S. History surpassed only by Hurricane Katrina (2005). To save lives and mitigate economic damage, a central question to be addressed is to what extent the lead time of severe storm prediction such as Sandy can be extended (e.g., Emanuel 2012; Kerr 2012). In this study, we present 10 numerical experiments initialized at 00 and 1200 UTC Oct. 22-26, 2012, with the NASA coupled advanced global modeling and visualization systems (CAMVis). All of the predictions realistically capture Sandy's movement with the northwestward turn prior to its landfall. However, three experiments (initialized at 0000 UTC Oct. 22 and 24 and 1200 UTC Oct. 22) produce larger errors. Among the 10 experiments, the control run initialized at 0000 UTC Oct. 23 produces a remarkable 7-day forecast. To illustrate the impact of environmental flows on the predictability of Sandy, we produce and discuss four-dimensional (4-D) visualizations with the control run. 4-D visualizations clearly demonstrate the following multiscale processes that led to the sinuous track of Sandy: the initial steering impact of an upper-level trough (appearing over the northwestern Caribbean Sea and Gulf of Mexico), the blocking impact of systems to the northeast of Sandy, and the binary interaction with a mid-latitude, upper-level trough that appeared at 130degrees west longitude on Oct. 23, moved to the East Coast and intensified during the period of Oct. 29-30 prior to Sandy's landfall.
International Journal of Bifurcation and Chaos, Oct 1, 2022
Accurate predictions for the spread and evolution of epidemics have significant societal and econ... more Accurate predictions for the spread and evolution of epidemics have significant societal and economic impacts. The temporal evolution of infected (or dead) persons has been described as an epidemic wave with an isolated peak and tails. Epidemic waves have been simulated and studied using the classical SIR model that describes the evolution of susceptible (S), infected (I), and recovered (R) individuals. To illustrate the fundamental dynamics of an epidemic wave, the dependence of solutions on parameters, and the dependence of predictability horizons on various types of solutions, we propose a Korteweg–de Vries (KdV)–SIR equation and obtain its analytical solutions. Among classical and simplified SIR models, our KdV–SIR equation represents the simplest system that produces a solution with both exponential and oscillatory components. The KdV–SIR model is mathematically identical to the nondissipative Lorenz 1963 model and the KdV equation in a traveling-wave coordinate. As a result, the dynamics of an epidemic wave and its predictability can be understood by applying approaches used in nonlinear dynamics, and by comparing the aforementioned systems. For example, a typical solitary wave solution is a homoclinic orbit that connects a stable and an unstable manifold at the saddle point within the [Formula: see text]–[Formula: see text] space. The KdV–SIR equation additionally produces two other types of solutions, including oscillatory and unbounded solutions. The analysis of two critical points makes it possible to reveal the features of solutions near a turning point. Using analytical solutions and hypothetical observed data, we derive a simple formula for determining predictability horizons, and propose a method for predicting timing for the peak of an epidemic wave.
Recent advances in computational and global modeling technology have provided the potential to im... more Recent advances in computational and global modeling technology have provided the potential to improve weather predictions at extended-range scales. In earlier studies by the author and his coauthors, realistic 30-day simulations of multiple African easterly waves (AEWs) and an averaged African easterly jet (AEJ) were obtained. The formation of hurricane Helene (2006) was also realistically simulated from Day 22 to Day 30. In this study, such extended predictability was further analyzed based on recent understandings of chaos and instability within Lorenz models and the generalized Lorenz model. The analysis suggested that a statement of the theoretical predictability of two weeks is not universal. New insight into chaotic and non-chaotic processes revealed by the generalized Lorenz model (GLM) indicated the potential for extending prediction lead times. Two major features within the GLM included: (1) three types of attractors (that also appeared in the original Lorenz model) and (2) two kinds of attractor coexistence. The features suggest a refined view on the nature of weather, as follows: The entirety of weather is a superset that consists of chaotic and non-chaotic processes. Better predictability can be obtained for stable, steady-state solutions and nonlinear periodic solutions that occur at small and large Rayleigh parameters, respectively. By comparison, chaotic solutions appear only at moderate Rayleigh parameters. Errors associated with dissipative small-scale processes do not necessarily contaminate the simulations of large scale processes. Based on the nonlinear periodic solutions (also known as limit cycle solutions), here, we propose a hypothetical mechanism for the recurrence (or periodicity) of successive AEWs. The insensitivity of limit cycles to initial conditions implies that AEW simulations with strong heating and balanced nonlinearity could be more predictable. Based on the hypothetical mechanism, the possibility of extending prediction lead times at extended range scales is discussed. Future work will include refining the model to better examine the validity of the mechanism to explain the recurrence of multiple AEWs.
In this study, we present a new nine-dimensional Lorenz model (9DLM) that requires a larger criti... more In this study, we present a new nine-dimensional Lorenz model (9DLM) that requires a larger critical value for the Rayleigh parameter (a rc of 679.8) for the onset of chaos, as compared to a rc of 24.74 for the 3DLM, a rc of 42.9 for the 5DLM, and a rc 116.9 for the 7DLM. Major features within the 9DLM include: (1) the coexistence of chaotic and non-chaotic orbits with moderate Rayleigh parameters, and (2) the coexistence of limit cycle/torus orbits and spiral sinks with large Rayleigh parameters. Version 2 of the 9DLM, referred to as the 9DLM-V2, is derived to show that: (i) based on a linear stability analysis, two non-trivial critical points are stable for all Rayleigh parameters greater than one; (ii) under non-dissipative and linear conditions, the extended nonlinear feedback loop produces four incommensurate frequencies; and (iii) for a stable orbit, small deviations away from equilibrium (e.g., the stable critical point) do not have a significant impact on orbital stability. Based on our results, we suggest that the entirety of weather is a superset that consists of both chaotic and non-chaotic processes.
In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM)... more In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM) integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial l-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (l) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, the microphysics developments of the multi-scale modeling system will be presented. In particular, the results from using multi-scale modeling system to study the heavy precipitation processes will be presented. https://ntrs.nasa.gov/search.jsp?R=20110015159 2020-01-26T22:02:49+00:00Z
ABSTRACT Very Severe Cyclonic Storm Nargis, the deadliest named tropical cyclone (TC) in the Nort... more ABSTRACT Very Severe Cyclonic Storm Nargis, the deadliest named tropical cyclone (TC) in the North Indian Ocean Basin, devastated Burma (Myanmar) in May 2008, causing tremendous damage and numerous fatalities. An increased lead time in the prediction of TC Nargis would have increased the warning time and may therefore have saved lives and reduced economic damage. Recent advances in high-resolution global models and supercomputers have shown the potential for improving TC track and intensity forecasts, presumably by improving multi-scale simulations. The key but challenging questions to be answered include: (1) if and how realistic, in terms of timing, location and TC general structure, the global mesoscale model (GMM) can simulate TC genesis and (2) under what conditions can the model extend the lead time of TC genesis forecasts. In this study, we focus on genesis prediction for TCs in the Indian Ocean with the GMM. Preliminary real-data simulations show that the initial formation and intensity variations of TC Nargis can be realistically predicted at a lead time of up to 5 days. These simulations also suggest that the accurate representations of a westerly wind burst (WWB) and an equatorial trough, associated with monsoon circulations and/or a Madden-Julian Oscillation (MJO), are important for predicting the formation of this kind of TC. In addition to the WWB and equatorial trough, other favorable environmental conditions will be examined, which include enhanced monsoonal circulation, upper-level outflow, low- and middle-level moistening, and surface fluxes.
Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It co... more Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (1) a cloud-resolving model (CRM), (2) a regional-scale model, the NASA unified Weather Research and Forecasting Model (WRF), and (3) a coupled CRM-GCM (general circulation model, known as the Goddard Multi-scale Modeling Framework or MMF). The same cloud-microphysical processes, long-and shortwave radiative transfer and landsurface processes are applied in all of the models to study explicit cloud-radiation and cloud-surface interactive processes in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator for comparison and validation with NASA high-resolution satellite data. This paper reviews the development and presents some applications of the multi-scale modeling system, including results from using the multi-scale modeling system to study the interactions between clouds, precipitation, and aerosols. In addition, use of the multi-satellite simulator to identify the strengths and weaknesses of the model-simulated precipitation processes will be discussed as well as future model developments and applications.
In a recent study, a seven-dimensional Lorenz Model (7DLM) was derived based on an extension of t... more In a recent study, a seven-dimensional Lorenz Model (7DLM) was derived based on an extension of the nonlinear feedback loop within the five-dimensional LM (5DLM). An analysis of Lyapunov exponents indicated that the 7DLM requires a much larger critical value for the Rayleigh parameter (rc ∼ 116.9) for the onset of chaos as compared to the rc of 24.74 for the original three-dimensional (3D) LM and the rc of 42.9 for the 5DLM. To assure that the 7DLM is more stable than the 3DLM and 5DLM, analytical solutions of the critical points for the 7DLM were obtained and a linear stability analysis near the critical point solutions was performed using various values of the Rayleigh parameter (40 ≤ r ≤ 195) and the Prandtl number (5 ≤ σ ≤ 25). In derivations of the 7DLM, potential temperature is represented by the primary, secondary, and tertiary modes, while the streamfunction is represented only by the primary mode. I also further derive a nine-dimensional LM (9DLM) by extending the 7DLM with secondary and tertiary modes for the streamfunction. By comparing the 9DLM with the 7DLM, the negative nonlinear feedback associated with the tertiary temperature modes, as first identified in the 7DLM, is determined to play a dominant role in stabilizing solutions, while the secondary and tertiary modes for the streamfunction produce additional heating terms that slightly destabilize solutions. The critical value of the Rayleigh parameter for the 9DLM is determined to be 102.9, smaller than that of the 7DLM but still much larger than those within the 3DLM and 5DLM. Additionally, as indicated by the strong bivariate relationship among primary, secondary, and tertiary temperature modes, hierarchical scale dependence appears in the 9DLM as well as the 7DLM. Therefore, the comparison between the 7DLM and the 9DLM suggests that using the 7DLM is effective for examining the impact of high-wavenumber modes on solutions stability.
Storm Sandy first appeared as a tropical storm in the southern Caribbean Sea on Oct. 22, 2012, mo... more Storm Sandy first appeared as a tropical storm in the southern Caribbean Sea on Oct. 22, 2012, moved northeastward, turned northwestward, and made landfall near Brigantine, New Jersey in late October. Sandy devastated surrounding areas, caused an estimated damage of $50 billion, and became the second costliest tropical cyclone (TC) in U.S. History surpassed only by Hurricane Katrina (2005). To save lives and mitigate economic damage, a central question to be addressed is to what extent the lead time of severe storm prediction such as Sandy can be extended (e.g., Emanuel 2012; Kerr 2012). In this study, we present 10 numerical experiments initialized at 00 and 1200 UTC Oct. 22-26, 2012, with the NASA coupled advanced global modeling and visualization systems (CAMVis). All of the predictions realistically capture Sandy's movement with the northwestward turn prior to its landfall. However, three experiments (initialized at 0000 UTC Oct. 22 and 24 and 1200 UTC Oct. 22) produce larger errors. Among the 10 experiments, the control run initialized at 0000 UTC Oct. 23 produces a remarkable 7-day forecast. To illustrate the impact of environmental flows on the predictability of Sandy, we produce and discuss four-dimensional (4-D) visualizations with the control run. 4-D visualizations clearly demonstrate the following multiscale processes that led to the sinuous track of Sandy: the initial steering impact of an upper-level trough (appearing over the northwestern Caribbean Sea and Gulf of Mexico), the blocking impact of systems to the northeast of Sandy, and the binary interaction with a mid-latitude, upper-level trough that appeared at 130degrees west longitude on Oct. 23, moved to the East Coast and intensified during the period of Oct. 29-30 prior to Sandy's landfall.
International Journal of Bifurcation and Chaos, Oct 1, 2022
Accurate predictions for the spread and evolution of epidemics have significant societal and econ... more Accurate predictions for the spread and evolution of epidemics have significant societal and economic impacts. The temporal evolution of infected (or dead) persons has been described as an epidemic wave with an isolated peak and tails. Epidemic waves have been simulated and studied using the classical SIR model that describes the evolution of susceptible (S), infected (I), and recovered (R) individuals. To illustrate the fundamental dynamics of an epidemic wave, the dependence of solutions on parameters, and the dependence of predictability horizons on various types of solutions, we propose a Korteweg–de Vries (KdV)–SIR equation and obtain its analytical solutions. Among classical and simplified SIR models, our KdV–SIR equation represents the simplest system that produces a solution with both exponential and oscillatory components. The KdV–SIR model is mathematically identical to the nondissipative Lorenz 1963 model and the KdV equation in a traveling-wave coordinate. As a result, the dynamics of an epidemic wave and its predictability can be understood by applying approaches used in nonlinear dynamics, and by comparing the aforementioned systems. For example, a typical solitary wave solution is a homoclinic orbit that connects a stable and an unstable manifold at the saddle point within the [Formula: see text]–[Formula: see text] space. The KdV–SIR equation additionally produces two other types of solutions, including oscillatory and unbounded solutions. The analysis of two critical points makes it possible to reveal the features of solutions near a turning point. Using analytical solutions and hypothetical observed data, we derive a simple formula for determining predictability horizons, and propose a method for predicting timing for the peak of an epidemic wave.
Recent advances in computational and global modeling technology have provided the potential to im... more Recent advances in computational and global modeling technology have provided the potential to improve weather predictions at extended-range scales. In earlier studies by the author and his coauthors, realistic 30-day simulations of multiple African easterly waves (AEWs) and an averaged African easterly jet (AEJ) were obtained. The formation of hurricane Helene (2006) was also realistically simulated from Day 22 to Day 30. In this study, such extended predictability was further analyzed based on recent understandings of chaos and instability within Lorenz models and the generalized Lorenz model. The analysis suggested that a statement of the theoretical predictability of two weeks is not universal. New insight into chaotic and non-chaotic processes revealed by the generalized Lorenz model (GLM) indicated the potential for extending prediction lead times. Two major features within the GLM included: (1) three types of attractors (that also appeared in the original Lorenz model) and (2) two kinds of attractor coexistence. The features suggest a refined view on the nature of weather, as follows: The entirety of weather is a superset that consists of chaotic and non-chaotic processes. Better predictability can be obtained for stable, steady-state solutions and nonlinear periodic solutions that occur at small and large Rayleigh parameters, respectively. By comparison, chaotic solutions appear only at moderate Rayleigh parameters. Errors associated with dissipative small-scale processes do not necessarily contaminate the simulations of large scale processes. Based on the nonlinear periodic solutions (also known as limit cycle solutions), here, we propose a hypothetical mechanism for the recurrence (or periodicity) of successive AEWs. The insensitivity of limit cycles to initial conditions implies that AEW simulations with strong heating and balanced nonlinearity could be more predictable. Based on the hypothetical mechanism, the possibility of extending prediction lead times at extended range scales is discussed. Future work will include refining the model to better examine the validity of the mechanism to explain the recurrence of multiple AEWs.
In this study, we present a new nine-dimensional Lorenz model (9DLM) that requires a larger criti... more In this study, we present a new nine-dimensional Lorenz model (9DLM) that requires a larger critical value for the Rayleigh parameter (a rc of 679.8) for the onset of chaos, as compared to a rc of 24.74 for the 3DLM, a rc of 42.9 for the 5DLM, and a rc 116.9 for the 7DLM. Major features within the 9DLM include: (1) the coexistence of chaotic and non-chaotic orbits with moderate Rayleigh parameters, and (2) the coexistence of limit cycle/torus orbits and spiral sinks with large Rayleigh parameters. Version 2 of the 9DLM, referred to as the 9DLM-V2, is derived to show that: (i) based on a linear stability analysis, two non-trivial critical points are stable for all Rayleigh parameters greater than one; (ii) under non-dissipative and linear conditions, the extended nonlinear feedback loop produces four incommensurate frequencies; and (iii) for a stable orbit, small deviations away from equilibrium (e.g., the stable critical point) do not have a significant impact on orbital stability. Based on our results, we suggest that the entirety of weather is a superset that consists of both chaotic and non-chaotic processes.
In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM)... more In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM) integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial l-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (l) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, the microphysics developments of the multi-scale modeling system will be presented. In particular, the results from using multi-scale modeling system to study the heavy precipitation processes will be presented. https://ntrs.nasa.gov/search.jsp?R=20110015159 2020-01-26T22:02:49+00:00Z
ABSTRACT Very Severe Cyclonic Storm Nargis, the deadliest named tropical cyclone (TC) in the Nort... more ABSTRACT Very Severe Cyclonic Storm Nargis, the deadliest named tropical cyclone (TC) in the North Indian Ocean Basin, devastated Burma (Myanmar) in May 2008, causing tremendous damage and numerous fatalities. An increased lead time in the prediction of TC Nargis would have increased the warning time and may therefore have saved lives and reduced economic damage. Recent advances in high-resolution global models and supercomputers have shown the potential for improving TC track and intensity forecasts, presumably by improving multi-scale simulations. The key but challenging questions to be answered include: (1) if and how realistic, in terms of timing, location and TC general structure, the global mesoscale model (GMM) can simulate TC genesis and (2) under what conditions can the model extend the lead time of TC genesis forecasts. In this study, we focus on genesis prediction for TCs in the Indian Ocean with the GMM. Preliminary real-data simulations show that the initial formation and intensity variations of TC Nargis can be realistically predicted at a lead time of up to 5 days. These simulations also suggest that the accurate representations of a westerly wind burst (WWB) and an equatorial trough, associated with monsoon circulations and/or a Madden-Julian Oscillation (MJO), are important for predicting the formation of this kind of TC. In addition to the WWB and equatorial trough, other favorable environmental conditions will be examined, which include enhanced monsoonal circulation, upper-level outflow, low- and middle-level moistening, and surface fluxes.
Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It co... more Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (1) a cloud-resolving model (CRM), (2) a regional-scale model, the NASA unified Weather Research and Forecasting Model (WRF), and (3) a coupled CRM-GCM (general circulation model, known as the Goddard Multi-scale Modeling Framework or MMF). The same cloud-microphysical processes, long-and shortwave radiative transfer and landsurface processes are applied in all of the models to study explicit cloud-radiation and cloud-surface interactive processes in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator for comparison and validation with NASA high-resolution satellite data. This paper reviews the development and presents some applications of the multi-scale modeling system, including results from using the multi-scale modeling system to study the interactions between clouds, precipitation, and aerosols. In addition, use of the multi-satellite simulator to identify the strengths and weaknesses of the model-simulated precipitation processes will be discussed as well as future model developments and applications.
In a recent study, a seven-dimensional Lorenz Model (7DLM) was derived based on an extension of t... more In a recent study, a seven-dimensional Lorenz Model (7DLM) was derived based on an extension of the nonlinear feedback loop within the five-dimensional LM (5DLM). An analysis of Lyapunov exponents indicated that the 7DLM requires a much larger critical value for the Rayleigh parameter (rc ∼ 116.9) for the onset of chaos as compared to the rc of 24.74 for the original three-dimensional (3D) LM and the rc of 42.9 for the 5DLM. To assure that the 7DLM is more stable than the 3DLM and 5DLM, analytical solutions of the critical points for the 7DLM were obtained and a linear stability analysis near the critical point solutions was performed using various values of the Rayleigh parameter (40 ≤ r ≤ 195) and the Prandtl number (5 ≤ σ ≤ 25). In derivations of the 7DLM, potential temperature is represented by the primary, secondary, and tertiary modes, while the streamfunction is represented only by the primary mode. I also further derive a nine-dimensional LM (9DLM) by extending the 7DLM with secondary and tertiary modes for the streamfunction. By comparing the 9DLM with the 7DLM, the negative nonlinear feedback associated with the tertiary temperature modes, as first identified in the 7DLM, is determined to play a dominant role in stabilizing solutions, while the secondary and tertiary modes for the streamfunction produce additional heating terms that slightly destabilize solutions. The critical value of the Rayleigh parameter for the 9DLM is determined to be 102.9, smaller than that of the 7DLM but still much larger than those within the 3DLM and 5DLM. Additionally, as indicated by the strong bivariate relationship among primary, secondary, and tertiary temperature modes, hierarchical scale dependence appears in the 9DLM as well as the 7DLM. Therefore, the comparison between the 7DLM and the 9DLM suggests that using the 7DLM is effective for examining the impact of high-wavenumber modes on solutions stability.
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