This paper shall present a multifractal interpretation of turbulent atmospheric entities, conside... more This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding multifractal structures through non-differentiable functions in the form of an adaptation of scale relativity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation—all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described, an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are emplo...
In this paper, developments are made towards simulating complex atmospheric behavior using turbul... more In this paper, developments are made towards simulating complex atmospheric behavior using turbulent energy cascade staging models developed through scale relativity theories. Such theoretical considerations imply gauges that describe atmospheric parameters as multifractal functions undertaking scale symmetry breaking at each stage of the turbulent energy cascade. It is found that gauges of higher complexity (in this case, a Riccati-type gauge) can exhibit more complex behavior accordingly, such as both dilation and contraction, but properly parameterizing the solutions formed by these gauges in terms of turbulent staging can be challenging given the multiple constants and parameters. However, it is found that a logistic-type approximation of the multifractal equations of motion that describe turbulent atmospheric entities can be coupled with a model produced by a simpler gauge, and this combination can reveal instances of laminar, or otherwise non-chaotic, behavior in a given turbu...
This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model wi... more This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model with multiple instruments when applied to a humid continental region, in this case, the region around the city of Iași, Romania. A series of output parameters are compared with observed data, obtained on-site, with a focus on the Planetary Boundary Layer Height (PBLH) and on PBLH-related parametrizations used by the WRF model. The impact of each different parametrization on physical quantities is highlighted during the two chosen measurement intervals, both of them in the warm season of 2016 and 2017, respectively. The instruments used to obtain real data to compare to the WRF simulations are: a lidar platform, a photometer, and ground-level (GL) meteorological instrumentation for the measurement of temperature, average wind speed, and pressure. Maps of PBLH and 2 m above ground-level (AGL) atmospheric temperature are also presented, compared to a topological and relief map of the inner ...
The article is aimed at presenting a semi-empirical model coded and computed in the programming l... more The article is aimed at presenting a semi-empirical model coded and computed in the programming language Python, which utilizes data gathered with a standard biaxial elastic lidar platform in order to calculate the altitude profiles of the structure coefficients of the atmospheric refraction index C N 2 ( z ) and other associated turbulence parameters. Additionally, the model can be used to calculate the PBL (Planetary Boundary Layer) height, and other parameters typically employed in the field of astronomy. Solving the Fernard–Klett inversion by correlating sun-photometer data obtained through our AERONET site with lidar data, it can yield the atmospheric extinction and backscatter profiles α ( z ) and β ( z ) , and thus obtain the atmospheric optical depth. Finally, several theoretical notions of interest that utilize the solved parameters are presented, such as approximated relations between C N 2 ( z ) and the atmospheric temperature profile T ( z ) , and between the scintillati...
In this paper, developments are made towards simulating complex atmospheric behavior using turbul... more In this paper, developments are made towards simulating complex atmospheric behavior using turbulent energy cascade staging models developed through scale relativity theories. Such theoretical considerations imply gauges that describe atmospheric parameters as multifractal functions undertaking scale symmetry breaking at each stage of the turbulent energy cascade. It is found that gauges of higher complexity (in this case, a Riccati-type gauge) can exhibit more complex behavior accordingly, such as both dilation and contraction, but properly parameterizing the solutions formed by these gauges in terms of turbulent staging can be challenging given the multiple constants and parameters. However, it is found that a logistic-type approximation of the multifractal equations of motion that describe turbulent atmospheric entities can be coupled with a model produced by a simpler gauge, and this combination can reveal instances of laminar, or otherwise non-chaotic, behavior in a given turbulent flow at certain scales. Employing the theory with elastic lidar data, quasi-laminar behavior is found in the vicinity of the planetary boundary layer height, and laminar channels are revealed throughout an atmospheric column—these might be used to reveal complex vertical transport behavior in the atmospheric column.
This paper shall present a multifractal interpretation of turbulent atmospheric entities, conside... more This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding mul-tifractal structures through non-differentiable functions in the form of an adaptation of scale rela-tivity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation-all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described , an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are employed together, exemplifying the codependency of such models. Using turbulent medium wave propagation theory, certain relations are then extrapolated which allow the obtaining of the inner and outer length scales of the turbulent flow using lidar data. Finally, these altitude profiles are compiled and assembled into timeseries to exemplify the theory and to compare the results with known literature. This model is a generalization of our recent results published under the title "On a Multifractal Approach of Turbulent Atmosphere Dynamics".
This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model wi... more This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model with multiple instruments when applied to a humid continental region, in this case, the region around the city of Iasi, Romania. A series of output parameters are compared with observed data, obtained on-site, with a focus on the Planetary Boundary Layer Height (PBLH) and on PBLH-related parametrizations used by the WRF model. The impact of each different parametrization on physical quantities is highlighted during the two chosen measurement intervals, both of them in the warm season of 2016 and 2017, respectively. The instruments used to obtain real data to compare to the WRF simulations are: a lidar platform, a photometer, and ground-level (GL) meteorological instrumentation for the measurement of temperature, average wind speed, and pressure. Maps of PBLH and 2 m above ground-level (AGL) atmospheric temperature are also presented, compared to a topological and relief map of the inner nest of the WRF simulation. Finally, a comprehensive simulation performance evaluation of PBLH, temperature, wind speed, and pressure at the surface and total precipitable water vapor is performed.
The article is aimed at presenting a semi-empirical model coded and computed in the programming l... more The article is aimed at presenting a semi-empirical model coded and computed in the programming language Python, which utilizes data gathered with a standard biaxial elastic lidar platform in order to calculate the altitude profiles of the structure coefficients of the atmospheric refraction index C2N(z) and other associated turbulence parameters. Additionally, the model can be used to calculate the PBL (Planetary Boundary Layer) height, and other parameters typically employed in the field of astronomy. Solving the Fernard–Klett inversion by correlating sun-photometer data obtained through our AERONET site with lidar data, it can yield the atmospheric extinction and backscatter profiles a(z) and b(z), and thus obtain the atmospheric optical depth. Finally, several theoretical notions of interest that utilize the solved parameters are presented, such as approximated relations between C2N(z) and the atmospheric temperature profile T(z), and between the scintillation of backscattered lidar signal and the average wind speed profile U(z). These obtained profiles and parameters also have several environmental applications that are connected directly and indirectly to human health and well-being, ranging from understanding the transport of aerosols in the atmosphere and minimizing the errors in measuring it, to predicting extreme, and potentially-damaging, meteorological events.
This paper aims to present a multifractal approach of the turbulent atmosphere, by proposing that... more This paper aims to present a multifractal approach of the turbulent atmosphere, by proposing that it can be considered a complex system whose structural units support dynamics on continuous but non differentiable multifractal curves. Implementing the theoretical framework of multifractality through non-differentiable functions in the form of scale relativity theory with arbitrary and constant fractal dimension, the minimal vortex of an instance of turbulent flow is considered. The results of this assumption lead to an equation that describes the minimal vortex itself, and the velocity fields that compose it, the vortex and turbulent energy dissipation derived from the vortex being plotted and studied. With its structure mathematically described, while employing a classical dynamical turbulence model and relations between turbulent energy dissipation and the minimal vortex, relations are then extrapolated to allow for the solving of multiple turbulent parameters using the inner and outer length scales of the turbulent flow. These equations are then solved as altitude profiles with the necessary length scales obtained from processing lidar data. Finally, profiles are taken periodically and assembled into timeseries, in order to exemplify the method and to compare the results with known literature.
This paper shall present a multifractal interpretation of turbulent atmospheric entities, conside... more This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding multifractal structures through non-differentiable functions in the form of an adaptation of scale relativity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation—all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described, an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are emplo...
In this paper, developments are made towards simulating complex atmospheric behavior using turbul... more In this paper, developments are made towards simulating complex atmospheric behavior using turbulent energy cascade staging models developed through scale relativity theories. Such theoretical considerations imply gauges that describe atmospheric parameters as multifractal functions undertaking scale symmetry breaking at each stage of the turbulent energy cascade. It is found that gauges of higher complexity (in this case, a Riccati-type gauge) can exhibit more complex behavior accordingly, such as both dilation and contraction, but properly parameterizing the solutions formed by these gauges in terms of turbulent staging can be challenging given the multiple constants and parameters. However, it is found that a logistic-type approximation of the multifractal equations of motion that describe turbulent atmospheric entities can be coupled with a model produced by a simpler gauge, and this combination can reveal instances of laminar, or otherwise non-chaotic, behavior in a given turbu...
This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model wi... more This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model with multiple instruments when applied to a humid continental region, in this case, the region around the city of Iași, Romania. A series of output parameters are compared with observed data, obtained on-site, with a focus on the Planetary Boundary Layer Height (PBLH) and on PBLH-related parametrizations used by the WRF model. The impact of each different parametrization on physical quantities is highlighted during the two chosen measurement intervals, both of them in the warm season of 2016 and 2017, respectively. The instruments used to obtain real data to compare to the WRF simulations are: a lidar platform, a photometer, and ground-level (GL) meteorological instrumentation for the measurement of temperature, average wind speed, and pressure. Maps of PBLH and 2 m above ground-level (AGL) atmospheric temperature are also presented, compared to a topological and relief map of the inner ...
The article is aimed at presenting a semi-empirical model coded and computed in the programming l... more The article is aimed at presenting a semi-empirical model coded and computed in the programming language Python, which utilizes data gathered with a standard biaxial elastic lidar platform in order to calculate the altitude profiles of the structure coefficients of the atmospheric refraction index C N 2 ( z ) and other associated turbulence parameters. Additionally, the model can be used to calculate the PBL (Planetary Boundary Layer) height, and other parameters typically employed in the field of astronomy. Solving the Fernard–Klett inversion by correlating sun-photometer data obtained through our AERONET site with lidar data, it can yield the atmospheric extinction and backscatter profiles α ( z ) and β ( z ) , and thus obtain the atmospheric optical depth. Finally, several theoretical notions of interest that utilize the solved parameters are presented, such as approximated relations between C N 2 ( z ) and the atmospheric temperature profile T ( z ) , and between the scintillati...
In this paper, developments are made towards simulating complex atmospheric behavior using turbul... more In this paper, developments are made towards simulating complex atmospheric behavior using turbulent energy cascade staging models developed through scale relativity theories. Such theoretical considerations imply gauges that describe atmospheric parameters as multifractal functions undertaking scale symmetry breaking at each stage of the turbulent energy cascade. It is found that gauges of higher complexity (in this case, a Riccati-type gauge) can exhibit more complex behavior accordingly, such as both dilation and contraction, but properly parameterizing the solutions formed by these gauges in terms of turbulent staging can be challenging given the multiple constants and parameters. However, it is found that a logistic-type approximation of the multifractal equations of motion that describe turbulent atmospheric entities can be coupled with a model produced by a simpler gauge, and this combination can reveal instances of laminar, or otherwise non-chaotic, behavior in a given turbulent flow at certain scales. Employing the theory with elastic lidar data, quasi-laminar behavior is found in the vicinity of the planetary boundary layer height, and laminar channels are revealed throughout an atmospheric column—these might be used to reveal complex vertical transport behavior in the atmospheric column.
This paper shall present a multifractal interpretation of turbulent atmospheric entities, conside... more This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding mul-tifractal structures through non-differentiable functions in the form of an adaptation of scale rela-tivity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation-all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described , an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are employed together, exemplifying the codependency of such models. Using turbulent medium wave propagation theory, certain relations are then extrapolated which allow the obtaining of the inner and outer length scales of the turbulent flow using lidar data. Finally, these altitude profiles are compiled and assembled into timeseries to exemplify the theory and to compare the results with known literature. This model is a generalization of our recent results published under the title "On a Multifractal Approach of Turbulent Atmosphere Dynamics".
This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model wi... more This article aims to present an evaluation of the Weather Research and Forecasting (WRF) model with multiple instruments when applied to a humid continental region, in this case, the region around the city of Iasi, Romania. A series of output parameters are compared with observed data, obtained on-site, with a focus on the Planetary Boundary Layer Height (PBLH) and on PBLH-related parametrizations used by the WRF model. The impact of each different parametrization on physical quantities is highlighted during the two chosen measurement intervals, both of them in the warm season of 2016 and 2017, respectively. The instruments used to obtain real data to compare to the WRF simulations are: a lidar platform, a photometer, and ground-level (GL) meteorological instrumentation for the measurement of temperature, average wind speed, and pressure. Maps of PBLH and 2 m above ground-level (AGL) atmospheric temperature are also presented, compared to a topological and relief map of the inner nest of the WRF simulation. Finally, a comprehensive simulation performance evaluation of PBLH, temperature, wind speed, and pressure at the surface and total precipitable water vapor is performed.
The article is aimed at presenting a semi-empirical model coded and computed in the programming l... more The article is aimed at presenting a semi-empirical model coded and computed in the programming language Python, which utilizes data gathered with a standard biaxial elastic lidar platform in order to calculate the altitude profiles of the structure coefficients of the atmospheric refraction index C2N(z) and other associated turbulence parameters. Additionally, the model can be used to calculate the PBL (Planetary Boundary Layer) height, and other parameters typically employed in the field of astronomy. Solving the Fernard–Klett inversion by correlating sun-photometer data obtained through our AERONET site with lidar data, it can yield the atmospheric extinction and backscatter profiles a(z) and b(z), and thus obtain the atmospheric optical depth. Finally, several theoretical notions of interest that utilize the solved parameters are presented, such as approximated relations between C2N(z) and the atmospheric temperature profile T(z), and between the scintillation of backscattered lidar signal and the average wind speed profile U(z). These obtained profiles and parameters also have several environmental applications that are connected directly and indirectly to human health and well-being, ranging from understanding the transport of aerosols in the atmosphere and minimizing the errors in measuring it, to predicting extreme, and potentially-damaging, meteorological events.
This paper aims to present a multifractal approach of the turbulent atmosphere, by proposing that... more This paper aims to present a multifractal approach of the turbulent atmosphere, by proposing that it can be considered a complex system whose structural units support dynamics on continuous but non differentiable multifractal curves. Implementing the theoretical framework of multifractality through non-differentiable functions in the form of scale relativity theory with arbitrary and constant fractal dimension, the minimal vortex of an instance of turbulent flow is considered. The results of this assumption lead to an equation that describes the minimal vortex itself, and the velocity fields that compose it, the vortex and turbulent energy dissipation derived from the vortex being plotted and studied. With its structure mathematically described, while employing a classical dynamical turbulence model and relations between turbulent energy dissipation and the minimal vortex, relations are then extrapolated to allow for the solving of multiple turbulent parameters using the inner and outer length scales of the turbulent flow. These equations are then solved as altitude profiles with the necessary length scales obtained from processing lidar data. Finally, profiles are taken periodically and assembled into timeseries, in order to exemplify the method and to compare the results with known literature.
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parameters. However, it is found that a logistic-type approximation of the multifractal equations of motion that describe turbulent atmospheric entities can be coupled with a model produced by a simpler gauge, and this combination can reveal instances of laminar, or otherwise non-chaotic, behavior in a given turbulent flow at certain scales. Employing the theory with elastic lidar data, quasi-laminar behavior is found in the vicinity of the planetary boundary layer height, and laminar channels are revealed throughout an atmospheric column—these might be used to reveal complex vertical transport behavior in the atmospheric column.
it, the vortex and turbulent energy dissipation derived from the vortex being plotted and studied. With its structure mathematically described, while employing a classical dynamical turbulence model and relations between turbulent energy dissipation and the minimal vortex, relations are then extrapolated to allow for the solving of multiple turbulent parameters using the inner and outer length scales of the turbulent flow.
These equations are then solved as altitude profiles with the necessary length scales obtained from processing lidar data. Finally, profiles are taken periodically and assembled into timeseries, in order to exemplify the method and to compare the results with known literature.
parameters. However, it is found that a logistic-type approximation of the multifractal equations of motion that describe turbulent atmospheric entities can be coupled with a model produced by a simpler gauge, and this combination can reveal instances of laminar, or otherwise non-chaotic, behavior in a given turbulent flow at certain scales. Employing the theory with elastic lidar data, quasi-laminar behavior is found in the vicinity of the planetary boundary layer height, and laminar channels are revealed throughout an atmospheric column—these might be used to reveal complex vertical transport behavior in the atmospheric column.
it, the vortex and turbulent energy dissipation derived from the vortex being plotted and studied. With its structure mathematically described, while employing a classical dynamical turbulence model and relations between turbulent energy dissipation and the minimal vortex, relations are then extrapolated to allow for the solving of multiple turbulent parameters using the inner and outer length scales of the turbulent flow.
These equations are then solved as altitude profiles with the necessary length scales obtained from processing lidar data. Finally, profiles are taken periodically and assembled into timeseries, in order to exemplify the method and to compare the results with known literature.