Comparison of closure schemes used to specify the velocity PDF in Lagrangian stochastic dispersion models for convective conditions

Luhar, Ashok K.; Hibberd, Mark F.; Hurley, Peter

doi:10.1016/1352-2310(95)00464-5

Cited by 71 publications

(63 citation statements)

References 17 publications

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“…3) for the PDF in Eq. 5 has been given by Luhar and Britter (1989) and in a slightly more general form by Luhar (1991) and Luhar et al (1996). For the present case of a vertically variable density flow the distribution is given by…”

Section: Model Descriptionmentioning

confidence: 99%

“…Luhar and Britter (1989), Luhar and Sawford (1995) and Franzese et al (1999). For the specific case of the CBL, and following Baerentsen and Berkowicz (1984), Luhar and Britter (1989) and Luhar et al (1996), the PDF for the vertical velocity statistics can be assumed to be defined as the sum of two Gaussian PDFs,…”

Section: Model Descriptionmentioning

confidence: 99%

“…and the drift formulation for constant mean density of Luhar et al (1996) must be accordingly modified to,…”

Section: Model Descriptionmentioning

confidence: 99%

“…One Gaussian distribution represents the updraft and the other represents the downdraft. Therefore, here we extend the work of Stohl and Thomson (1999) including a density correction in the model of Luhar et al (1996), formulated using the well-mixed criterion and assuming a skewed PDF based on the sum of two Gaussians PDFs. Since backward-in-time modelling is extensively used in many applications (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Flesch et al 1995;Kljun et al 2002;Seibert and Frank 2004), for completeness and clarity we discuss in some detail the backward-in-time formulation of this model based on Thomson (1987), and we perform consistency tests between backward and forward simulations. The formulation of Luhar et al (1996) assumes that the turbulent statistics are horizontally homogeneous and stationary and, to our knowledge, many operational implementations of the Lagrangian stochastic model used nowadays neglect the horizontal and time derivatives of the turbulence statistics in the model formulation. A noticeable exception is the TAPM model described in Luhar and Hurley (2003) that uses an unsteady extension of the quadratic model of Franzese et al (1999).…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

Cassiani

Stohl

Brioude

2014

Boundary-Layer Meteorol

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A correction for the vertical gradient of air density has been incorporated into a skewed probability density function formulation for turbulence in the convective boundary layer. The related drift term for Lagrangian stochastic dispersion modelling has been derived based on the well-mixed condition. Furthermore, the formulation has been extended to include unsteady turbulence statistics and the related additional component of the drift term obtained. These formulations are an extension of the drift formulation reported by Luhar et al. (Atmos Environ 30:1407-1418, 1996 following the well-mixed condition proposed by Thomson (J Fluid Mech 180:529-556, 1987). Comprehensive tests were carried out to validate the formulations including consistency between forward and backward simulations and preservation of a well-mixed state with unsteady conditions. The stationary state CBL drift term with density correction was incorporated into the FLEXPART and FLEXPART-WRF Lagrangian models, and included the use of an ad hoc transition function that modulates the third moment of the vertical velocity based on stability parameters. Due to the current implementation of the FLEXPART models, only a steady-state horizontally homogeneous drift term could be included. To avoid numerical instability, in the presence of non-stationary and horizontally inhomogeneous conditions, a re-initialization procedure for particle velocity was used. The criteria for re-initialization and resulting errors were assessed for the case of non-stationary conditions by comparing a reference numerical solution in simplified unsteady conditions, obtained using the non-stationary drift term, and a solution based on the steady drift with re-initialization. Two examples of "real-world" numerical simulations were performed under different convective conditions to demonstrate the effect of the vertical gradient in density on the particle dispersion in the CBL.

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Section: Model Descriptionmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

“…and the drift formulation for constant mean density of Luhar et al (1996) must be accordingly modified to,…”

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

Cassiani

Stohl

Brioude

2014

Boundary-Layer Meteorol

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A Diagnostic PDF Cloud Scheme to Improve Subtropical Low Clouds in NCAR Community Atmosphere Model (CAM5)

Qin

Wang

et al. 2018

J Adv Model Earth Syst

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Low clouds strongly impact the radiation budget of the climate system, but their simulation in most GCMs has remained a challenge, especially over the subtropical stratocumulus region. Assuming a Gaussian distribution for the subgrid‐scale total water and liquid water potential temperature, a new statistical cloud scheme is proposed and tested in NCAR Community Atmospheric Model version 5 (CAM5). The subgrid‐scale variance is diagnosed from the turbulent and shallow convective processes in CAM5. The approach is able to maintain the consistency between cloud fraction and cloud condensate and thus alleviates the adjustment needed in the default relative humidity‐based cloud fraction scheme. Short‐term forecast simulations indicate that low cloud fraction and liquid water content, including their diurnal cycle, are improved due to a proper consideration of subgrid‐scale variance over the southeastern Pacific Ocean region. Compared with the default cloud scheme, the new approach produced the mean climate reasonably well with improved shortwave cloud forcing (SWCF) due to more reasonable low cloud fraction and liquid water path over regions with predominant low clouds. Meanwhile, the SWCF bias over the tropical land regions is also alleviated. Furthermore, the simulated marine boundary layer clouds with the new approach extend further offshore and agree better with observations. The new approach is able to obtain the top of atmosphere (TOA) radiation balance with a slightly alleviated double ITCZ problem in preliminary coupled simulations. This study implies that a close coupling of cloud processes with other subgrid‐scale physical processes is a promising approach to improve cloud simulations.

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Meteorology for Air Dispersion Modelers

Visscher

2013

Air Dispersion Modeling

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Comparison of closure schemes used to specify the velocity PDF in Lagrangian stochastic dispersion models for convective conditions

Cited by 71 publications

References 17 publications

Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

A Diagnostic PDF Cloud Scheme to Improve Subtropical Low Clouds in NCAR Community Atmosphere Model (CAM5)

Meteorology for Air Dispersion Modelers

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