Eulerian—Lagrangian relationships in monte carlo simulations of turbulent diffusion

Lee, J.T.; Stone, G.L.

doi:10.1016/0004-6981(83)90073-2

Cited by 18 publications

(4 citation statements)

References 10 publications

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“…In the Eulerian approach, the mass concentration of fluid elements is calculated as a function of space and time instead of calculating trajectories of fluid elements. Despite this difference, these two approaches solve numerically the same partial differential equation; hence theoretically they lead to identical results when the temporal and spatial resolutions are sufficiently increased and if the same parameterization for sub-grid scale transport is applied in each of them (Hanna, 1979;Lee and Stone, 1983). Both approaches are used in the inverse modeling community to estimate source-sink distributions (Gerbig et al, 2003a;Lauvaux, 2008;Rödenbeck et al, 2003) The atmospheric distribution of passive inert trace gases is variable on small scales (both temporal and spatial), caused…”

Section: Introductionmentioning

confidence: 99%

Comparing Lagrangian and Eulerian models for CO2 transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

et al. 2012

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Abstract. We present simulations of atmospheric CO 2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO 2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO 2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO 2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.

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Section: Introductionmentioning

confidence: 99%

Comparing Lagrangian and Eulerian models for CO2 transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

et al. 2012

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“…It is also generally found that the proportionality between Eulerian and Lagrangian scales is a function of the turbulence intensity at the position of interest. The idea of proportionality is generally attributed to Hay and Pasquill (1960) with further analysis by Wandel and Kofoed-Hansen (1962) and Lee and Stone (1983). The basic functional form is:…”

Section: Cross-stream Lagrangian Time Scale T LVmentioning

confidence: 99%

Predicting plume meandering and averaging time effects on mean and fluctuating concentrations in atmospheric dispersion simulated in a water channel

Hilderman

Wilson

2006

Boundary-Layer Meteorol

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Plume meandering and averaging time effects were measured directly using a high spatial resolution, high frequency, linescan laser-induced fluorescence (LIF) technique for measuring scalar concentrations in a plume dispersing in a water channel. Post-processing of the collected data removed time dependent background dye levels and corrected for attenuation across the laser beam to produce accurate measurements over long sample times in both a rough surface boundary-layer shear flow and shear free grid-generated turbulent flow. The data were used to verify the applicability of a meandering plume model for predicting the properties of mean and fluctuating concentrations. The centroid position of the crosswind concentration profile was found to have a Gaussian probability density function and the instantaneous plume spread about the centroid fluctuated log-normally. A modified travel-time power law model for averaging time adjustment was developed and compared to the widely used, but much less accurate, 0.2 power-law model.

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Section: Introductionmentioning

confidence: 99%

Comparing Lagrangian and Eulerian models for CO2 transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Pillai¹,

Gerbig²,

Kretschmer³

et al. 2012

Preprint

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We present simulations of atmospheric CO₂ concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO₂ concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO₂ concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO₂ time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport

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Eulerian—Lagrangian relationships in monte carlo simulations of turbulent diffusion

Cited by 18 publications

References 10 publications

Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Predicting plume meandering and averaging time effects on mean and fluctuating concentrations in atmospheric dispersion simulated in a water channel

Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

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Eulerian—Lagrangian relationships in monte carlo simulations of turbulent diffusion

Cited by 18 publications

References 10 publications

Comparing Lagrangian and Eulerian models for CO&lt;sub&gt;2&lt;/sub&gt; transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Comparing Lagrangian and Eulerian models for CO&lt;sub&gt;2&lt;/sub&gt; transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Predicting plume meandering and averaging time effects on mean and fluctuating concentrations in atmospheric dispersion simulated in a water channel

Comparing Lagrangian and Eulerian models for CO&lt;sub&gt;2&lt;/sub&gt; transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

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Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM