edmf
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edmf [2018/09/07 12:08] – neggers | edmf [2022/09/14 17:47] (current) – ibartolo | ||
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where subgrid $tc$ indicates turbulence and convection, the overline indicates a horizontal Reynolds' | where subgrid $tc$ indicates turbulence and convection, the overline indicates a horizontal Reynolds' | ||
\begin{eqnarray*} | \begin{eqnarray*} | ||
- | \overline{w' | + | \overline{w' |
\end{eqnarray*} | \end{eqnarray*} | ||
where $K_{\phi}$ is the eddy diffusivity coefficient. As expressed by the dependence on the vertical gradient, in principle this model acts purely down-gradient, | where $K_{\phi}$ is the eddy diffusivity coefficient. As expressed by the dependence on the vertical gradient, in principle this model acts purely down-gradient, | ||
\begin{eqnarray*} | \begin{eqnarray*} | ||
- | \overline{w' | + | \overline{w' |
\end{eqnarray*} | \end{eqnarray*} | ||
where $M_c$ is the volumetric //Mass Flux// (MF) by the convective elements, defined (in approximation) as the product of their area fraction and their vertical velocity. Such motions can transport in counter-gradient directions, and can maintain differences between a convective plume ( c) and its environment (e) for some time. The Eddy Diffusivity - Mass Flux (EDMF) approach is a relatively new method that aims to combine the benefits of both ways of describing transport, | where $M_c$ is the volumetric //Mass Flux// (MF) by the convective elements, defined (in approximation) as the product of their area fraction and their vertical velocity. Such motions can transport in counter-gradient directions, and can maintain differences between a convective plume ( c) and its environment (e) for some time. The Eddy Diffusivity - Mass Flux (EDMF) approach is a relatively new method that aims to combine the benefits of both ways of describing transport, | ||
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where subscript $i$ indicates the average properties of plume //i//. This yields a spectrum of plumes, each slightly different, as illustrated in Fig. 2. What each plume represents depends on its definition, for which various options have been proposed. What unites these EDMF versions however is the use of a spectrum of plumes, which enables them to overcome non-linearities that are hard to capture by advective schemes that carry less complexity. | where subscript $i$ indicates the average properties of plume //i//. This yields a spectrum of plumes, each slightly different, as illustrated in Fig. 2. What each plume represents depends on its definition, for which various options have been proposed. What unites these EDMF versions however is the use of a spectrum of plumes, which enables them to overcome non-linearities that are hard to capture by advective schemes that carry less complexity. | ||
- | {{: | + | {{: |
- | {{: | + | {{: |
- | {{: | + | |
- | {{: | + | |
- | //Figure 3. Results | + | //Figure 3. Single Column Model (SCM) results |
A benefit of multi plume models is that bulk properties can in principle be diagnosed from the reconstructed spectrum of rising plumes, making classically-used bulk closures obsolete. For example, plumes can condense or not, depending on their proximity to saturation. As a result, the scheme becomes sensitive to environmental humidity, a behavior that recent research has found to be an essential feature in convection schemes. The number of plumes that reach their lifting condensation level and continue as transporting cumulus clouds is automatically found by the scheme itself (see also Fig 2). An environment closer to saturation will yield a higher number of rising plumes that will condense at the top of the mixed layer, which immediately boosts the cloud base mass flux. This allows the scheme to effectively, | A benefit of multi plume models is that bulk properties can in principle be diagnosed from the reconstructed spectrum of rising plumes, making classically-used bulk closures obsolete. For example, plumes can condense or not, depending on their proximity to saturation. As a result, the scheme becomes sensitive to environmental humidity, a behavior that recent research has found to be an essential feature in convection schemes. The number of plumes that reach their lifting condensation level and continue as transporting cumulus clouds is automatically found by the scheme itself (see also Fig 2). An environment closer to saturation will yield a higher number of rising plumes that will condense at the top of the mixed layer, which immediately boosts the cloud base mass flux. This allows the scheme to effectively, | ||
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An ensemble of plumes can be differentiated based on updraft properties such as thermodynamic state, vertical velocity or buoyancy. Alternatively one can define a plume spectrum in size-space, as schematically illustrated in Fig. 4. This has some important consequences. For example, the size distribution of plume properties becomes the foundation of the EDMF framework. This can be understood by rewriting the multi-plume MF flux at some height $z$ as a function of plume size $l$, | An ensemble of plumes can be differentiated based on updraft properties such as thermodynamic state, vertical velocity or buoyancy. Alternatively one can define a plume spectrum in size-space, as schematically illustrated in Fig. 4. This has some important consequences. For example, the size distribution of plume properties becomes the foundation of the EDMF framework. This can be understood by rewriting the multi-plume MF flux at some height $z$ as a function of plume size $l$, | ||
\begin{eqnarray*} | \begin{eqnarray*} | ||
- | \overline{w' | + | \overline{w' |
& \approx & \int_{l} \mathcal{M}(l, | & \approx & \int_{l} \mathcal{M}(l, | ||
& = & \int_{l} \mathcal{A}(l, | & = & \int_{l} \mathcal{A}(l, | ||
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- | ==== DALES-ED(MF)n showcase | + | ==== Results for prototype cumulus cases ===== |
- | ED(MF)< | + | DALES-ED(MF)< |
- | RICO\\ | + | The cases for which the scheme is tested cover different climate regimes and convective types. Marine subtropical shallow cumulus conditions are described by the RICO and BOMEX case. Continental diurnal cycles of shallow cumulus are represented by the classic "ARM SGP" case (21 June 1997), various LASSO cases, and selected days at the mid-latitude JOYCE site in Germany. Transitional cases from stratocumulus to cumulus include the ASTEX case and the SLOW, REFERENCE and FAST case as described by Sandu et al., all of which featured in the recent SCM intercomparison study by Neggers et al. (2017) as part of the EUCLIPSE project. Finally, deep convective conditions are covered by the humidity-convection case of Derbyshire et al (2004) and a variation of the BOMEX case with modified surface fluxes described by Kuang and Bretherton (2000). |
- | {{:thl_2d.png?& | + | |
- | {{:qt_2d.png?& | + | |
- | {{: | + | |
- | {{:abulk_2d.png?& | + | |
- | BOMEX | + | ==== Contact ===== |
- | + | ||
- | ARM Shallow cumulus case (Brown et al, 2001) | + | |
- | + | ||
- | A convective day at JOYCE on 5 June 2013 | + | |
- | + | ||
- | === References | + | |
- | + | ||
- | FIXME | + | |
+ | For more information get in contact with [[http:// | ||
edmf.1536314910.txt.gz · Last modified: 2018/09/07 12:08 by neggers