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edmf [2018/09/07 10:55] – [Introducing scale-adaptivity and stochastic behavior in EDMF] neggersedmf [2022/09/14 17:47] (current) – ibartolo
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 where subgrid $tc$ indicates turbulence and convection, the overline indicates a horizontal Reynolds' average, and the prime a perturbation from this mean. Ever since the advent of numerical simulation of atmospheric flow the closure of the flux $\overline{w'\phi'}$ has been subject to intense research, and many different methods have been proposed. At the foundation of most schemes are two basic transport models. The first is the //Eddy Diffusive// (ED) transport model which describes the behavior by small-scale turbulent processes, acting to even out differences.  where subgrid $tc$ indicates turbulence and convection, the overline indicates a horizontal Reynolds' average, and the prime a perturbation from this mean. Ever since the advent of numerical simulation of atmospheric flow the closure of the flux $\overline{w'\phi'}$ has been subject to intense research, and many different methods have been proposed. At the foundation of most schemes are two basic transport models. The first is the //Eddy Diffusive// (ED) transport model which describes the behavior by small-scale turbulent processes, acting to even out differences. 
 \begin{eqnarray*} \begin{eqnarray*}
-\overline{w'\phi'}_{\mbox{\tiny ED}} \sim - K_{\phi} \frac{\partial \overline{\phi}}{\partial z}+\overline{w'\phi'}_{ED} \sim - K_{\phi} \frac{\partial \overline{\phi}}{\partial z}
 \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, and can not penetrate inversions very deeply. The second basic transport model is //advective//, and describes the behavior of larger-scale convective motions (or plumes) that have enough inertia to overcome stable layers, 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, and can not penetrate inversions very deeply. The second basic transport model is //advective//, and describes the behavior of larger-scale convective motions (or plumes) that have enough inertia to overcome stable layers,
 \begin{eqnarray*} \begin{eqnarray*}
-\overline{w'\phi'}_{\mbox{\tiny MF}} \approx M_c \left( \phi_c -\phi_e \right)+\overline{w'\phi'}_{MF} \approx M_c \left( \phi_c -\phi_e \right)
 \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.
  
-{{:thl_2d.png?&300|}} +{{:qt_2d.png?&400|}} 
-{{:qt_2d.png?&300|}} +{{:mbulk_c_2d.png?&400|}}
-{{:mbulk_c_2d.png?&300|}} +
-{{:abulk_2d.png?&300|}}+
  
-//Figure 3. Results with the multi-plume EDMF scheme for the RICO shallow cumulus case. Clockwise from the top left: liquid water potential temperature $\theta_l$, total specific humidity $q_t$, total area fraction of the EDMF plumes, and the volumetric mass flux of the condensed EDMF plumes. The simulation was performed with ED(MF)<sup>n</sup> implemented in DALES as a subgrid scheme, using an ensemble of 10 plumes. DALES was run on an 8x8 grid at 10km horizontal grid-spacing and a time-integration step of 300 s.//+//Figure 3. Single Column Model (SCM) results with the multi-plume ED(MF)<sup>n</sup> scheme based on discretized size distributions for the RICO shallow cumulus case. Clockwise from the top left: liquid water potential temperature $\theta_l$, total specific humidity $q_t$, and the total area fraction and volumetric mass flux of all condensed EDMF plumes combined. The simulation was performed with ED(MF)<sup>n</sup> implemented in DALES as a subgrid scheme, using an ensemble of 10 plumes. DALES was run on an 8x8 grid at grid-spacing of 10km horizontally and 40 m vertically, using a time-integration step of 300 s. More results with the DALES-ED(MF)<sup>n</sup> model, also for other cumulus cases, can be found on this [[http://atmos.meteo.uni-koeln.de/~neggers/EDMFn/EDMFn_plots.php|QUICKLOOK]] page. //
  
 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, and swiftly, find the point at which the vertical transport of mass, heat and humidity through cloud base by all plumes together exactly counteracts the effect of the destabilizing large-scale forcings. This situation corresponds to a quasi-equilibrium state, and the feedback mechanism that establishes it is called the //shallow cumulus valve// mechanism. An advantage of multi-plume MF models is that this process can be captured automatically, yielding smooth simulations for idealized prototype cumulus cases (see Fig. 3). 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, and swiftly, find the point at which the vertical transport of mass, heat and humidity through cloud base by all plumes together exactly counteracts the effect of the destabilizing large-scale forcings. This situation corresponds to a quasi-equilibrium state, and the feedback mechanism that establishes it is called the //shallow cumulus valve// mechanism. An advantage of multi-plume MF models is that this process can be captured automatically, yielding smooth simulations for idealized prototype cumulus cases (see Fig. 3).
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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' \phi'}_{\mbox{\tiny MF}}(z) +\overline{w' \phi'}_{MF}(z) 
 & \approx & \int_{l} \mathcal{M}(l,z) \left[ \phi(l,z) - \phi_e(z) \right] dl \\ & \approx & \int_{l} \mathcal{M}(l,z) \left[ \phi(l,z) - \phi_e(z) \right] dl \\
 & = &  \int_{l} \mathcal{A}(l,z) \left[ w(l,z) - w_e(z) \right] \left[ \phi(l,z) - \phi_e(z) \right] dl & = &  \int_{l} \mathcal{A}(l,z) \left[ w(l,z) - w_e(z) \right] \left[ \phi(l,z) - \phi_e(z) \right] dl
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-==== SCM on microgrids: LES as a non-hydrostatic testing ground for ED(MF)<sup>n</sup> =====+==== Results for prototype cumulus cases =====
  
-ED(MF)<sup>n</sup> is implemented into DALES as a subgrid scheme, replacing the original Sub-Filter Scale (SFS) scheme (Smagorinsky or TKE).+DALES-ED(MF)<sup>n</sup> basically stands for the DALES code with the ED(MF)<sup>n</sup> scheme implemented as a subgrid scheme, replacing the original Sub-Filter Scale (SFS) scheme (Smagorinsky or TKE). Results with this scheme for a set of well-known prototype cumulus cases  are provided on this [[http://atmos.meteo.uni-koeln.de/~neggers/EDMFn/EDMFn_plots.php|QUICKLOOK]] page. All simulations were performed on a 8x8 microgrid with dx=dy=10 km and dt=300 sec.
  
-Results for some prototype shallow cumulus cases are shown below. All simulations were performed on a 8x8 microgrid with dx=dy=10 km and dt=300 sec.+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).
  
-RICO +==== Contact =====
- +
-BOMEX +
- +
-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://www.geomet.uni-koeln.de/das-institut/mitarbeiter/neggers/|Roel Neggers]].
  
edmf.1536310530.txt.gz · Last modified: 2018/09/07 10:55 by neggers