Changes between Version 12 and Version 13 of doc/tec/lsf


Ignore:
Timestamp:
May 4, 2016 6:22:29 PM (9 years ago)
Author:
Giersch
Comment:

--

Legend:

Unmodified
Added
Removed
Modified
  • doc/tec/lsf

    v12 v13  
    11=== Large scale forcing ===
    22
    3 Usually, the LES model PALM is used to simulate the flow in the boundary layer which is a certain part of the atmosphere. Processes occurring on larger scales than those in the boundary layer including large scale advection of scalars, large scale pressure gradients or large scale subsidence have also to be considered in the model, especially when focusing on realistic situations observed during measurement campaigns. In limited domain models with non-cyclic boundary conditions the large scale state enters through the boundary conditions at the lateral walls, and is usually taken from larger-scale models. This method isn't possible with cyclic horizontal boundary conditions (because there are no real lateral boundaries). In case of cyclic boundary conditions PALM uses a method developed by Neggers et al. (2012), which is switched on by parameter [../../app/inipar#large_scale_forcing large_scale_forcing]. '''This method does not work with non-cyclic horizontal boundary conditions! ''' Furthermore, it requires to use a flat topography.
    4 \\
    5 
    6 '''Horizontal large scale (LS) advection:
    7 
    8 Effects of horizontal large scale advection are taken into account by adding large scale tendencies
     3Usually, the LES model PALM is used to simulate the flow in the boundary layer which is a certain part of the atmosphere. Processes occurring on larger scales than those in the boundary layer including large scale advection of scalars, large scale pressure gradients or large scale subsidence have also to be considered in the model, especially when focusing on realistic situations observed during measurement campaigns. In limited domain models with non-cyclic boundary conditions the large scale state enters through the boundary conditions at the lateral walls, and is usually taken from larger-scale models. This method isn't possible with cyclic horizontal boundary conditions (because there are no real lateral boundaries). In case of cyclic boundary conditions PALM uses a method developed by Neggers et al. (2012), which is switched on by parameter [../../app/inipar#large_scale_forcing large_scale_forcing]. '''This method does not work with non-cyclic horizontal boundary conditions! ''' Furthermore, it requires to use a flat topography. In case of cyclic boundary conditions, this forcing is prescribed homogeneously in the horizontal directions and thus depends on height and time only. The relation between larger scales (LS) pressure
     4(''p'',,LS,,) gradient and geostrophic wind is given by
    95{{{
    106#!Latex
    11 $\left. \dfrac{\partial \varphi}{\partial t} \right|_{\text{LS}} = - \left( u_{\text{LS}} \dfrac{\partial \varphi_{\text{LS}}}{\partial x \vphantom{y}} + v_{\text{LS}} \dfrac{\partial \varphi_{\text{LS}}}{\partial y} \right)$ \quad with \quad $\varphi \in \{\theta,q\}$
     7\begin{align*}
     8 \frac{\partial p_{\text{LS}}}{\partial
     9  x_{i}}=-\rho_{0}\varepsilon_{i3j}f_{3}u_{\mathrm{g},j}
     10\end{align*}
    1211}}}
    13 to the prognostic equations. These tendencies are typically derived from larger scale models and should be spatially averaged over a large domain so that local-scale perturbations are avoided.
    14 
    15 \\
    16 
    17 '''Large scale subsidence:'''\\
    18 
    19 Effects of large scale subsidence and ascent can be considered by two different methods in PALM. The default method uses a large scale subsidence velocity '''w_subs''' which is usually taken from larger scale models. For the vertical advection of the prognostic variables an additional tendencies are computed:
     12and enters the first equation in Sect. [wiki:doc/tec/gov governing equations].\\
     13LS vertical advection (subsidence or ascent) tendencies can be prescribed for the scalar prognostic variables ''φ ∈ {θ, q, s}'' by means of
    2014{{{
    2115#!Latex
    22 $\left. \dfrac{\partial \varphi}{\partial t} \right|_{\text{subs}} = - w_{\text{subs}} \dfrac{\partial \varphi_{\text{LES}}}{\partial z \vphantom{y}} = - w_{\text{LS}} \dfrac{\partial \varphi_{\text{LES}}}{\partial z \vphantom{y}}.$
     16\begin{align*}
     17\left.\frac{\partial \varphi}{\partial t}\right\vert_{\text{SUB}} =
     18  -w_{\text{LS}}\frac{\partial \varphi}{\partial z}.
     19\end{align*}
    2320}}}
    24 \\
    25 Alternatively, large scale subsidence tendencies, derived from larger scale models, can be directly applied to the prognostic equations:
     21
     22The so-called subsidence velocity ''w'',,LS,, and the geostrophic wind components ''u'',,g,, and ''v'',,g,, can either be prescribed gradient-wise or they can be provided in an external file. Moreover, an external pressure gradient can be applied for simulations with Coriolis force switched off, which is usually required for simulations to be compared with wind tunnel experiments.\\
     23To account for less-idealized flow situations, time-dependent surface fluxes (or surface temperature and humidity) can be
     24prescribed. Moreover, LS horizontal advective (LSA) tendencies can be added to the scalar quantities by means of
    2625{{{
    2726#!Latex
    28 $\left. \dfrac{\partial \varphi}{\partial t} \right|_{\text{subs}} = - w_{\text{LS}} \dfrac{\partial \varphi_{\text{LS}}}{\partial z \vphantom{y}} .$
     27\begin{align*}
     28  & \left.\frac{\partial \varphi}{\partial t}\right\vert_{\text{LSA}} =
     29  -\left(u_{\text{LS}}\frac{\partial \varphi_{\text{LS}}}{\partial
     30      x}+v_{\text{LS}}\frac{\partial \varphi_{\text{LS}}}{\partial
     31      y}\right).
     32\end{align*}
    2933}}}
    30 This method can be used by setting the control parameter [wiki:doc/app/inipar#use_subsidence_tendencies use_subsidence_tendencies] to ''.T.''.
    31 
    32 Note that in any case [../../app/inipar#large_scale_subsidence large_scale_subsidence] has to be set to ''.T.'' in the parameter file.
    33 
    34 \\
    35 
    36 '''Nudging:'''\\
    37 
    38 When performing runs with large scale forcing it is recommended to use additional [wiki:doc/tec/nudging  nudging], so that excessive model drift in time is prevented (Neggers et al., 2012).
    39 
    40 \\
    41 
    42 A complete example for a PALM run with large scale forcing and nudging is documented [../../app/examples/lsf here].
     34These tendencies are typically derived from larger scale models or observations and should be spatially averaged over a~large domain so
     35that local-scale perturbations are avoided.\\
     36Newtonian relaxation (nudging) towards given large-scale profiles
     37$\varphi_{\text{LS}}$ can be used for ''φ ∈ {u, v, θ, q, s}'' via
     38{{{
     39#!Latex
     40\begin{align*}
     41  \left.\frac{\partial \varphi}{\partial t}\right\vert_{\text{NUD}} =
     42  -\frac{\left\langle\varphi\right\rangle-\varphi_{\text{LS}}}{\tau_{\text{LS}}}\;.
     43\end{align*}
     44}}}
     45''τ'',,LS,, is a relaxation time-scale which, on the one hand, should be chosen large enough in the order of several hours to allow
     46an undisturbed development of the small-scale turbulence in the LES model. On the other hand, it should be chosen small enough to account
     47for synoptic disturbances ([#neggers2012 Neggers et al., 2012]). In this way, the nudging can prevent considerable model drift in time.
    4348
    4449=== References ===
    45 * '''Neggers, R. A. J., A. P. Siebesma and T. Heus, 2012:''' Continous single-column model evaluation at a permanent meteorological supersite. ''Bull. Amer. Meteor. Soc'', '''29''', 91-115. [http://dx.doi.org/10.1175/BAMS-D-11-00162.1 doi]
     50*[=#neggers2012] '''Neggers RAJ, Siebesma AP, Heus T.''' 2012. Continous single-column model evaluation at a permanent meteorological supersite. Bull. Amer. Meteor. Soc. 29: 91-115. [http://dx.doi.org/10.1175/BAMS-D-11-00162.1 doi]