[[NoteBox(warn,This site is currently under construction!)]] = Cloud mircrophysics = PALM offers an embedded bulk cloud microphysics representation that takes into account the liquid water specific humidity and warm (i.e., no ice) cloud-microphysical processes. Therefore, PALM solves the prognostic equations for the total water content {{{ #!Latex \begin{align*} & q = q_\mathrm{v} + q_\mathrm{l}, \end{align*} }}} instead of ''q'',,v,,, and for a linear approximation of the liquid water potential temperature ([#emanuel1994 e.g., Emanuel, 1994]) {{{ #!Latex \begin{align*} \theta_\mathrm{l} = \theta - \frac{L_\mathrm{V}}{c_p \Pi} q_\mathrm{l}\,, \end{align*} }}} instead of ''θ'' as described in Sect. [wiki:doc/tec/gov governing equations]. Since ''q'' and ''θ'',,l,, are conserved quantities for wet adiabatic processes, condensation/evaporation is not considered for these variables. Liquid phase microphysics are parametrized following the two-moment scheme of [#seifert2001 Seifert and Beheng (2001],[#seifert2006 2006)], which is based on the separation of the droplet spectrum into droplets with radii < 40 μm (cloud droplets) and droplets with radii ≥ 40 μm (rain droplets). The model predicts the first two moments of these partial droplet spectra, namely cloud and rain droplet number concentration (''N'',,c,, and ''N'',,r,,, respectively) as well as cloud and rain water specific humidity (''q'',,c,, and ''q'',,r,,, respectively). Consequently, ''q'',,l,, is the sum of both ''q'',,c,, and ''q'',,r,,. The moments' corresponding microphysical tendencies are derived by assuming the partial droplet spectra to follow a gamma distribution that can be described by the predicted quantities and empirical relationships for the distribution's slope and shape parameters. For a detailed derivation of these terms, see [#seifert2001 Seifert and Beheng (2001],[#seifert2006 2006)]. We employ the computational efficient implementation of this scheme as used in the UCLA-LES ([#savic2008 Savic-Jovcic and Stevens, 2008]) and DALES ([#heus2010 Heus et al., 2010]) models. We thus solve only two additional prognostic equations for ''N'',,r,, and ''q'',,r,,: {{{ #!Latex \begin{align*} \frac{\partial N_\mathrm{r}}{\partial t} = - u_j \frac{\partial N_\mathrm{r}}{\partial x_j} - \frac{\partial}{\partial x_j}\left(\overline{u_j^{\prime\prime}N_\mathrm{r}^{\prime\prime}}\right) + \Psi_{N_\mathrm{r}},\\ \frac{\partial q_\mathrm{r}}{\partial t} = - u_j \frac{\partial q_\mathrm{r}}{\partial x_j} - \frac{\partial}{\partial x_j}\left(\overline{u_j^{\prime\prime}q_\mathrm{r}^{\prime\prime}}\right) + \Psi_{q_\mathrm{r}}, \end{align*} }}} with the sink/source terms ''Ψ'',,Nr,, and ''Ψ'',,qr,,, and the SGS fluxes {{{ #!Latex \begin{align*} & \overline{u_j^{\prime\prime}N_\mathrm{r}^{\prime\prime}} = -K_\mathrm{h} \:\frac{\partial q_\mathrm{r}} {\partial x_{i}}\,\\ & \overline{u_j^{\prime\prime}q_\mathrm{r}^{\prime\prime}} = -K_\mathrm{h} \:\frac{\partial N_\mathrm{r}} {\partial x_{i}}\, \end{align*} }}} with ''N'',,c,, and ''q'',,c,, being a fixed parameter and a diagnostic quantity, respectively. In the next subsections we will describe the diagnostic determination of ''q'',,c,,. From Sect. [wiki:doc/tec/microphysics#Autoconversion autoconversion] on, the microphysical processes considered in the sink/source terms of ''θ'',,l,,, ''q'', ''N'',,r,, and ''q'',,r,,, {{{ #!Latex \begin{align*} & \Psi_{\theta_\mathrm{l}} = - \frac{L_\mathrm{v}}{c_p \Pi} \varphi_q,\\ & \Psi_{q} = \left.\frac{\partial q}{\partial t} \right|_\text{sed, c} + \left.\frac{\partial q}{\partial t} \right|_\text{sed, r},\\ & \Psi_{N_\mathrm{r}} = \left.\frac{\partial N_\mathrm{r}}{\partial t} \right|_{\text{auto}}+ \left.\frac{\partial N_\mathrm{r}}{\partial t} \right|_\text{slf/brk}+ \left.\frac{\partial N_\mathrm{r}}{\partial t} \right|_{\text{evap}}+ \left.\frac{\partial N_\mathrm{r}}{\partial t} \right|_\text{sed, r},\\ & \Psi_{q_\mathrm{r}} = \left.\frac{\partial q_\mathrm{r}}{\partial t} \right|_{\text{auto}} + \left.\frac{\partial q_\mathrm{r}}{\partial t} \right|_{\text{accr}}+ \left.\frac{\partial q_\mathrm{r}}{\partial t} \right|_{\text{evap}}+ \left.\frac{\partial q_\mathrm{r}}{\partial t} \right|_\text{sed, r}, \end{align*} }}} are used in the formulations of [#seifert2006 Seifert and Beheng (2006)] unless explicitly specified. Section [wiki:doc/tec/microphysics#Turbulenceclosure turbulence closure] gives an overview of the necessary changes for the turbulence closure [wiki:doc/tec/sgs#Turbulenceclosure (cf. Sect. turbulence closure)] using ''q'' and ''θ'',,l,, instead of ''q'',,v,, and $θ$, respectively. [[Image(Table4.png,600px,border=1)]] [[Image(Table5.png,600px,border=1)]] [[Image(Table6.png,600px,border=1)]] == Diffusional growth of cloud water == The diagnostic estimation of ''q'',,c,, is based on the assumption that water supersaturations are immediately removed by the diffusional growth of cloud droplets only. This can be justified since the bulk surface area of cloud droplets exceeds that of rain drops considerably ([#stevens2008 Stevens and Seifert, 2008]). Following this saturation adjustment approach, ''q'',,c,, is obtained by {{{ #!Latex \begin{align*} & q_\mathrm{c}=\max{\left(0, q - q_\mathrm{r} - q_\mathrm{s} \right)}, \end{align*} }}} where ''q'',,s,, is the saturation specific humidity. Because ''q'',,s,, is a function of ''T'' (not predicted), ''q'',,s,, is computed from the liquid water temperature ''T'',,l,, = ''Π θ,,l,, in a first step: {{{ #!Latex \begin{align*} q_\mathrm{s}(T_\mathrm{l}) = \frac{R_\mathrm{d}}{R_\mathrm{v}} \frac{p_\text{v, s}(T_\mathrm{l})}{p-\left(1-R_\mathrm{d}/R_\mathrm{v}\right)\,p_\text{v, s}(T_\mathrm{l})}, \end{align*} }}} using an empirical relationship for the saturation water vapor pressure ''p'',,v,s,, ([#bougeault1981 Bougeault, 1981]): {{{ #!Latex \begin{align*} & p_\text{v, s}(T_\mathrm{l}) = 610.78 \text{Pa} \cdot \exp{\left(17.269\,\frac{T_\mathrm{l}-273.16\,\text{K}}{T_\mathrm{l}-35.86\,\text{K}} \right)}. \end{align*} }}} ''q'',,s,,(''T'') is subsequently calculated from a 1st-order Taylor series expansion of ''q'',,s,, at ''T'',,l,, ([#sommeria1977 Sommeria and Deardorff, 1977]): {{{ #!Latex \begin{align*} & q_\mathrm{s}(T)=q_\mathrm{s}(T_\mathrm{l})\frac{1+\beta\,q}{1+ \beta\,q_\mathrm{s}(T_\mathrm{l})}, \end{align*} }}} with {{{ #!Latex \begin{align*} & \beta = \frac{L_\mathrm{v}^2}{R_\mathrm{v} c_p T_\mathrm{l}^2}. \end{align*} }}} == Autoconversion == == Accretion == == Self-collection and breakup == == Evaporation of rainwater == == Sedimentation of rainwater == Turbulence closure == == Recent applications == == References == * [=#emanuel1994]'''Emanuel KA.''' 1994. Atmospheric Convection. Oxford University Press. * [=#seifert2001]'''Seifert A, Beheng KD.''' 2001. A double-moment parameterization for simulating autoconversion, accretion and selfcollection. Atmos. Res. 59: 265–281. * [=#seifert2006]'''Seifert A, Beheng KD.''' 2006. A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Meteorol. Atmos. Phys. 92: 45–66. * [=#savic2008]'''Savic-Jovcic V, Stevens B.''' 2008. The structure and mesoscale organization of precipitating stratocumulus. J. Atmos. Sci. 65: 1587–1605. [http://dx.doi.org/10.1175/2007JAS2456.1 doi] * [=#heus2010]'''Heus T, van Heerwaarden CC, Jonker HJJ, Pier Siebesma A, Axelsen S, van den Dries K, Geoffroy O, Moene AF, Pino D, de Roode SR, Vilà-Guerau de Arellano J.''' 2010. Formulation of the Dutch Atmospheric Large-Eddy Simulation (DALES) and overview of its applications. Geosci. Model Dev. 3: 415–444. [http://dx.doi.org/10.5194/gmd-3-415-2010 doi] * [=#stevens2008]'''Stevens B, Seifert A.''' 2008. Understanding macrophysical outcomes of microphysical choices in simulations of shallow cumulus convection. J. Meteor. Soc. Jpn. 86: 143–162. * [=#bougeault1981]'''Bougeault, P.''' 1981. Modeling the trade-wind cumulus boundary layer. Part I: Testing the ensemble cloud relations against numerical data. J. Atmos. Sci. 38: 2414–2428. * [=#sommeria1977]'''Sommeria G, Deardorff JW.''' 1977. Subgrid-scale condensation in models of nonprecipitating clouds. J. Atmos. Sci. 34: 344–355.