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\section{Fizhi: High-end Atmospheric Physics} |
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|
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\subsection{Introduction} |
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The fizhi (high-end atmospheric physics) package includes a collection of state-of-the-art |
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physical parameterizations for atmospheric radiation, cumulus convection, atmospheric |
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boundary layer turbulence, and land surface processes. |
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|
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% ************************************************************************* |
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% ************************************************************************* |
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|
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\subsection{Equations} |
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|
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\subsubsection{Moist Convective Processes} |
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|
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\subsubsubsection{Sub-grid and Large-scale Convection} |
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\label{sec:fizhi:mc} |
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|
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Sub-grid scale cumulus convection is parameterized using the Relaxed Arakawa |
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Schubert (RAS) scheme of Moorthi and Suarez (1992), which is a linearized Arakawa Schubert |
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type scheme. RAS predicts the mass flux from an ensemble of clouds. Each subensemble is identified |
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by its entrainment rate and level of neutral bouyancy which are determined by the grid-scale properties. |
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|
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The thermodynamic variables that are used in RAS to describe the grid scale vertical profile are |
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the dry static energy, $s=c_pT +gz$, and the moist static energy, $h=c_p T + gz + Lq$. |
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The conceptual model behind RAS depicts each subensemble as a rising plume cloud, entraining |
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mass from the environment during ascent, and detraining all cloud air at the level of neutral |
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buoyancy. RAS assumes that the normalized cloud mass flux, $\eta$, normalized by the cloud base |
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mass flux, is a linear function of height, expressed as: |
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\[ |
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\pp{\eta(z)}{z} = \lambda \hspace{0.4cm}or\hspace{0.4cm} \pp{\eta(P^{\kappa})}{P^{\kappa}} = |
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-{c_p \over {g}}\theta\lambda |
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\] |
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where we have used the hydrostatic equation written in the form: |
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\[ |
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\pp{z}{P^{\kappa}} = -{c_p \over {g}}\theta |
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\] |
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|
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The entrainment parameter, $\lambda$, characterizes a particular subensemble based on its |
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detrainment level, and is obtained by assuming that the level of detrainment is the level of neutral |
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buoyancy, ie., the level at which the moist static energy of the cloud, $h_c$, is equal |
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to the saturation moist static energy of the environment, $h^*$. Following Moorthi and Suarez (1992), |
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$\lambda$ may be written as |
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\[ |
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\lambda = { {h_B - h^*_D} \over { {c_p \over g} {\int_{P_D}^{P_B}\theta(h^*_D-h)dP^{\kappa}}} } , |
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\] |
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|
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where the subscript $B$ refers to cloud base, and the subscript $D$ refers to the detrainment level. |
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|
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|
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The convective instability is measured in terms of the cloud work function $A$, defined as the |
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rate of change of cumulus kinetic energy. The cloud work function is |
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related to the buoyancy, or the difference |
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between the moist static energy in the cloud and in the environment: |
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\[ |
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A = \int_{P_D}^{P_B} { {\eta \over {1 + \gamma} } |
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\left[ {{h_c-h^*} \over {P^{\kappa}}} \right] dP^{\kappa}} |
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\] |
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|
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where $\gamma$ is ${L \over {c_p}}\pp{q^*}{T}$ obtained from the Claussius Clapeyron equation, |
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and the subscript $c$ refers to the value inside the cloud. |
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|
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|
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To determine the cloud base mass flux, the rate of change of $A$ in time {\em due to dissipation by |
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the clouds} is assumed to approximately balance the rate of change of $A$ {\em due to the generation |
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by the large scale}. This is the quasi-equilibrium assumption, and results in an expression for $m_B$: |
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\[ |
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m_B = {{- \left.{dA \over dt} \right|_{ls}} \over K} |
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\] |
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|
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where $K$ is the cloud kernel, defined as the rate of change of the cloud work function per |
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unit cloud base mass flux, and is currently obtained by analytically differentiating the |
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expression for $A$ in time. |
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The rate of change of $A$ due to the generation by the large scale can be written as the |
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difference between the current $A(t+\Delta t)$ and its equillibrated value after the previous |
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convective time step |
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$A(t)$, divided by the time step. $A(t)$ is approximated as some critical $A_{crit}$, |
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computed by Lord (1982) from $in situ$ observations. |
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|
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|
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The predicted convective mass fluxes are used to solve grid-scale temperature |
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and moisture budget equations to determine the impact of convection on the large scale fields of |
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temperature (through latent heating and compensating subsidence) and moisture (through |
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precipitation and detrainment): |
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\[ |
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\left.{\pp{\theta}{t}}\right|_{c} = \alpha { m_B \over {c_p P^{\kappa}}} \eta \pp{s}{p} |
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\] |
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and |
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\[ |
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\left.{\pp{q}{t}}\right|_{c} = \alpha { m_B \over {L}} \eta (\pp{h}{p}-\pp{s}{p}) |
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\] |
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where $\theta = {T \over P^{\kappa}}$, $P = (p/p_0)$, and $\alpha$ is the relaxation parameter. |
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|
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As an approximation to a full interaction between the different allowable subensembles, |
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many clouds are simulated frequently, each modifying the large scale environment some fraction |
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$\alpha$ of the total adjustment. The parameterization thereby ``relaxes'' the large scale environment |
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towards equillibrium. |
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|
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In addition to the RAS cumulus convection scheme, the fizhi package employs a |
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Kessler-type scheme for the re-evaporation of falling rain (Sud and Molod, 1988), which |
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correspondingly adjusts the temperature assuming $h$ is conserved. RAS in its current |
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formulation assumes that all cloud water is deposited into the detrainment level as rain. |
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All of the rain is available for re-evaporation, which begins in the level below detrainment. |
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The scheme accounts for some microphysics such as |
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the rainfall intensity, the drop size distribution, as well as the temperature, |
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pressure and relative humidity of the surrounding air. The fraction of the moisture deficit |
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in any model layer into which the rain may re-evaporate is controlled by a free parameter, |
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which allows for a relatively efficient re-evaporation of liquid precipitate and larger rainout |
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for frozen precipitation. |
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|
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Due to the increased vertical resolution near the surface, the lowest model |
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layers are averaged to provide a 50 mb thick sub-cloud layer for RAS. Each time RAS is |
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invoked (every ten simulated minutes), |
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a number of randomly chosen subensembles are checked for the possibility |
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of convection, from just above cloud base to 10 mb. |
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|
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Supersaturation or large-scale precipitation is initiated in the fizhi package whenever |
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the relative humidity in any grid-box exceeds a critical value, currently 100 \%. |
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The large-scale precipitation re-evaporates during descent to partially saturate |
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lower layers in a process identical to the re-evaporation of convective rain. |
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|
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|
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\subsubsubsection{Cloud Formation} |
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\label{sec:fizhi:clouds} |
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|
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Convective and large-scale cloud fractons which are used for cloud-radiative interactions are determined |
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diagnostically as part of the cumulus and large-scale parameterizations. |
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Convective cloud fractions produced by RAS are proportional to the |
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detrained liquid water amount given by |
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|
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\[ |
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F_{RAS} = \min\left[ {l_{RAS}\over l_c}, 1.0 \right] |
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\] |
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|
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where $l_c$ is an assigned critical value equal to $1.25$ g/kg. |
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A memory is associated with convective clouds defined by: |
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|
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\[ |
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F_{RAS}^n = \min\left[ F_{RAS} + (1-{\Delta t_{RAS}\over\tau})F_{RAS}^{n-1}, 1.0 \right] |
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\] |
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|
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where $F_{RAS}$ is the instantanious cloud fraction and $F_{RAS}^{n-1}$ is the cloud fraction |
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from the previous RAS timestep. The memory coefficient is computed using a RAS cloud timescale, |
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$\tau$, equal to 1 hour. RAS cloud fractions are cleared when they fall below 5 \%. |
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|
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Large-scale cloudiness is defined, following Slingo and Ritter (1985), as a function of relative |
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humidity: |
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|
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\[ |
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F_{LS} = \min\left[ { \left( {RH-RH_c \over 1-RH_c} \right) }^2, 1.0 \right] |
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\] |
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|
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where |
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|
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\bqa |
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RH_c & = & 1-s(1-s)(2-\sqrt{3}+2\sqrt{3} \, s)r \nonumber \\ |
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s & = & p/p_{surf} \nonumber \\ |
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r & = & \left( {1.0-RH_{min} \over \alpha} \right) \nonumber \\ |
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RH_{min} & = & 0.75 \nonumber \\ |
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\alpha & = & 0.573285 \nonumber . |
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\eqa |
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|
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These cloud fractions are suppressed, however, in regions where the convective |
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sub-cloud layer is conditionally unstable. The functional form of $RH_c$ is shown in |
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Figure (\ref{fig:fizhi:rhcrit}). |
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|
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\begin{figure*}[htbp] |
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\vspace{0.4in} |
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\centerline{ \epsfysize=4.0in \epsfbox{rhcrit.ps}} |
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\vspace{0.4in} |
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\caption [Critical Relative Humidity for Clouds.] |
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{Critical Relative Humidity for Clouds.} |
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\label{fig:fizhi:rhcrit} |
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\end{figure*} |
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|
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The total cloud fraction in a grid box is determined by the larger of the two cloud fractions: |
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|
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\[ |
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F_{CLD} = \max \left[ F_{RAS},F_{LS} \right] . |
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\] |
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|
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Finally, cloud fractions are time-averaged between calls to the radiation packages. |
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|
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|
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\subsubsection{Radiation} |
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|
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The parameterization of radiative heating in the fizhi package includes effects |
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from both shortwave and longwave processes. |
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Radiative fluxes are calculated at each |
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model edge-level in both up and down directions. |
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The heating rates/cooling rates are then obtained |
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from the vertical divergence of the net radiative fluxes. |
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|
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The net flux is |
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\[ |
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F = F^\uparrow - F^\downarrow |
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\] |
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where $F$ is the net flux, $F^\uparrow$ is the upward flux and $F^\downarrow$ is |
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the downward flux. |
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|
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The heating rate due to the divergence of the radiative flux is given by |
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\[ |
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\pp{\rho c_p T}{t} = - \pp{F}{z} |
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\] |
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or |
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\[ |
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\pp{T}{t} = \frac{g}{c_p \pi} \pp{F}{\sigma} |
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\] |
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where $g$ is the accelation due to gravity |
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and $c_p$ is the heat capacity of air at constant pressure. |
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|
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The time tendency for Longwave |
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Radiation is updated every 3 hours. The time tendency for Shortwave Radiation is updated once |
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every three hours assuming a normalized incident solar radiation, and subsequently modified at |
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every model time step by the true incident radiation. |
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The solar constant value used in the package is equal to 1365 $W/m^2$ |
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and a $CO_2$ mixing ratio of 330 ppm. |
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For the ozone mixing ratio, monthly mean zonally averaged |
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climatological values specified as a function |
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of latitude and height (Rosenfield, et al., 1987) are linearly interpolated to the current time. |
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|
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|
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\subsubsubsection{Shortwave Radiation} |
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|
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The shortwave radiation package used in the package computes solar radiative |
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heating due to the absoption by water vapor, ozone, carbon dioxide, oxygen, |
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clouds, and aerosols and due to the |
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scattering by clouds, aerosols, and gases. |
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The shortwave radiative processes are described by |
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Chou (1990,1992). This shortwave package |
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uses the Delta-Eddington approximation to compute the |
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bulk scattering properties of a single layer following King and Harshvardhan (JAS, 1986). |
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The transmittance and reflectance of diffuse radiation |
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follow the procedures of Sagan and Pollock (JGR, 1967) and Lacis and Hansen (JAS, 1974). |
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|
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Highly accurate heating rate calculations are obtained through the use |
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of an optimal grouping strategy of spectral bands. By grouping the UV and visible regions |
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as indicated in Table \ref{tab:fizhi:solar2}, the Rayleigh scattering and the ozone absorption of solar radiation |
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can be accurately computed in the ultraviolet region and the photosynthetically |
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active radiation (PAR) region. |
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The computation of solar flux in the infrared region is performed with a broadband |
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parameterization using the spectrum regions shown in Table \ref{tab:fizhi:solar1}. |
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The solar radiation algorithm used in the fizhi package can be applied not only for climate studies but |
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also for studies on the photolysis in the upper atmosphere and the photosynthesis in the biosphere. |
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|
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\begin{table}[htb] |
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\begin{center} |
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{\bf UV and Visible Spectral Regions} \\ |
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\vspace{0.1in} |
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\begin{tabular}{|c|c|c|} |
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\hline |
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Region & Band & Wavelength (micron) \\ \hline |
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\hline |
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UV-C & 1. & .175 - .225 \\ |
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& 2. & .225 - .245 \\ |
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& & .260 - .280 \\ |
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& 3. & .245 - .260 \\ \hline |
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UV-B & 4. & .280 - .295 \\ |
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& 5. & .295 - .310 \\ |
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& 6. & .310 - .320 \\ \hline |
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UV-A & 7. & .320 - .400 \\ \hline |
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PAR & 8. & .400 - .700 \\ |
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\hline |
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\end{tabular} |
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\end{center} |
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\caption{UV and Visible Spectral Regions used in shortwave radiation package.} |
266 |
\label{tab:fizhi:solar2} |
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\end{table} |
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|
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\begin{table}[htb] |
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\begin{center} |
271 |
{\bf Infrared Spectral Regions} \\ |
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\vspace{0.1in} |
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\begin{tabular}{|c|c|c|} |
274 |
\hline |
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Band & Wavenumber(cm$^{-1}$) & Wavelength (micron) \\ \hline |
276 |
\hline |
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1 & 1000-4400 & 2.27-10.0 \\ |
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2 & 4400-8200 & 1.22-2.27 \\ |
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3 & 8200-14300 & 0.70-1.22 \\ |
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\hline |
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\end{tabular} |
282 |
\end{center} |
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\caption{Infrared Spectral Regions used in shortwave radiation package.} |
284 |
\label{tab:fizhi:solar1} |
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\end{table} |
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|
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Within the shortwave radiation package, |
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both ice and liquid cloud particles are allowed to co-exist in any of the model layers. |
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Two sets of cloud parameters are used, one for ice paticles and the other for liquid particles. |
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Cloud parameters are defined as the cloud optical thickness and the effective cloud particle size. |
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In the fizhi package, the effective radius for water droplets is given as 10 microns, |
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while 65 microns is used for ice particles. The absorption due to aerosols is currently |
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set to zero. |
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|
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To simplify calculations in a cloudy atmosphere, clouds are |
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grouped into low ($p>700$ mb), middle (700 mb $\ge p > 400$ mb), and high ($p < 400$ mb) cloud regions. |
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Within each of the three regions, clouds are assumed maximally |
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overlapped, and the cloud cover of the group is the maximum |
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cloud cover of all the layers in the group. The optical thickness |
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of a given layer is then scaled for both the direct (as a function of the |
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solar zenith angle) and diffuse beam radiation |
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so that the grouped layer reflectance is the same as the original reflectance. |
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The solar flux is computed for each of the eight cloud realizations possible |
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(see Figure \ref{fig:fizhi:cloud}) within this |
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low/middle/high classification, and appropriately averaged to produce the net solar flux. |
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|
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\begin{figure*}[htbp] |
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\vspace{0.4in} |
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\centerline{ \epsfysize=4.0in %\epsfbox{rhcrit.ps} |
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} |
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\vspace{0.4in} |
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\caption {Low-Middle-High Cloud Configurations} |
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\label{fig:fizhi:cloud} |
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\end{figure*} |
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|
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|
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\subsubsubsection{Longwave Radiation} |
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|
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The longwave radiation package used in the fizhi package is thoroughly described by Chou and Suarez (1994). |
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As described in that document, IR fluxes are computed due to absorption by water vapor, carbon |
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dioxide, and ozone. The spectral bands together with their absorbers and parameterization methods, |
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configured for the fizhi package, are shown in Table \ref{tab:fizhi:longwave}. |
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|
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|
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\begin{table}[htb] |
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\begin{center} |
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{\bf IR Spectral Bands} \\ |
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\vspace{0.1in} |
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\begin{tabular}{|c|c|l|c| } |
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\hline |
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Band & Spectral Range (cm$^{-1}$) & Absorber & Method \\ \hline |
332 |
\hline |
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1 & 0-340 & H$_2$O line & T \\ \hline |
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2 & 340-540 & H$_2$O line & T \\ \hline |
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3a & 540-620 & H$_2$O line & K \\ |
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3b & 620-720 & H$_2$O continuum & S \\ |
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3b & 720-800 & CO$_2$ & T \\ \hline |
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4 & 800-980 & H$_2$O line & K \\ |
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& & H$_2$O continuum & S \\ \hline |
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& & H$_2$O line & K \\ |
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5 & 980-1100 & H$_2$O continuum & S \\ |
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& & O$_3$ & T \\ \hline |
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6 & 1100-1380 & H$_2$O line & K \\ |
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& & H$_2$O continuum & S \\ \hline |
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7 & 1380-1900 & H$_2$O line & T \\ \hline |
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8 & 1900-3000 & H$_2$O line & K \\ \hline |
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\hline |
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\multicolumn{4}{|l|}{ \quad K: {\em k}-distribution method with linear pressure scaling } \\ |
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\multicolumn{4}{|l|}{ \quad T: Table look-up with temperature and pressure scaling } \\ |
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\multicolumn{4}{|l|}{ \quad S: One-parameter temperature scaling } \\ |
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\hline |
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\end{tabular} |
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\end{center} |
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\vspace{0.1in} |
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\caption{IR Spectral Bands, Absorbers, and Parameterization Method (from Chou and Suarez, 1994)} |
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\label{tab:fizhi:longwave} |
357 |
\end{table} |
358 |
|
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|
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The longwave radiation package accurately computes cooling rates for the middle and |
361 |
lower atmosphere from 0.01 mb to the surface. Errors are $<$ 0.4 C day$^{-1}$ in cooling |
362 |
rates and $<$ 1\% in fluxes. From Chou and Suarez, it is estimated that the total effect of |
363 |
neglecting all minor absorption bands and the effects of minor infrared absorbers such as |
364 |
nitrous oxide (N$_2$O), methane (CH$_4$), and the chlorofluorocarbons (CFCs), is an underestimate |
365 |
of $\approx$ 5 W/m$^2$ in the downward flux at the surface and an overestimate of $\approx$ 3 W/m$^2$ |
366 |
in the upward flux at the top of the atmosphere. |
367 |
|
368 |
Similar to the procedure used in the shortwave radiation package, clouds are grouped into |
369 |
three regions catagorized as low/middle/high. |
370 |
The net clear line-of-site probability $(P)$ between any two levels, $p_1$ and $p_2 \quad (p_2 > p_1)$, |
371 |
assuming randomly overlapped cloud groups, is simply the product of the probabilities within each group: |
372 |
|
373 |
\[ P_{net} = P_{low} \times P_{mid} \times P_{hi} . \] |
374 |
|
375 |
Since all clouds within a group are assumed maximally overlapped, the clear line-of-site probability within |
376 |
a group is given by: |
377 |
|
378 |
\[ P_{group} = 1 - F_{max} , \] |
379 |
|
380 |
where $F_{max}$ is the maximum cloud fraction encountered between $p_1$ and $p_2$ within that group. |
381 |
For groups and/or levels outside the range of $p_1$ and $p_2$, a clear line-of-site probability equal to 1 is |
382 |
assigned. |
383 |
|
384 |
|
385 |
\subsubsubsection{Cloud-Radiation Interaction} |
386 |
\label{sec:fizhi:radcloud} |
387 |
|
388 |
The cloud fractions and diagnosed cloud liquid water produced by moist processes |
389 |
within the fizhi package are used in the radiation packages to produce cloud-radiative forcing. |
390 |
The cloud optical thickness associated with large-scale cloudiness is made |
391 |
proportional to the diagnosed large-scale liquid water, $\ell$, detrained due to super-saturation. |
392 |
Two values are used corresponding to cloud ice particles and water droplets. |
393 |
The range of optical thickness for these clouds is given as |
394 |
|
395 |
\[ 0.0002 \le \tau_{ice} (mb^{-1}) \le 0.002 \quad\mbox{for}\quad 0 \le \ell \le 2 \quad\mbox{mg/kg} , \] |
396 |
\[ 0.02 \le \tau_{h_2o} (mb^{-1}) \le 0.2 \quad\mbox{for}\quad 0 \le \ell \le 10 \quad\mbox{mg/kg} . \] |
397 |
|
398 |
The partitioning, $\alpha$, between ice particles and water droplets is achieved through a linear scaling |
399 |
in temperature: |
400 |
|
401 |
\[ 0 \le \alpha \le 1 \quad\mbox{for}\quad 233.15 \le T \le 253.15 . \] |
402 |
|
403 |
The resulting optical depth associated with large-scale cloudiness is given as |
404 |
|
405 |
\[ \tau_{LS} = \alpha \tau_{h_2o} + (1-\alpha)\tau_{ice} . \] |
406 |
|
407 |
The optical thickness associated with sub-grid scale convective clouds produced by RAS is given as |
408 |
|
409 |
\[ \tau_{RAS} = 0.16 \quad mb^{-1} . \] |
410 |
|
411 |
The total optical depth in a given model layer is computed as a weighted average between |
412 |
the large-scale and sub-grid scale optical depths, normalized by the total cloud fraction in the |
413 |
layer: |
414 |
|
415 |
\[ \tau = \left( {F_{RAS} \,\,\, \tau_{RAS} + F_{LS} \,\,\, \tau_{LS} \over F_{RAS}+F_{LS} } \right) \Delta p, \] |
416 |
|
417 |
where $F_{RAS}$ and $F_{LS}$ are the time-averaged cloud fractions associated with RAS and large-scale |
418 |
processes described in Section \ref{sec:fizhi:clouds}. |
419 |
The optical thickness for the longwave radiative feedback is assumed to be 75 $\%$ of these values. |
420 |
|
421 |
The entire Moist Convective Processes Module is called with a frequency of 10 minutes. |
422 |
The cloud fraction values are time-averaged over the period between Radiation calls (every 3 |
423 |
hours). Therefore, in a time-averaged sense, both convective and large-scale |
424 |
cloudiness can exist in a given grid-box. |
425 |
|
426 |
\subsubsection{Turbulence} |
427 |
Turbulence is parameterized in the fizhi package to account for its contribution to the |
428 |
vertical exchange of heat, moisture, and momentum. |
429 |
The turbulence scheme is invoked every 30 minutes, and employs a backward-implicit iterative |
430 |
time scheme with an internal time step of 5 minutes. |
431 |
The tendencies of atmospheric state variables due to turbulent diffusion are calculated using |
432 |
the diffusion equations: |
433 |
|
434 |
\[ |
435 |
{\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} |
436 |
= {\pp{}{z} }{(K_m \pp{u}{z})} |
437 |
\] |
438 |
\[ |
439 |
{\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} |
440 |
= {\pp{}{z} }{(K_m \pp{v}{z})} |
441 |
\] |
442 |
\[ |
443 |
{\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} = |
444 |
P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} |
445 |
= P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} |
446 |
\] |
447 |
\[ |
448 |
{\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} |
449 |
= {\pp{}{z} }{(K_h \pp{q}{z})} |
450 |
\] |
451 |
|
452 |
Within the atmosphere, the time evolution |
453 |
of second turbulent moments is explicitly modeled by representing the third moments in terms of |
454 |
the first and second moments. This approach is known as a second-order closure modeling. |
455 |
To simplify and streamline the computation of the second moments, the level 2.5 assumption |
456 |
of Mellor and Yamada (1974) and Yamada (1977) is employed, in which only the turbulent |
457 |
kinetic energy (TKE), |
458 |
|
459 |
\[ {\h}{q^2}={\overline{{u^{\prime}}^2}}+{\overline{{v^{\prime}}^2}}+{\overline{{w^{\prime}}^2}}, \] |
460 |
|
461 |
is solved prognostically and the other second moments are solved diagnostically. |
462 |
The prognostic equation for TKE allows the scheme to simulate |
463 |
some of the transient and diffusive effects in the turbulence. The TKE budget equation |
464 |
is solved numerically using an implicit backward computation of the terms linear in $q^2$ |
465 |
and is written: |
466 |
|
467 |
\[ |
468 |
{\dd{}{t} ({{\h} q^2})} - { \pp{}{z} ({ {5 \over 3} {{\lambda}_1} q { \pp {}{z} |
469 |
({\h}q^2)} })} = |
470 |
{- \overline{{u^{\prime}}{w^{\prime}}} { \pp{U}{z} }} - {\overline{{v^{\prime}}{w^{\prime}}} |
471 |
{ \pp{V}{z} }} + {{g \over {\Theta_0}}{\overline{{w^{\prime}}{{{\theta}_v}^{\prime}}}} } |
472 |
- { q^3 \over {{\Lambda} _1} } |
473 |
\] |
474 |
|
475 |
where $q$ is the turbulent velocity, ${u^{\prime}}$, ${v^{\prime}}$, ${w^{\prime}}$ and |
476 |
${{\theta}^{\prime}}$ are the fluctuating parts of the velocity components and potential |
477 |
temperature, $U$ and $V$ are the mean velocity components, ${\Theta_0}^{-1}$ is the |
478 |
coefficient of thermal expansion, and ${{\lambda}_1}$ and ${{\Lambda} _1}$ are constant |
479 |
multiples of the master length scale, $\ell$, which is designed to be a characteristic measure |
480 |
of the vertical structure of the turbulent layers. |
481 |
|
482 |
The first term on the left-hand side represents the time rate of change of TKE, and |
483 |
the second term is a representation of the triple correlation, or turbulent |
484 |
transport term. The first three terms on the right-hand side represent the sources of |
485 |
TKE due to shear and bouyancy, and the last term on the right hand side is the dissipation |
486 |
of TKE. |
487 |
|
488 |
In the level 2.5 approach, the vertical fluxes of the scalars $\theta_v$ and $q$ and the |
489 |
wind components $u$ and $v$ are expressed in terms of the diffusion coefficients $K_h$ and |
490 |
$K_m$, respectively. In the statisically realizable level 2.5 turbulence scheme of Helfand |
491 |
and Labraga (1988), these diffusion coefficients are expressed as |
492 |
|
493 |
\[ |
494 |
K_h |
495 |
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) \, & \mbox{decaying turbulence} |
496 |
\\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right. |
497 |
\] |
498 |
|
499 |
and |
500 |
|
501 |
\[ |
502 |
K_m |
503 |
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) \, & \mbox{decaying turbulence} |
504 |
\\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right. |
505 |
\] |
506 |
|
507 |
where the subscript $e$ refers to the value under conditions of local equillibrium |
508 |
(obtained from the Level 2.0 Model), $\ell$ is the master length scale related to the |
509 |
vertical structure of the atmosphere, |
510 |
and $S_M$ and $S_H$ are functions of $G_H$ and $G_M$, the dimensionless buoyancy and |
511 |
wind shear parameters, respectively. |
512 |
Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
513 |
are functions of the Richardson number: |
514 |
|
515 |
\[ |
516 |
{\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
517 |
= { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } . |
518 |
\] |
519 |
|
520 |
Negative values indicate unstable buoyancy and shear, small positive values ($<0.2$) |
521 |
indicate dominantly unstable shear, and large positive values indicate dominantly stable |
522 |
stratification. |
523 |
|
524 |
Turbulent eddy diffusion coefficients of momentum, heat and moisture in the surface layer, |
525 |
which corresponds to the lowest GCM level (see \ref{tab:fizhi:sigma}), |
526 |
are calculated using stability-dependant functions based on Monin-Obukhov theory: |
527 |
\[ |
528 |
{K_m} (surface) = C_u \times u_* = C_D W_s |
529 |
\] |
530 |
and |
531 |
\[ |
532 |
{K_h} (surface) = C_t \times u_* = C_H W_s |
533 |
\] |
534 |
where $u_*=C_uW_s$ is the surface friction velocity, |
535 |
$C_D$ is termed the surface drag coefficient, $C_H$ the heat transfer coefficient, |
536 |
and $W_s$ is the magnitude of the surface layer wind. |
537 |
|
538 |
$C_u$ is the dimensionless exchange coefficient for momentum from the surface layer |
539 |
similarity functions: |
540 |
\[ |
541 |
{C_u} = {u_* \over W_s} = { k \over \psi_{m} } |
542 |
\] |
543 |
where k is the Von Karman constant and $\psi_m$ is the surface layer non-dimensional |
544 |
wind shear given by |
545 |
\[ |
546 |
\psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} . |
547 |
\] |
548 |
Here $\zeta$ is the non-dimensional stability parameter, and |
549 |
$\phi_m$ is the similarity function of $\zeta$ which expresses the stability dependance of |
550 |
the momentum gradient. The functional form of $\phi_m$ is specified differently for stable and unstable |
551 |
layers. |
552 |
|
553 |
$C_t$ is the dimensionless exchange coefficient for heat and |
554 |
moisture from the surface layer similarity functions: |
555 |
\[ |
556 |
{C_t} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} = |
557 |
-{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} = |
558 |
{ k \over { (\psi_{h} + \psi_{g}) } } |
559 |
\] |
560 |
where $\psi_h$ is the surface layer non-dimensional temperature gradient given by |
561 |
\[ |
562 |
\psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} . |
563 |
\] |
564 |
Here $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of |
565 |
the temperature and moisture gradients, and is specified differently for stable and unstable |
566 |
layers according to Helfand and Schubert, 1995. |
567 |
|
568 |
$\psi_g$ is the non-dimensional temperature or moisture gradient in the viscous sublayer, |
569 |
which is the mosstly laminar region between the surface and the tops of the roughness |
570 |
elements, in which temperature and moisture gradients can be quite large. |
571 |
Based on Yaglom and Kader (1974): |
572 |
\[ |
573 |
\psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} } |
574 |
(h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} |
575 |
\] |
576 |
where Pr is the Prandtl number for air, $\nu$ is the molecular viscosity, $z_{0}$ is the |
577 |
surface roughness length, and the subscript {\em ref} refers to a reference value. |
578 |
$h_{0} = 30z_{0}$ with a maximum value over land of 0.01 |
579 |
|
580 |
The surface roughness length over oceans is is a function of the surface-stress velocity, |
581 |
\[ |
582 |
{z_0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}} |
583 |
\] |
584 |
where the constants are chosen to interpolate between the reciprocal relation of |
585 |
Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981) |
586 |
for moderate to large winds. Roughness lengths over land are specified |
587 |
from the climatology of Dorman and Sellers (1989). |
588 |
|
589 |
For an unstable surface layer, the stability functions, chosen to interpolate between the |
590 |
condition of small values of $\beta$ and the convective limit, are the KEYPS function |
591 |
(Panofsky, 1973) for momentum, and its generalization for heat and moisture: |
592 |
\[ |
593 |
{\phi_m}^4 - 18 \zeta {\phi_m}^3 = 1 \hspace{1cm} ; \hspace{1cm} |
594 |
{\phi_h}^2 - 18 \zeta {\phi_h}^3 = 1 \hspace{1cm} . |
595 |
\] |
596 |
The function for heat and moisture assures non-vanishing heat and moisture fluxes as the wind |
597 |
speed approaches zero. |
598 |
|
599 |
For a stable surface layer, the stability functions are the observationally |
600 |
based functions of Clarke (1970), slightly modified for |
601 |
the momemtum flux: |
602 |
\[ |
603 |
{\phi_m} = { { 1 + 5 {{\zeta}_1} } \over { 1 + 0.00794 {{\zeta}_1} |
604 |
(1+ 5 {{\zeta}_1}) } } \hspace{1cm} ; \hspace{1cm} |
605 |
{\phi_h} = { { 1 + 5 {{\zeta}_1} } \over { 1 + 0.00794 {\zeta} |
606 |
(1+ 5 {{\zeta}_1}) } } . |
607 |
\] |
608 |
The moisture flux also depends on a specified evapotranspiration |
609 |
coefficient, set to unity over oceans and dependant on the climatological ground wetness over |
610 |
land. |
611 |
|
612 |
Once all the diffusion coefficients are calculated, the diffusion equations are solved numerically |
613 |
using an implicit backward operator. |
614 |
|
615 |
\subsubsubsection{Atmospheric Boundary Layer} |
616 |
|
617 |
The depth of the atmospheric boundary layer (ABL) is diagnosed by the parameterization as the |
618 |
level at which the turbulent kinetic energy is reduced to a tenth of its maximum near surface value. |
619 |
The vertical structure of the ABL is explicitly resolved by the lowest few (3-8) model layers. |
620 |
|
621 |
\subsubsubsection{Surface Energy Budget} |
622 |
|
623 |
The ground temperature equation is solved as part of the turbulence package |
624 |
using a backward implicit time differencing scheme: |
625 |
\[ |
626 |
C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE |
627 |
\] |
628 |
where $R_{sw}$ is the net surface downward shortwave radiative flux and $R_{lw}$ is the |
629 |
net surface upward longwave radiative flux. |
630 |
|
631 |
$H$ is the upward sensible heat flux, given by: |
632 |
\[ |
633 |
{H} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{NLAY}) |
634 |
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
635 |
\] |
636 |
where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific |
637 |
heat of air at constant pressure, and $\theta$ represents the potential temperature |
638 |
of the surface and of the lowest $\sigma$-level, respectively. |
639 |
|
640 |
The upward latent heat flux, $LE$, is given by |
641 |
\[ |
642 |
{LE} = \rho \beta L C_{H} W_s (q_{surface} - q_{NLAY}) |
643 |
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
644 |
\] |
645 |
where $\beta$ is the fraction of the potential evapotranspiration actually evaporated, |
646 |
L is the latent heat of evaporation, and $q_{surface}$ and $q_{NLAY}$ are the specific |
647 |
humidity of the surface and of the lowest $\sigma$-level, respectively. |
648 |
|
649 |
The heat conduction through sea ice, $Q_{ice}$, is given by |
650 |
\[ |
651 |
{Q_{ice}} = {C_{ti} \over {H_i}} (T_i-T_g) |
652 |
\] |
653 |
where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to |
654 |
be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and $T_g$ is the |
655 |
surface temperature of the ice. |
656 |
|
657 |
$C_g$ is the total heat capacity of the ground, obtained by solving a heat diffusion equation |
658 |
for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by: |
659 |
\[ |
660 |
C_g = \sqrt{ {\lambda C_s \over 2\omega} } = \sqrt{(0.386 + 0.536W + 0.15W^2)2\times10^{-3} |
661 |
{86400 \over 2 \pi} } \, \, . |
662 |
\] |
663 |
Here, the thermal conductivity, $\lambda$, is equal to $2\times10^{-3}$ ${ly\over{ sec}} |
664 |
{cm \over {^oK}}$, |
665 |
the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided |
666 |
by $2 \pi$ $radians/ |
667 |
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
668 |
is a function of the ground wetness, $W$. |
669 |
|
670 |
\subsubsection{Land Surface Processes} |
671 |
|
672 |
\subsubsubsection{Surface Type} |
673 |
The fizhi package surface Types are designated using the Koster-Suarez (1992) mosaic |
674 |
philosophy which allows multiple ``tiles'', or multiple surface types, in any one |
675 |
grid cell. The Koster-Suarez Land Surface Model (LSM) surface type classifications |
676 |
are shown in Table \ref{tab:fizhi:surftype}. The surface types and the percent of the grid |
677 |
cell occupied by any surface type were derived from the surface classification of |
678 |
Defries and Townshend (1994), and information about the location of permanent |
679 |
ice was obtained from the classifications of Dorman and Sellers (1989). |
680 |
The surface type for the \txt GCM grid is shown in Figure \ref{fig:fizhi:surftype}. |
681 |
The determination of the land or sea category of surface type was made from NCAR's |
682 |
10 minute by 10 minute Navy topography |
683 |
dataset, which includes information about the percentage of water-cover at any point. |
684 |
The data were averaged to the model's \fxf and \txt grid resolutions, |
685 |
and any grid-box whose averaged water percentage was $\geq 60 \%$ was |
686 |
defined as a water point. The \fxf grid Land-Water designation was further modified |
687 |
subjectively to ensure sufficient representation from small but isolated land and water regions. |
688 |
|
689 |
\begin{table} |
690 |
\begin{center} |
691 |
{\bf Surface Type Designation} \\ |
692 |
\vspace{0.1in} |
693 |
\begin{tabular}{ |c|l| } |
694 |
\hline |
695 |
Type & Vegetation Designation \\ \hline |
696 |
\hline |
697 |
1 & Broadleaf Evergreen Trees \\ \hline |
698 |
2 & Broadleaf Deciduous Trees \\ \hline |
699 |
3 & Needleleaf Trees \\ \hline |
700 |
4 & Ground Cover \\ \hline |
701 |
5 & Broadleaf Shrubs \\ \hline |
702 |
6 & Dwarf Trees (Tundra) \\ \hline |
703 |
7 & Bare Soil \\ \hline |
704 |
8 & Desert (Bright) \\ \hline |
705 |
9 & Glacier \\ \hline |
706 |
10 & Desert (Dark) \\ \hline |
707 |
100 & Ocean \\ \hline |
708 |
\end{tabular} |
709 |
\end{center} |
710 |
\caption{Surface type designations used to compute surface roughness (over land) |
711 |
and surface albedo.} |
712 |
\label{tab:fizhi:surftype} |
713 |
\end{table} |
714 |
|
715 |
|
716 |
\begin{figure*}[htbp] |
717 |
\centerline{ \epsfysize=7in \epsfbox{surftypes.ps}} |
718 |
\vspace{0.3in} |
719 |
\caption {Surface Type Compinations at \txt resolution.} |
720 |
\label{fig:fizhi:surftype} |
721 |
\end{figure*} |
722 |
|
723 |
\begin{figure*}[htbp] |
724 |
\centerline{ \epsfysize=7in \epsfbox{surftypes.descrip.ps}} |
725 |
\vspace{0.3in} |
726 |
\caption {Surface Type Descriptions.} |
727 |
\label{fig:fizhi:surftype.desc} |
728 |
\end{figure*} |
729 |
|
730 |
|
731 |
\subsubsubsection{Surface Roughness} |
732 |
The surface roughness length over oceans is computed iteratively with the wind |
733 |
stress by the surface layer parameterization (Helfand and Schubert, 1991). |
734 |
It employs an interpolation between the functions of Large and Pond (1981) |
735 |
for high winds and of Kondo (1975) for weak winds. |
736 |
|
737 |
|
738 |
\subsubsubsection{Albedo} |
739 |
The surface albedo computation, described in Koster and Suarez (1991), |
740 |
employs the ``two stream'' approximation used in Sellers' (1987) Simple Biosphere (SiB) |
741 |
Model which distinguishes between the direct and diffuse albedos in the visible |
742 |
and in the near infra-red spectral ranges. The albedos are functions of the observed |
743 |
leaf area index (a description of the relative orientation of the leaves to the |
744 |
sun), the greenness fraction, the vegetation type, and the solar zenith angle. |
745 |
Modifications are made to account for the presence of snow, and its depth relative |
746 |
to the height of the vegetation elements. |
747 |
|
748 |
\subsubsection{Gravity Wave Drag} |
749 |
The fizhi package employs the gravity wave drag scheme of Zhou et al. (1996). |
750 |
This scheme is a modified version of Vernekar et al. (1992), |
751 |
which was based on Alpert et al. (1988) and Helfand et al. (1987). |
752 |
In this version, the gravity wave stress at the surface is |
753 |
based on that derived by Pierrehumbert (1986) and is given by: |
754 |
|
755 |
\bq |
756 |
|\vec{\tau}_{sfc}| = {\rho U^3\over{N \ell^*}} \left(F_r^2 \over{1+F_r^2}\right) \, \, , |
757 |
\eq |
758 |
|
759 |
where $F_r = N h /U$ is the Froude number, $N$ is the {\em Brunt - V\"{a}is\"{a}l\"{a}} frequency, $U$ is the |
760 |
surface wind speed, $h$ is the standard deviation of the sub-grid scale orography, |
761 |
and $\ell^*$ is the wavelength of the monochromatic gravity wave in the direction of the low-level wind. |
762 |
A modification introduced by Zhou et al. allows for the momentum flux to |
763 |
escape through the top of the model, although this effect is small for the current 70-level model. |
764 |
The subgrid scale standard deviation is defined by $h$, and is not allowed to exceed 400 m. |
765 |
|
766 |
The effects of using this scheme within a GCM are shown in Takacs and Suarez (1996). |
767 |
Experiments using the gravity wave drag parameterization yielded significant and |
768 |
beneficial impacts on both the time-mean flow and the transient statistics of the |
769 |
a GCM climatology, and have eliminated most of the worst dynamically driven biases |
770 |
in the a GCM simulation. |
771 |
An examination of the angular momentum budget during climate runs indicates that the |
772 |
resulting gravity wave torque is similar to the data-driven torque produced by a data |
773 |
assimilation which was performed without gravity |
774 |
wave drag. It was shown that the inclusion of gravity wave drag results in |
775 |
large changes in both the mean flow and in eddy fluxes. |
776 |
The result is a more |
777 |
accurate simulation of surface stress (through a reduction in the surface wind strength), |
778 |
of mountain torque (through a redistribution of mean sea-level pressure), and of momentum |
779 |
convergence (through a reduction in the flux of westerly momentum by transient flow eddies). |
780 |
|
781 |
|
782 |
\subsubsection{Boundary Conditions and other Input Data} |
783 |
|
784 |
Required fields which are not explicitly predicted or diagnosed during model execution must |
785 |
either be prescribed internally or obtained from external data sets. In the fizhi package these |
786 |
fields include: sea surface temperature, sea ice estent, surface geopotential variance, |
787 |
vegetation index, and the radiation-related background levels of: ozone, carbon dioxide, |
788 |
and stratospheric moisture. |
789 |
|
790 |
Boundary condition data sets are available at the model's \fxf and \txt |
791 |
resolutions for either climatological or yearly varying conditions. |
792 |
Any frequency of boundary condition data can be used in the fizhi package; |
793 |
however, the current selection of data is summarized in Table \ref{tab:fizhi:bcdata}\@. |
794 |
The time mean values are interpolated during each model timestep to the |
795 |
current time. Future model versions will incorporate boundary conditions at |
796 |
higher spatial \mbox{($1^\circ$ x $1^\circ$)} resolutions. |
797 |
|
798 |
\begin{table}[htb] |
799 |
\begin{center} |
800 |
{\bf Fizhi Input Datasets} \\ |
801 |
\vspace{0.1in} |
802 |
\begin{tabular}{|l|c|r|} \hline |
803 |
\multicolumn{1}{|c}{Variable} & \multicolumn{1}{|c}{Frequency} & \multicolumn{1}{|c|}{Years} \\ \hline\hline |
804 |
Sea Ice Extent & monthly & 1979-current, climatology \\ \hline |
805 |
Sea Ice Extent & weekly & 1982-current, climatology \\ \hline |
806 |
Sea Surface Temperature & monthly & 1979-current, climatology \\ \hline |
807 |
Sea Surface Temperature & weekly & 1982-current, climatology \\ \hline |
808 |
Zonally Averaged Upper-Level Moisture & monthly & climatology \\ \hline |
809 |
Zonally Averaged Ozone Concentration & monthly & climatology \\ \hline |
810 |
\end{tabular} |
811 |
\end{center} |
812 |
\caption{Boundary conditions and other input data used in the fizhi package. Also noted are the |
813 |
current years and frequencies available.} |
814 |
\label{tab:fizhi:bcdata} |
815 |
\end{table} |
816 |
|
817 |
|
818 |
\subsubsubsection{Topography and Topography Variance} |
819 |
|
820 |
Surface geopotential heights are provided from an averaging of the Navy 10 minute |
821 |
by 10 minute dataset supplied by the National Center for Atmospheric Research (NCAR) to the |
822 |
model's grid resolution. The original topography is first rotated to the proper grid-orientation |
823 |
which is being run, and then |
824 |
averages the data to the model resolution. |
825 |
The averaged topography is then passed through a Lanczos (1966) filter in both dimensions |
826 |
which removes the smallest |
827 |
scales while inhibiting Gibbs phenomena. |
828 |
|
829 |
In one dimension, we may define a cyclic function in $x$ as: |
830 |
\begin{equation} |
831 |
f(x) = {a_0 \over 2} + \sum_{k=1}^N \left( a_k \cos(kx) + b_k \sin(kx) \right) |
832 |
\label{eq:fizhi:filt} |
833 |
\end{equation} |
834 |
where $N = { {\rm IM} \over 2 }$ and ${\rm IM}$ is the total number of points in the $x$ direction. |
835 |
Defining $\Delta x = { 2 \pi \over {\rm IM}}$, we may define the average of $f(x)$ over a |
836 |
$2 \Delta x$ region as: |
837 |
|
838 |
\begin{equation} |
839 |
\overline {f(x)} = {1 \over {2 \Delta x}} \int_{x-\Delta x}^{x+\Delta x} f(x^{\prime}) dx^{\prime} |
840 |
\label{eq:fizhi:fave1} |
841 |
\end{equation} |
842 |
|
843 |
Using equation (\ref{eq:fizhi:filt}) in equation (\ref{eq:fizhi:fave1}) and integrating, we may write: |
844 |
|
845 |
\begin{equation} |
846 |
\overline {f(x)} = {a_0 \over 2} + {1 \over {2 \Delta x}} |
847 |
\sum_{k=1}^N \left [ |
848 |
\left. a_k { \sin(kx^{\prime}) \over k } \right /_{x-\Delta x}^{x+\Delta x} - |
849 |
\left. b_k { \cos(kx^{\prime}) \over k } \right /_{x-\Delta x}^{x+\Delta x} |
850 |
\right] |
851 |
\end{equation} |
852 |
or |
853 |
|
854 |
\begin{equation} |
855 |
\overline {f(x)} = {a_0 \over 2} + \sum_{k=1}^N {\sin(k \Delta x) \over {k \Delta x}} |
856 |
\left( a_k \cos(kx) + b_k \sin(kx) \right) |
857 |
\label{eq:fizhi:fave2} |
858 |
\end{equation} |
859 |
|
860 |
Thus, the Fourier wave amplitudes are simply modified by the Lanczos filter response |
861 |
function ${\sin(k\Delta x) \over {k \Delta x}}$. This may be compared with an $mth$-order |
862 |
Shapiro (1970) filter response function, defined as $1-\sin^m({k \Delta x \over 2})$, |
863 |
shown in Figure \ref{fig:fizhi:lanczos}. |
864 |
It should be noted that negative values in the topography resulting from |
865 |
the filtering procedure are {\em not} filled. |
866 |
|
867 |
\begin{figure*}[htbp] |
868 |
\centerline{ \epsfysize=7.0in \epsfbox{lanczos.ps}} |
869 |
\caption{ \label{fig:fizhi:lanczos} Comparison between the Lanczos and $mth$-order Shapiro filter |
870 |
response functions for $m$ = 2, 4, and 8. } |
871 |
\end{figure*} |
872 |
|
873 |
The standard deviation of the subgrid-scale topography |
874 |
is computed from a modified version of the the Navy 10 minute by 10 minute dataset. |
875 |
The 10 minute by 10 minute topography is passed through a wavelet |
876 |
filter in both dimensions which removes the scale smaller than 20 minutes. |
877 |
The topography is then averaged to $1^\circ x 1^\circ$ grid resolution, and then |
878 |
re-interpolated back to the 10 minute by 10 minute resolution. |
879 |
The sub-grid scale variance is constructed based on this smoothed dataset. |
880 |
|
881 |
|
882 |
\subsubsubsection{Upper Level Moisture} |
883 |
The fizhi package uses climatological water vapor data above 100 mb from the Stratospheric Aerosol and Gas |
884 |
Experiment (SAGE) as input into the model's radiation packages. The SAGE data is archived |
885 |
as monthly zonal means at 5$^\circ$ latitudinal resolution. The data is interpolated to the |
886 |
model's grid location and current time, and blended with the GCM's moisture data. Below 300 mb, |
887 |
the model's moisture data is used. Above 100 mb, the SAGE data is used. Between 100 and 300 mb, |
888 |
a linear interpolation (in pressure) is performed using the data from SAGE and the GCM. |
889 |
|