521 lines
23 KiB
TeX
521 lines
23 KiB
TeX
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\begin{document}
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{\pagestyle{empty}
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\begin{center}
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{\LARGE \bf Shallow water model SAM}
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\vspace{1.in}
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{\LARGE \bf Reference Manual}
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\vspace{1.in}
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{\LARGE \bf Version 1.0}
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\vspace{1.in}
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{\large ~T. Frisius, K. Fraedrich, E. Kirk and F. Lunkeit}
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\end{center}
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}
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{\bf 1 Model equations}
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The shallow water model SAM solves the shallow water equations on a
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spherical planet with shallow orography. The model equations and the
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numerical solution procedure will be described in the following subsections.
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1.1 Continuity equation
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\nopagebreak[4]
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In a shallow water model it is assumed
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that the density $\rho$ is constant. Consequently, the continuity equation reduces to the
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condition that the threedimensional flow is nondivergent.
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In spherical coordinates the nondivergence condition reads
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\begin{equation}
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\left ( \frac 1 {r \cos \varphi} \frac {\partial u} {\partial \lambda}
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+\frac 1 {r \cos \varphi} \frac {\partial } {\partial \varphi} (\cos \varphi v)
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+ \frac {\partial w} {\partial r} + \frac {2 w} r \right ) =0,
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\end{equation}
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In this equation $\lambda$, $\varphi$ and $r$ are the spherical coordinates longitude, latitude and
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radius, respectively and $u$, $v$ and $w$ denote the zonal, meridional and vertical velocity components, respectively. The last term on the left hand side of this equation can be neglected since it is assumed that
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the shallow water system is contained within a thin spherical shell. Furthermore, the radius $r$ can be approximately
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replaced be the mean planet radius $a$ where it appears in a factor.
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Therefore, the continuity equation will be simplified to give
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\begin{equation}
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\left ( \frac 1 {a \cos \varphi} \frac {\partial u} {\partial \lambda}
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+\frac 1 {a \cos \varphi} \frac {\partial } {\partial \varphi} (\cos \varphi v)
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+ \frac {\partial w} {\partial z} \right ) =0,
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\end{equation}
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where $z=r-a$ denotes the height above the spherical surface having the radius $r=a$.
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In a shallow water model it is assumed that the horizontal velocity components are vertically
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independent. Therefore, the continuity equation can be vertically integrated over the whole
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shallow water fluid. This gives
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\begin{equation}
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\frac {D h} {Dt} - \frac {D h_s} {Dt} + (h-h_s) \nabla_h \cdot {\bf v}_h = 0~,
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\end{equation}
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where $\nabla_h \cdot {\bf v}_h$ denotes the divergence of the horizontal flow, $h$
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the height of the shallow water surface, $h_s$ the height of the shallow water bottom
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and
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\[
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\frac {D} {Dt}=\frac {\partial } {\partial t} + \frac u {a \cos {\varphi}}
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\frac {\partial} {\partial \lambda} + \frac v {a}
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\frac {\partial} {\partial \varphi}
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\]
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is the individual time derivative operator.
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1.2 Momentum equation
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\nopagebreak[4]
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The fluid of the shallow water model is treated as a nondivergent ideal fluid. Therefore,
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the momentum equation is given by {\sc Euler}s' equation in a rotating coordinate frame:
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\begin{equation}
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\frac {\partial {\bf v}} {\partial t} + \nabla \left(\frac 1 2 {\bf v}^2 \right)
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+ (\nabla \times {\bf v} + 2 \mbox{\boldmath $\Omega$}) \times {\bf v}
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= - \frac 1 {\rho} \nabla p - \nabla \phi,
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\end{equation}
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where
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$p$ is the pressure, $\phi$ the geopotential and \mbox{\boldmath $\Omega$} the angular velocity vector of the planet rotation which is directed perpendicular to the
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equatorial plane ($\varphi=0$).
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The shallow water model describes
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flow phenomena having a vertical scale that is much smaller than its horizontal
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scale. In this case the hydrostatic balance is satisfied to a high degree.
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Therefore, it is assumed that the following hydrostatic balance equation holds
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\begin{equation}
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\frac {\partial p} {\partial z} = - \rho \frac {\partial \phi} {\partial z}
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\end{equation}
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In this equation $p$ denotes the pressure and
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$\phi$ the geopotential.
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Since density is constant, this equation can easily be
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integrated in vertical direction over the whole fluid depth. This gives
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\begin{equation}
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p_s - \left . p \right |_{z=h} = \rho ( \left . \phi \right |_{z=h} - \phi_s )~,
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\end{equation}
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where the index $s$ means that the variable is evaluated at the bottom of
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the shallow water.
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For shallow water systems it is usally assumed that the pressure at the free upper surface vanishes. Furtheremore, for earth-like planets the gravitational attraction force in addition with the centrifugal force of the planet rotation give rise to geopotential
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isosurfaces that are nearly spherical. Therefore, it is assumed that the geopotential only
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depends upon height $z$ and is, furthemore, proportional to height since the corresponding acceleration
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is nearly constant with in a thin
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spherical shell. Consequently, surface pressure is related to the shallow water elevation
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and surface orography by
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\begin{equation}
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p_s = g \rho (h - h_s)~,
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\end{equation}
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where $g$ denotes the gravitational acceleration.
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Due to this equation the continuity equation (1.3) becomes a tendency equation for surface
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pressure:
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\begin{equation}
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\frac {D p_s} {Dt} + p_s \nabla_h \cdot {\bf v}_h
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= \frac {\partial p_s} {\partial t} + \nabla_h \cdot ( {\bf v}_h p_s)=0 ~,
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\end{equation}
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The horizontal components of {\sc Euler}s equation are retained
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with little approximation.
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We obtain for the horizontal components of $(\nabla \times {\bf v} + 2 \mbox{\boldmath $\Omega$}) \times {\bf v}$:
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{\setlength{\mathindent}{1em}
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\begin{equation}
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((\nabla \times {\bf v} + 2 \mbox{\boldmath $\Omega$}) \times {\bf v})_h
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\end{equation}
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\[
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\hspace{3.cm}=\Omega (\zeta + 2 \sin \varphi) {\bf e}_z \times {\bf v}_h
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- \nabla_h \left(\frac 1 2 w ^2 \right) + \frac {{\bf v}_h w} r
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+ 2 \Omega \cos {\varphi} w {\bf e}_{\lambda}~,
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\]
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}
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where $\zeta$ is the nondimensional vertical component of the vorticity vector $\nabla \times {\bf v}$
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(relative vorticity) and the index $h$ denotes that the vector has only horizontal components.
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The last two terms on the right hand side can be neglected due to the small magnitude of
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vertical velocity in the shallow water model.
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Therefore, the {\sc Euler}-equation for the horizontal velocity vector becomes:
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\begin{equation}
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\frac {\partial {\bf v}_h} {\partial t} + \nabla_h \left(\frac 1 2 {\bf v}_h^2 \right)
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+ \Omega (\zeta + 2 \sin (\varphi)) {\bf e}_z \times {\bf v}_h
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= - \frac 1 {\rho} \nabla_h p_s - \nabla \phi_s ~.
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\end{equation}
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1.3 Nondimensional model equations
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\nopagebreak[4]
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Applying the operators $\Omega^{-2} {\bf e}_z \nabla_h \times$ and $\Omega^{-2} \nabla_h \cdot$ gives the nondimensional vorticity and divergence equations, respectively
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{\setlength{\mathindent}{1em}
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\begin{equation}
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\frac {\partial \eta } {\partial \tau}
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= - \frac 1 {1 - \mu^2} \frac {\partial } {\partial \lambda}
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\left ( \eta U \right ) - \frac {\partial } {\partial \mu}
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\left (\eta V \right)~,
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\end{equation}
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\begin{equation}
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\frac {\partial D} {\partial \tau}
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= \frac 1 {1 - \mu^2} \frac {\partial } {\partial \lambda}
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\left(\eta V \right ) - \frac {\partial } {\partial \mu}
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\left (\eta U\right)
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- \Delta_h \left(\frac {U^2 + V^2} {2 (1 - \mu^2)}+ \Phi_s + {\rm Bu} P \right) ~,
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\end{equation}
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}
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Here, we have used the following notations
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{\setlength{\mathindent}{0em}
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\begin{eqnarray}
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\nonumber \mu & =& \sin \varphi ~~~{\rm sine~ of~ latitude} \\ \nonumber
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\tau & = & \Omega t~~~{\rm nondimensional~ time} \\ \nonumber
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\eta & = & \zeta + 2 \mu ~~~{\rm nondimensional~absolute~vorticity} \\ \nonumber
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D & = & \Omega^{-1} \nabla_h \cdot {\bf v}_h~~~{\rm nondimensional~ divergence} \\ \nonumber (U,V) & =& \cos\varphi (\Omega a)^{-1} (u,v)~~~{\rm nondimensional~ velocity~ components~multiplied~by~} \cos{\varphi} \\ \nonumber
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P & = & \frac {p_s-p_0} {p_0}~~~{\rm nondimensional~ surface~ pressure~ anomaly} \\ \nonumber
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\Phi_s & = & \frac {\phi_s} {\Omega^2 a^2}~~~{\rm nondimensional~surface~geopotential}\\ \nonumber
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{\rm Bu} & = & \frac {p_0} {\Omega^2 a^2 \rho}~~~{\rm {\sc Burger} ~ number} \\ \nonumber
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\Delta_h & = & \displaystyle \frac 1 {1- \mu^2} \frac {\partial^2 } {\partial \lambda^2} + \frac {\partial } {\partial \mu} (1 - \mu^2)
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\frac {\partial } {\partial \mu} ~~~{\rm nondimensional~{\sc Laplace}-operator}
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\end{eqnarray}
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}
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Similarly, we obtain for the nondimensional surface pressure equation:
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\begin{equation}
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\frac {\partial P} {\partial \tau}
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= - \frac 1 {1 - \mu^2} \frac {\partial } {\partial \lambda}
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\left(U P \right ) - \frac {\partial } {\partial \mu}
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\left (V P \right) - D~,
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\end{equation}
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It remains to compute the horizontal velocity components from vorticity and
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divergence fields. This can be done with the {\sc Helmholtz} decomposition of the velocity vector field:
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\begin{equation}
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{\bf v}_h=\Omega a^ 2 \left ( \nabla \chi + \nabla \times {\bf A} \right)~.
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\end{equation}
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where $\chi$ is a nondimensional velocity potential and ${\bf A}$ a nondimensional vector stream potential. Because only
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the horizontal velocity field is related to vorticity and divergence, it is sufficient to
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restrict the vector potential to a single vertical component, the so called streamfunction $\psi$.
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Therefore:
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\begin{equation}
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U = \displaystyle - ( 1 - \mu^2) \frac {\partial \psi} {\partial \mu} + \frac {\partial \chi} {\partial \lambda}~,~~~~
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V = \displaystyle \frac {\partial \psi} {\partial \lambda} + ( 1 - \mu^2) \frac {\partial \chi} {\partial \mu}~.
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\end{equation}
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Streamfunction and velocity potential are related to vorticity and divergence via
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{\sc Poisson}-equations:
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\begin{equation}
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\eta= 2 \mu + \Delta_h \psi~,~~~~D
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= \Delta_h \chi ~.
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\end{equation}
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Equation (1.11)-(1.13), (1.15) and (1.16) form the governing equations of the shallow water model.
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They are solved with a semispectral method which is described in some detail in the next subsections.
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{1.4 Spectral representation of the model equations}
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\nopagebreak[4]
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All fields are projected onto a new base, namely, the so-called spherical harmonics $Y_n^m(\lambda,\mu)$. This gives for a field function $Q(\lambda,\mu,\tau)$:
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\begin{equation}
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Q(\lambda, \mu,\tau)=\sum_{m=-\infty}^{\infty} \sum_{n=|m|}^{\infty} Q_n^m(\tau) Y_n^m(\lambda,\mu)~.
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\end{equation}
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The spherical harmonics are defined by
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\begin{equation}
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Y^m_n(\lambda,\mu)=
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\sqrt{\frac {2 n + 1} 2 \frac {(n-m)!} {(n+m)!}} \frac {(1- \mu^2)^{\frac m 2}} {2^n n!}
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\frac {\partial^{m+n}} {\partial \mu^{m+n}} \left [ (\mu^2 - 1)^n \right ]
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e^{i m \lambda}~.
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\end{equation}
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Since $Q$ must be a real function we have the constraint $Q_n^m=Q_n^{-m*}$. Therefore, it is sufficient
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to calculate only the coefficients with $m \ge0$ and the following representation is equivalent to (1.19):
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\begin{equation}
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Q(\lambda, \mu,\tau)=\sum_{n=1}^{\infty} Q_n^0(\tau) Y_n^0(\mu) + 2 \sum_{m=1}^{\infty} \sum_{n=m}^{\infty} {\rm Re} \left (Q_n^m(\tau) Y_n^m(\lambda,\mu) \right )~.
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\end{equation}
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The spherical harmonics form an orthogonal base with respect to the scalar product
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\begin{equation}
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\left < Q_1 | Q_2 \right > := \frac 1 {2 \pi} \int_{-1}^{1} \int_{0}^{2\pi} Q_1^*(\lambda,\mu) Q_2({\lambda,\mu}) d\lambda d\mu~
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\end{equation}
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Therefore:
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\begin{equation}
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\left < Y_n^m | Y_{n^{\prime}}^{m^{\prime}} \right > = \delta_{m,m^{\prime}} \delta_{n,n^{\prime}}
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\end{equation}
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Furthermore, the spherical harmonics are eigenfunctions of the nondimensional
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{\sc Laplace}-operator $\Delta_h$:
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\begin{equation}
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\Delta_h Y_n^m=- n (n+1) Y_n^m~.
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\end{equation}
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Further useful relations are:
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\begin{equation}
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\frac {\partial Y^m_n} {\partial \lambda}
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= i m Y^m_n~,
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\end{equation}
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\begin{equation}
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(1 - \mu^2) \frac {\partial } {\partial \mu} Y^m_n
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= n d_{m,n+1} Y^m_{n+1} - (n+1) d_{m,n} Y^m_{n-1}~,
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\end{equation}
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where
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\[
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d_{m,n}=\sqrt{ \frac {n^2 - m^2} {4 n^2 -1} }~.
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\]
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With (1.22) - (1.24) the governing model equations can be converted into component form after applying the scalar product
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$<Y^m_n|..>$:
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{\setlength{\mathindent}{1em}
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\begin{equation}
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\frac {d \eta_n^m} {d\tau}= -\left < Y^m_n ~|~ \frac {im\eta U} {1-\mu^2}\right >
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- \left < Y^m_n ~|~ \frac {\partial (\eta V)} {\partial \mu} \right >~,
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\end{equation}
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\begin{eqnarray}
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\frac {d D_n^m} {d\tau} & = & \left < Y^m_n ~|~ \frac {im \eta V} {1-\mu^2} \right >
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- \left < Y^m_n ~|~ \frac {\partial (\eta U)} {\partial \mu} \right > \\ \nonumber
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& & + n(n+1)
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\left < Y^m_n ~|~ \frac 1 2 \frac {U^2+V^2} {1-\mu^2} \right > + n(n+1) \left [ {\rm Bu} P_n^m + {\Phi_s}^m_n \right ]~,
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\end{eqnarray}
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\begin{equation}
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\frac {d P_n^m} {d\tau}= -\left < Y^m_n ~|~ \frac {im P U} {1-\mu^2} \right >
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- \left < Y^m_n ~|~ \frac {\partial (P V)} {\partial \mu} \right > - D_n^m~,
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\end{equation}
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\begin{equation}
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U^m_n = (n - 1) d_{m,n} \psi^m_n - (n+2) d_{m,n+1} \psi^m_{n+1} + i m~ \chi^m_n~,
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\end{equation}
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\begin{equation}
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V^m_n = i m ~ \psi^m_n - (q - 1) d_{m,n} \chi^m_{n-1}
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+ (n+2) d_{m,n+1} \chi^m_{n+1}~,
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\end{equation}
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\begin{equation}
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\psi^m_n = - \frac 1 {n(n+1)} \left(\eta^m_n - \sqrt {\frac 8 3}~
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\delta_{m,0}\delta_{n,1}\right) ~,
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\end{equation}
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\begin{equation}
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\chi^m_n = - \frac 1 {n(n+1)} D^m_n~.
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\end{equation}
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}
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1.4 Numerical solution technique
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\nopagebreak[4]
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An approximative solution of the model is determined by
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time integration of the truncated spectral equations. In the truncated model
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the first summation operator
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in (1.17) runs only from $-M$ to $M$. This gives a triangular truncation
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T$M$.
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The terms in brackets of Eqs.(1.25)-(1.27) are nonlinear. The computation of these scalar products is very complicated and
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consumes a lot of computer time.
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Therefore, these terms are evaluated in the numerical model
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with the so-called spectral transform method [Orszag (1970)
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and Eliasen et al. (1970)]. This method uses an auxiliary grid in the physical space where point values of the
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dependent variables are computed. The auxiliary grid in the physical space ({\sc Gauss}ian grid) is defined
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by $M_g$ equally spaced longitudes and $J_g$ {\sc Gauss}ian latitudes.
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For the transformation from gridpoint space into spectral space the spectral coefficients are obtained by
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{\sc Gauss}ian quadrature of the {\sc Fourier} coefficients. With this method bilinear products are
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calculated without error when $M_g \ge 3M+1$ and $J_g \ge (3M+1)/2$. Since only bilinear products
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appear as nonlinearities in the equations the spectral transform method is equivalent to the analytical
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determination of the nonlinear products using interaction coefficients.
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Time integration is done with the semi-implicit time stepping procedure. This has the advantage that for a stable integration
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the time-step $\Delta \tau$ can be larger than the period of high-frequency inertial gravity modes.
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The time derivatives are approximated by a centered difference so that
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\begin{equation}
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\frac {d Q} {d \tau} \approx \delta_t Q := \frac {Q(\tau+\Delta \tau) - Q(\tau+\Delta \tau)} {2 \Delta \tau}~.
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\end{equation}
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The tendency is splitted into an explicit and an implicit part. The explicit part is related to the sum of all nonlinear terms
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and is evaluated at the present time $\tau$. The linear terms form the implicit part. They only occur in the divergence and pressure
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equation and enter the equations as a time mean of time step $\tau +\Delta \tau$ and $\tau - \Delta \tau$. Altogether, the finite-difference form of the prognostic model equations reads:
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{\setlength{\mathindent}{1em}
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\begin{equation}
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\delta_t \eta_n^m =
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{\cal N}_{\eta}(\tau)~,
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\end{equation}
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\begin{equation}
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\delta_t D_n^m = {\cal N}_{D}(\tau)
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+ {\rm Bu}\frac {n(n+1)} {2} [P_n^m(\tau-\Delta \tau) + P_n^m(\tau+\Delta \tau)
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+ 2 {\Phi_s}^m_n]
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\end{equation}
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\begin{equation}
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\delta_t P_n^m = {\cal N}_{P}(\tau)
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- \frac 1 2 [D_n^m(\tau-\Delta \tau) + D_n^m(\tau+\Delta \tau)]~,
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\end{equation}
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where ${\cal N}_{\eta}$, ${\cal N}_{D}$ and ${\cal N}_{P}$ denote the
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respective nonlinear tendency terms. Eliminating $P_n^m(\tau+\Delta \tau)$ in (1.35) gives
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\begin{equation}
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\left [1 + \Delta \tau^2 {\rm Bu}~{n(n+1)} \right ] \overline{D_n^m}^{\tau}
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\end{equation}
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\[ \hspace{0.1in}
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=
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D_n^m(\tau - \Delta \tau)
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+ \Delta \tau \left \{ {\cal N}_{D}(\tau)
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+ {\rm Bu}~{n(n+1)} \left [
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P_n^m(\tau - \Delta \tau) + {\Phi_s}^m_n + \Delta \tau {\cal N}_P(\tau) \right ] \right \}~,
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|
\]
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|
}
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|
where $\overline{D_n^m}^{\tau}= [D_n^m(\tau +� \Delta \tau)+D_n^m(\tau - \Delta \tau)]/2$.
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|
|
|
The time averaged value $\overline{D_n^m}^{\tau}$ can be easily calculated from equation (1.36).
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With this value it is straightforward to determine the future values $D^m_n(\tau + \Delta \tau)$
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|
and $P^m_n(\tau + \Delta \tau)$.
|
|
|
|
For noise reduction a {\sc Robert}/{\sc Asselin}-Filter [Haltiner and Williams
|
|
(1982)] is applied
|
|
at every timestep to a spectral coefficient $Q_n^m$ as follows:
|
|
\begin{equation}
|
|
Q^m_n(\tau)=(1-2 \gamma)Q^m_n(\tau)
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|
+ \gamma [Q^m_n(\tau+\Delta \tau)+Q^m_n(\tau-\Delta \tau)]~.
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|
\end{equation}
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In the model SAM $\gamma$ takes the value 0.02 by default.
|
|
|
|
1.5 Hyperdiffusion
|
|
|
|
In a turbulent flow regime a cascade from large scales to the dissipative range
|
|
of the wavenumber spectrum takes place. The model cannot resolve such small scales.
|
|
Therefore, kinetic energy dissipation must occur at resolvable scales in the model without
|
|
affecting the large scale too much. This is achieved by introducing hyperdiffusion by
|
|
adding the terms
|
|
\begin{equation}
|
|
{\cal H}_{\eta~n}^m= K \left [ - n(n+1) \right ]^{n_h} \left(\eta^m_n - \sqrt {\frac 8 3}~
|
|
\delta_{m,0}\delta_{n,1}\right)
|
|
\end{equation}
|
|
and
|
|
\begin{equation}
|
|
{\cal H}_{D~n}^m= K \left [ - n(n+1) \right ]^{n_h} D^m_n
|
|
\end{equation}
|
|
to the vorticity and divergence equations, respectively. $n_h$ denotes the order of
|
|
hyperdiffusion. Without additional terms the corresponding vorticity or divergence component
|
|
is damped with the dimensional $e$-folding timescale
|
|
\begin{equation}
|
|
\tau_H= \left \{ \Omega K [n (n+1)]^{n_h} \right \}^{-1} ~.
|
|
\end{equation}
|
|
In the model $\tau_H$ at the wavenumber where the expansion is truncated will be prescribed.
|
|
Therefore, the coefficient $K$ becomes:
|
|
\begin{equation}
|
|
K= \left \{ \Omega \tau_H [M (M+1)]^{n_h} \right \}^{-1}~.
|
|
\end{equation}
|
|
|
|
1.6 Parameterization of baroclinic and dissipative processes
|
|
|
|
To perform simulations with baroclinic forcing and dissipative damping additional terms must
|
|
be added to the spectral vorticity and divergence equations.
|
|
These are given by
|
|
\begin{eqnarray}
|
|
\left . \frac {d \eta_n^m} {d\tau} \right |^P & = & \frac {\eta_{ne}^m -\eta_n^m } {\tau^m_{nR}}
|
|
+ S^m_n (\tau)
|
|
- \frac {\eta_n^m - \sqrt{8/3} \delta_{m,0} \delta_{n,1} } {\tau_F} \\ \nonumber
|
|
& & - A_{h} \left ( n^2 + n - 2 \right )
|
|
\left (\eta_n^m - \sqrt{8/3} \delta_{m,0} \delta_{n,1} \right ) ~,
|
|
\end{eqnarray}
|
|
\begin{equation}
|
|
\left . \frac {d D_n^m} {d\tau}\right |^P = - \frac {D_n^m } {\tau_F} - A_{h} { n (n+1)} D^m_n ~,
|
|
\end{equation}
|
|
where $\eta_{ne}^m$ is the equilibrium state of the climatological baroclinic forcing, $\tau^m_{nR}$ the timescale of the
|
|
climatological forcing (depends upon wavenumbers), $S^m_n(\tau)$ the time dependent baroclinic forcing (stochastic),
|
|
$\tau_F$ the timescale of Rayleigh friction and $A_h$ the horizontal momentum exchange coefficient.
|
|
|
|
|
|
{\bf 2 User guide}
|
|
|
|
\nopagebreak[4]
|
|
|
|
SAM can like PUMA and PlaSim be compiled and started with the model starter program most.x.
|
|
SAM also supports the Graphical User Interface (GUI) developed for PUMA and PlaSim.
|
|
In the code several initial conditions are specified with the integer parameter iexp (1-13).
|
|
The various experiments are documented in the initialization subroutine initfd. Further
|
|
initial conditions can be added at discretion. The model resolution has to be specified with the
|
|
namelist {\it resolution\_namelist}. It contains the parameter NLAT that denotes the number of
|
|
latitudes. NLAT should be represented by $2^{n}$ with $n$ being an integer to ensure
|
|
optimal parallelization and consistency with the fast Fourier transform.
|
|
|
|
The namelist for SAM {\it somnamelist} contains the following parameters
|
|
|
|
\begin{tabular}{|l|c|l|}
|
|
\hline
|
|
Parameter & Default & Meaning\\
|
|
\hline
|
|
KICK & 1 & Initial noise (not implemented in the current version)\\
|
|
NAFTER & 12 & Output after intervals of NAFTER timesteps\\
|
|
NCOEFF & 0 & Number of spectral modes to be print in wrspam\\
|
|
NDEL & 6 & Order of hyperdiffusion\\
|
|
NDIAG & 12 & Parameter to determine that ASCII diagnostics \\
|
|
& & are written after intervals of NDIAG timesteps\\
|
|
NKITS & 3 & Number of initial timesteps\\
|
|
NRUN & 0 & Number of timesteps to run - 0: use nyears and\\
|
|
NWSPINI & 1 & 1: Write initial sp(:) to file puma\_sp\_ini\\
|
|
NOUTPUT & 1 & 1: Write model output to file sam\_output\\
|
|
NSTEP & 0 & Current timestep\\
|
|
NSTOP & 0 & Stop step - 0: compute from nyears and nmonths\\
|
|
NTSPD & 1 & Number of timesteps per day\\
|
|
NCU & 0 & Check unit (for debug output only)\\
|
|
NGUI & 0 & 1: Run with GUI\\
|
|
NGUIDBG & 0 & 1: Switch on GUI debug output\\
|
|
NYEARS & 0 & Simulation time in years\\
|
|
DISS & 0.25 & Hyper diffusion time scale [days]\\
|
|
NRUIDO & 0 & 1: Add noise on every time step\\
|
|
DISP & 0.0 & Noise amplitude for nruido = 1\\
|
|
AH & 0.0 & Horizontal momentum exchange coefficient [m$^2$/s]\\
|
|
RESTIM & 0.0 & Timescale for climatological forcing [days] (0.0$\rightarrow$ no forcing)\\
|
|
NDL & 0 & 1: Print spectral vorticity and divergence modes\\
|
|
ROTSPD & 0. & Rotations per day (should be set as in PlaSim)\\
|
|
TFRC & 0. & Rayleigh friction timescale in days (0.0 $\rightarrow$ no friction)\\
|
|
LLID & .false. & Switch for introducing a rigid lid\\
|
|
LEQUIV & .false. & Switch for equivalent barotropic model\\
|
|
LBAL & .false. & Switch for balanced initial state\\
|
|
IEXP & 4 & Number of experiment (1-13, see initfd)\\
|
|
MMAX & 0 & Maximum zonal waven. for climat. forcing \\
|
|
NMAX & 42 & Maximum total waven. for climat. forcing \\
|
|
\hline
|
|
\end{tabular}
|
|
|
|
Other parameters can be set in the module pumamod of the code. These are:
|
|
\begin{tabular}{|l|c|l|}
|
|
\hline
|
|
Parameter & Default & Meaning\\
|
|
\hline
|
|
GA & 9.81 & Gravity acceleration [m/s$^2$]\\
|
|
PLARAD & 6371000.0 & Radius of the sphere [m]\\
|
|
WW & 0.00007292 & Angular velocity of the rotating sphere [1/s]\\
|
|
RHO0 & 1. & Density of the shallow water [kg/m$^3$]\\
|
|
HS & 12000. & Height of the shallow water [m]\\
|
|
F0 & 1.e-4 & Mean Coriolis parameter [1/s] (only LEQUIV=.true.)\\
|
|
\hline
|
|
\end{tabular}
|
|
|
|
SAM writes output into the file {\it sam\_output}. It contains
|
|
spectral coefficients of i) surface geopotential
|
|
(code 129), ii) logarithm of surface pressue (code 152),
|
|
iii) divergence (code 155) and iv) relative vorticity (code 138).
|
|
The pumaburner
|
|
can process the file {\it sam\_output} for further diagnostics.
|
|
|
|
\end{document}
|
|
|
|
|