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fix latex errors
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doc/phys_pkgs/exf.rst

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@@ -124,7 +124,7 @@ General flags and parameters
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+-------------------------+------------------+-------------------------------------------------------------------------------+
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| twoDigitYear | :code:`.FALSE.` | instead of appending ``_YYYY`` append ``YY`` |
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+-------------------------+------------------+-------------------------------------------------------------------------------+
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| repeatPeriod | 0.0 | :math:`\gt` 0: cycle through all input fields at the same period (in seconds) |
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| repeatPeriod | 0.0 | > 0: cycle through all input fields at the same period (in seconds) |
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+ + +-------------------------------------------------------------------------------+
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| | | = 0: use period assigned to each field |
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+-------------------------+------------------+-------------------------------------------------------------------------------+

doc/phys_pkgs/gmredi.rst

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@@ -443,7 +443,7 @@ The LDD97 tapering scheme is activated in the model by setting
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**GM\_taper\_scheme = ’ldd97’** in *data.gmredi*.
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.. figure:: figure_missing
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.. figure::
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:width: 70%
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:align: center
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:alt: Mixed layer depth with GM

doc/phys_pkgs/kl10.rst

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@@ -29,9 +29,9 @@ with the strength of the turbulence :math:`\epsilon`, and the
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stratification :math:`N`, as
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.. math::
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:label: eq-pkg-kl10-Lo
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\label{eq:pkg:kl10:Lo}
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L_O^2 \approx \epsilon N^{-3}.
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L_O^2 \approx \epsilon N^{-3}.
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The Osborn relation relates the strength of the dissipation to the
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vertical diffusivity as

doc/phys_pkgs/seaice.rst

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@@ -374,7 +374,7 @@ The momentum equation of the sea-ice model is
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:label: eq_momseaice
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m \frac{D\mathbf{u}}{Dt} = -mf\mathbf{k}\times\mathbf{u} +
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\mathbf{\tau}_{air} + \mathbf\tau}_{ocean}
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\mathbf{\tau}_{air} + \mathbf{\tau}_{ocean}
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- m \nabla{\phi(0)} + \mathbf{F},
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where :math:`m=m_{i}+m_{s}` is the ice and snow mass per unit area;
@@ -448,9 +448,9 @@ depends on both thickness :math:`h` and compactness (concentration)
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:math:`c`:
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.. math::
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:label: eq_icestrength
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P_{\max} = P^{*}c\,h\,\exp\{-C^{*}\cdot(1-c)\},
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\label{eq:icestrength}
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with the constants :math:`P^{*}` (run-time parameter ``SEAICE_strength``) and
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:math:`C^{*}=20`. The nonlinear bulk and shear viscosities :math:`\eta`
@@ -487,8 +487,8 @@ Defining the CPP-flag ``SEAICE_ZETA_SMOOTHREG`` in ``SEAICE_OPTIONS.h`` before c
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bounding :math:`\zeta` by a smooth (differentiable) expression:
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.. math::
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:label: eq_zetaregsmooth
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\label{eq:zetaregsmooth}
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\begin{split}
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\zeta &= \zeta_{\max}\tanh\left(\frac{P}{2\,\min(\Delta,\Delta_{\min})
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\,\zeta_{\max}}\right)\\
@@ -693,17 +693,22 @@ shearing strain rates, :math:`D_T =
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the equations :eq:`eq_evpequation` can be written as:
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.. math::
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:label: eq_evpstresstensor1
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\begin{aligned}
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\label{eq:evpstresstensor1}
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\frac{\partial\sigma_{1}}{\partial{t}} + \frac{\sigma_{1}}{2T} +
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\frac{P}{2T} &= \frac{P}{2T\Delta} D_D \\
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\label{eq:evpstresstensor2}
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\frac{P}{2T} &= \frac{P}{2T\Delta} D_D
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.. math::
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:label: eq_evpstresstensor2
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\frac{\partial\sigma_{2}}{\partial{t}} + \frac{\sigma_{2} e^{2}}{2T}
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&= \frac{P}{2T\Delta} D_T \\
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\label{eq:evpstresstensor12}
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&= \frac{P}{2T\Delta} D_T
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.. math::
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:label: eq_evpstresstensor12
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\frac{\partial\sigma_{12}}{\partial{t}} + \frac{\sigma_{12} e^{2}}{2T}
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&= \frac{P}{4T\Delta} D_S \end{aligned}
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&= \frac{P}{4T\Delta} D_S
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Here, the elastic parameter :math:`E` is redefined in terms of a damping
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timescale :math:`T` for elastic waves
@@ -751,17 +756,19 @@ terminology of , the evolution equations of stress :math:`\sigma_{ij}`
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and momentum :math:`\mathbf{u}` can be written as:
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.. math::
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:label: eq_evpstarsigma
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\begin{aligned}
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\label{eq:evpstarsigma}
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\sigma_{ij}^{p+1}&=\sigma_{ij}^p+\frac{1}{\alpha}
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\Big(\sigma_{ij}(\mathbf{u}^p)-\sigma_{ij}^p\Big),
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\phantom{\int}\\
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\label{eq:evpstarmom}
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\phantom{\int}
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.. math::
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:label: eq_evpstarmom
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\mathbf{u}^{p+1}&=\mathbf{u}^p+\frac{1}{\beta}
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\Big(\frac{\Delta t}{m}\nabla \cdot{\bf \sigma}^{p+1}+
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\frac{\Delta t}{m}\mathbf{R}^{p}+\mathbf{u}_n
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-\mathbf{u}^p\Big).\end{aligned}
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-\mathbf{u}^p\Big).
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:math:`\mathbf{R}` contains all terms in the momentum equations except
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for the rheology terms and the time derivative; :math:`\alpha` and
@@ -782,8 +789,8 @@ Another variant is the aEVP scheme :cite:`kimmritz16`, where the value
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of :math:`\alpha` is set dynamically based on the stability criterion
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.. math::
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:label: eq_aevpalpha
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\label{eq:aevpalpha}
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\alpha = \beta = \max\left( \tilde{c}\pi\sqrt{c \frac{\zeta}{A_{c}}
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\frac{\Delta{t}}{\max(m,10^{-4}\text{\,kg})}},\alpha_{\min} \right)
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@@ -805,8 +812,8 @@ Truncated ellipse method (TEM) for yield curve
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In the so-called truncated ellipse method the shear viscosity :math:`\eta` is capped to suppress any tensile stress:
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.. math::
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:label: eq_etatem
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\label{eq:etatem}
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\eta = \min\left(\frac{\zeta}{e^2},
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\frac{\frac{P}{2}-\zeta(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})}
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{\sqrt{\max(\Delta_{\min}^{2},(\dot{\epsilon}_{11}-\dot{\epsilon}_{22})^2
@@ -1085,8 +1092,8 @@ concentration :math:`c` and effective snow thickness
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(:math:`c\cdot{h}_{s}`) are advected by ice velocities:
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.. math::
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:label: eq_advection
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\label{eq:advection}
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\frac{\partial{X}}{\partial{t}} = - \nabla\cdot\left({{\vec{\mathbf{u}}}}\,X\right) +
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\Gamma_{X} + D_{X}
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