Changeset 11043 for NEMO/trunk/doc/latex/SI3/subfiles/chap_ridging_rafting.tex

Timestamp:

2019-05-23T15:51:08+02:00 (5 years ago)

Author:

nicolasmartin

Message:

Several fixes for the LaTeX compilation of the manuals

File:

• NEMO/trunk/doc/latex/SI3/subfiles/chap_ridging_rafting.tex (modified) (3 diffs)

NEMO/trunk/doc/latex/SI3/subfiles/chap_ridging_rafting.tex

@@ -70 +70 @@
 \textbf{Rafting} is the piling of two ice sheets on top of each other. Rafting doubles the participating ice thickness and is a volume-conserving process. \cite{babko_2002} concluded that rafting plays a significant role during initial ice growth in fall, therefore we included it into the model. 
 
-\textbf{Ridging} is the piling of a series of broken ice blocks into pressure ridges. Ridging redistributes participating ice on a various range of thicknesses. Ridging does not conserve ice volume, as pressure ridges are porous. Therefore, the volume of ridged ice is larger than the volume of new ice being ridged. In the model, newly ridged is has a prescribed porosity $p=30\%$ (\textit{ridge\_por} in \textit{namelist\_ice}), following observations \citep{lepp_ranta_1995,h_yland_2002}. The importance of ridging is now since the early works of \citep{thorndike_1975}.
+\textbf{Ridging} is the piling of a series of broken ice blocks into pressure ridges. Ridging redistributes participating ice on a various range of thicknesses. Ridging does not conserve ice volume, as pressure ridges are porous. Therefore, the volume of ridged ice is larger than the volume of new ice being ridged. In the model, newly ridged is has a prescribed porosity $p=30\%$ (\textit{ridge\_por} in \textit{namelist\_ice}), following observations \citep{lepparanta_1995,hoyland_2002}. The importance of ridging is now since the early works of \citep{thorndike_1975}.
 
 The deformation modes are formulated using \textbf{participation} and \textbf{transfer} functions with specific contributions from ridging and rafting:
@@ -115 +115 @@
 \label{eq:nri}
 \end{equation}
-The redistributor $\gamma(h',h)$ specifies how area of thickness $h'$ is redistributed on area of thickness $h$. We follow \citep{hibler_1980} who constructed a rule, based on observations, that forces all ice participating in ridging with thickness $h'$ to be linearly distributed between ice that is between $2h'$ and $2\sqrt{H^*h'}$ thick, where $H^\star=100$ m (\textit{Hstar} in \textit{namelist\_ice}). This in turn determines how to construct the ice volume redistribution function $\Psi^v$. Volumes equal to participating area times thickness are removed from thin ice. They are redistributed following Hibler's rule. The factor $(1+p)$ accounts for initial ridge porosity $p$ (\textit{ridge\_por} in \textit{namelist\_ice}, defined as the fractional volume of seawater initially included into ridges. In many previous models, the initial ridge porosity has been assumed to be 0, which is not the case in reality since newly formed ridges are porous, as indicated by in-situ observations \citep{lepp_ranta_1995,h_yland_2002}. In other words, LIM3 creates a higher volume of ridged ice with the same participating ice.
+The redistributor $\gamma(h',h)$ specifies how area of thickness $h'$ is redistributed on area of thickness $h$. We follow \citep{hibler_1980} who constructed a rule, based on observations, that forces all ice participating in ridging with thickness $h'$ to be linearly distributed between ice that is between $2h'$ and $2\sqrt{H^*h'}$ thick, where $H^\star=100$ m (\textit{Hstar} in \textit{namelist\_ice}). This in turn determines how to construct the ice volume redistribution function $\Psi^v$. Volumes equal to participating area times thickness are removed from thin ice. They are redistributed following Hibler's rule. The factor $(1+p)$ accounts for initial ridge porosity $p$ (\textit{ridge\_por} in \textit{namelist\_ice}, defined as the fractional volume of seawater initially included into ridges. In many previous models, the initial ridge porosity has been assumed to be 0, which is not the case in reality since newly formed ridges are porous, as indicated by in-situ observations \citep{lepparanta_1995,hoyland_2002}. In other words, LIM3 creates a higher volume of ridged ice with the same participating ice.
 
 For the numerical computation of the integrals, we have to compute several temporary values:
@@ -152 +152 @@
 \section{Mechanical redistribution for other global ice variables}
 
-The other global ice state variables redistribution functions $\Psi^X$ are computed based on $\Psi^g$ for the ice age content and on $\Psi^{v^i}$ for the remainder (ice enthalpy and salt content, snow volume and enthalpy). The general principles behind this derivation are described in Appendix A of \cite{bitz_2001}. A fraction $f_s=0.5$ (\textit{fsnowrdg} and \textit{fsnowrft} in \textit{namelist\_ice}) of the snow volume and enthalpy is assumed to be lost during ridging and rafting and transferred to the ocean. The contribution of the seawater trapped into the porous ridges is included in the computation of the redistribution of ice enthalpy and salt content (i.e., $\Psi^{e^i}$ and $\Psi^{M^s}$). During this computation, seawater is supposed to be in thermal equilibrium with the surrounding ice blocks. Ridged ice desalination induces an implicit decrease in internal brine volume, and heat supply to the ocean, which accounts for ridge consolidation as described by \cite{h_yland_2002}. The inclusion of seawater in ridges does not imply any net change in ocean salinity. The energy used to cool down the seawater trapped in porous ridges until the seawater freezing point is rejected into the ocean.
+The other global ice state variables redistribution functions $\Psi^X$ are computed based on $\Psi^g$ for the ice age content and on $\Psi^{v^i}$ for the remainder (ice enthalpy and salt content, snow volume and enthalpy). The general principles behind this derivation are described in Appendix A of \cite{bitz_2001}. A fraction $f_s=0.5$ (\textit{fsnowrdg} and \textit{fsnowrft} in \textit{namelist\_ice}) of the snow volume and enthalpy is assumed to be lost during ridging and rafting and transferred to the ocean. The contribution of the seawater trapped into the porous ridges is included in the computation of the redistribution of ice enthalpy and salt content (i.e., $\Psi^{e^i}$ and $\Psi^{M^s}$). During this computation, seawater is supposed to be in thermal equilibrium with the surrounding ice blocks. Ridged ice desalination induces an implicit decrease in internal brine volume, and heat supply to the ocean, which accounts for ridge consolidation as described by \cite{hoyland_2002}. The inclusion of seawater in ridges does not imply any net change in ocean salinity. The energy used to cool down the seawater trapped in porous ridges until the seawater freezing point is rejected into the ocean.
 
 \end{document}