Fixes

docs/model_docs/lateral/kinwave.qmd

@@ -8,8 +8,10 @@ channel and overland flow, assuming that water flow is mostly controlled by topo
 kinematic wave equations are (Chow, 1988):
 
 $$
-  \dfrac{\partial Q}{\partial x} + \dfrac{\partial A}{\partial t} = q, \\~\\
+\begin{gathered}
+  \dfrac{\partial Q}{\partial x} + \dfrac{\partial A}{\partial t} = q,\\
    A = \alpha Q^{\beta}.
+\end{gathered}
 $$
 
 These equations can then be combined as a function of streamflow only:

docs/model_docs/lateral/sediment_flux.qmd

@@ -28,6 +28,7 @@ mobilize 5 classes of sediment:
 - Large aggregates (mean diameter of $\SI{50}{\mu m}$).
 
 $$
+\begin{gathered}
    \mathrm{PSA} = \mathrm{SAN} (1-\mathrm{CLA})^{2.4} \\
    \mathrm{PSI} = 0.13\mathrm{SIL}\\
    \mathrm{PCL} = 0.20\mathrm{CLA} \\
@@ -42,21 +43,22 @@ $$
    \end{align*} \\
 
    \mathrm{LAG} = 1 - \mathrm{PSA} - \mathrm{PSI} - \mathrm{PCL} - \mathrm{SAG}
-```
+\end{gathered}
+$$
 
-where ``\mathrm{CLA}``, ``\mathrm{SIL}`` and ``\mathrm{SAN}`` are the primary clay, silt, sand fractions of the topsoil
-and ``\mathrm{PCL}``, ``\mathrm{PSI}``, ``\mathrm{PSA}``, ``\mathrm{SAG}`` and ``\mathrm{LAG}`` are the clay, silt, sand, small and large
+where $\mathrm{CLA}$, $\mathrm{SIL}$ and $\mathrm{SAN}$ are the primary clay, silt, sand fractions of the topsoil
+and $\mathrm{PCL}$, $\mathrm{PSI}$, $\mathrm{PSA}$, $\mathrm{SAG}$ and $\mathrm{LAG}$ are the clay, silt, sand, small and large
 aggregates fractions of the detached sediment respectively. The transport capacity of the
 flow using Yalin's equation with particle differentiation, developed by Foster (1982), is:
 $$
-   \mathbf{TC}_i = (P_e)_i  (S_g)_i \, \rho_w \,  g \, d_i  V_*
-```
-where ``\mathbf{TC}_i`` is the transport capacity of the flow for the particle class ``i``,
-``(P_e)_i`` is the effective number of particles of class ``i``, ``\SIb{(S_g)_i}{kg m^{-3}}`` is the
-specific gravity for the particle class ``i``, ``\SIb{\rho_w}{kg m^{-3}}`` is the mass density
-of the fluid, ``\SIb{g}{m s^{-2}}`` is the acceleration due to gravity,
-``\SIb{d_i}{m}`` is the diameter of the particle of class ``i`` and ``V_* = \SIb{(g R S)^{0.5}}{m s^{-1}}`` is the
-shear velocity of the flow with ``S`` the slope gradient and ``\SIb{R}{m}`` the
+   \mathrm{TC}_i = (P_e)_i  (S_g)_i \, \rho_w \,  g \, d_i  V_*
+$$
+where $\mathrm{TC}_i$ is the transport capacity of the flow for the particle class $i$,
+$(P_e)_i$ is the effective number of particles of class $i$, $\SIb{(S_g)_i}{kg m^{-3}}$ is the
+specific gravity for the particle class $i$, $\SIb{\rho_w}{kg m^{-3}}$ is the mass density
+of the fluid, $\SIb{g}{m s^{-2}}$ is the acceleration due to gravity,
+$\SIb{d_i}{m}$ is the diameter of the particle of class $i$ and $V_* = \SIb{(g R S)^{0.5}}{m s^{-1}}$ is the
+shear velocity of the flow with $S$ the slope gradient and $\SIb{R}{m}$ the
 hydraulic radius of the flow. The detached sediment are then routed down slope until the
 river network using the `accucapacityflux`, `accupacitystate` functions depending on the
 transport capacity from Yalin.
@@ -192,7 +194,7 @@ $$
    \log\left(C_{ppm}\right) = 5.435 - 0.286\log\left(\frac{\omega_{s,50}D_{50}}{\nu}\right)-0.457\log\left(\frac{u_*}{\omega_{s,50}}\right) \\
    +\left(1.799-0.409\log\left(\frac{\omega_{s,50}D_{50}}{\nu}\right)-0.314\log\left(\frac{u_*}{\omega_{s,50}}\right)\right)\log\left(\frac{uS}{\omega_{s,50}}-\frac{u_{cr}S}{\omega_{s,50}}\right)
 $$
-And the gravel equation (``\SI{2.0}{mm} \leq D_{50} < \SI{10.0}{mm}``) is:
+And the gravel equation ($\SI{2.0}{mm} \leq D_{50} < \SI{10.0}{mm}$) is:
 $$
    \log\left(C_{ppm}\right) = 6.681 - 0.633\log\left(\frac{\omega_{s,50}D_{50}}{\nu}\right)-4.816\log\left(\frac{u_*}{\omega_{s,50}}\right) \\
    +\left(2.784-0.305\log\left(\frac{\omega_{s,50}D_{50}}{\nu}\right)-0.282\log\left(\frac{u_*}{\omega_{s,50}}\right)\right)\log\left(\frac{uS}{\omega_{s,50}}-\frac{u_{cr}S}{\omega_{s,50}}\right)
@@ -236,8 +238,10 @@ their material ``E_{R,\mathrm{bed}}`` for the bed and ``E_{R,\mathrm{bank}}`` fo
 rectangular channel, assuming it is meandering and thus only one bank is prone to erosion,
 they are calculated from the equations (Neitsch et al, 2011):
 $$
-   E_{R,\mathrm{bed}} = k_{d,\mathrm{bed}} \left( \tau_{e,\mathrm{bed}} - \tau_{cr,\mathrm{bed}} \right) 10^{-6}  L  W  \rho_{b, \mathrm{bed}}  \Delta t \\~\\
+\begin{gathered}
+   E_{R,\mathrm{bed}} = k_{d,\mathrm{bed}} \left( \tau_{e,\mathrm{bed}} - \tau_{cr,\mathrm{bed}} \right) 10^{-6}  L  W  \rho_{b, \mathrm{bed}}  \Delta t \\
    E_{R,\mathrm{bank}} = k_{d,\mathrm{bank}} \left( \tau_{e,\mathrm{bank}} - \tau_{cr,\mathrm{bank}} \right) 10^{-6} L h \rho_{b, \mathrm{bank}}  \Delta t
+\end{gathered}
 $$
 where $\SIb{E_R}{ton}$ is the potential bed/bank erosion rates, $\SIb{k_d}{cm^3 N^{-1}, s^{-1}}$ is the erodibility
 of the bed/bank material, $\SIb{\tau_e}{N m^{-2}}$ is the effective
@@ -271,7 +275,7 @@ order, the smaller the diameter is. As the median diameter is only used in wflow
 for the estimation of the river bed/bank sediment composition, this supposition should be
 enough. Actual refined data or calibration may however be needed if the median diameter is
 also required for the transport formula. In a similar way, the bulk densities of river bed
-and bank are also just assumed to be of respectively 1.5 and 1.4 g cm$^{-3}$.
+and bank are also just assumed to be of respectively $\SI{1.5}{g cm^{-3}}$ and $\SI{1.4}{g cm^{-3}}$.
 
 Table: Classical values of the channel cover vegetation coefficient (Julian and Torres, 2006)
 
@@ -296,8 +300,10 @@ Then, the repartition of the flow shear stress is refined into the effective she
 and the bed and bank of the river using the equations developed by Knight (1984) for a
 rectangular channel:
 $$
-   \tau_{e,\mathrm{bed}} = \rho g R_{H} S  \left(1 - \dfrac{SF_{\mathrm{bank}}}{100}\right) \left(1+\dfrac{2h}{W}\right) \\~\\
+\begin{gathered}
+   \tau_{e,\mathrm{bed}} = \rho g R_{H} S  \left(1 - \dfrac{SF_{\mathrm{bank}}}{100}\right) \left(1+\dfrac{2h}{W}\right) \\
    \tau_{e,\mathrm{bank}} = \rho g R_{H} S  \left( SF_{\mathrm{bank}}\right)  \left(1+\dfrac{W}{2h}\right)
+\end{gathered}
 $$
 where $\rho g$ is the fluid specific weight ($\SI{9800}{N m^{-3}}$ for water), $\SIb{R_H}{m}$ is the
 hydraulic radius of the channel, $\SIb{h}{m}$ and $\SIb{W}{m}$ are the water level and river width. $SF_{\mathrm{bank}}$ is the proportion of shear stress acting on the bank (%) and is estimated
@@ -307,8 +313,10 @@ $$
 $$
 Finally the relative erosion potential of the bank and bed of the river is calculated by:
 $$
-   \mathrm{RTE}_{\mathrm{bed}} = \dfrac{E_{R,\mathrm{bed}}}{E_{R,\mathrm{bed}}+E_{R,\mathrm{bank}}} \\~\\
+\begin{gathered}
+   \mathrm{RTE}_{\mathrm{bed}} = \dfrac{E_{R,\mathrm{bed}}}{E_{R,\mathrm{bed}}+E_{R,\mathrm{bank}}} \\
    \mathrm{RTE}_{\mathrm{bank}} = 1 - RTE_{\mathrm{bed}}
+\end{gathered}
 $$
 And the final actual eroded amount for the bed and bank is the maximum between $\mathrm{RTE}
 \subtext{\mathrm{sed}}{exeff}$ and the erosion potential $E_R$. Total eroded amount of sediment

docs/model_docs/lateral/waterbodies.qmd

@@ -152,7 +152,7 @@ waterlevel = "lake_waterlevel"
 ### Additional settings
 Storage and rating curves from field measurement can be supplied to wflow via CSV files
 supplied in the same folder of the TOML file. Naming of the files uses the ID of the lakes
-where data are available and is of the form lake\_sh\_1.csv and lake\_hq\_1.csv for
+where data are available and is of the form `lake_sh_1.csv` and `lake_hq_1.csv` for
 respectively the storage and rating curves of lake with ID 1.
 
 The storage curve is stored in a CSV file with lake level $\SIb{}{m}$ in the first column `H` and

docs/model_docs/vertical/sbm.qmd

@@ -369,8 +369,10 @@ degree of the layer, and a Brooks-Corey power coefficient (parameter $c$) based
 pore size distribution index $\lambda$ (Brooks and Corey, 1964):
 
 $$
-    \mathrm{st}=\subtext{K}{sat}\left(\frac{\theta-\theta_r}{\theta_s-\theta_r}\right)^c\\~\\
+\begin{gathered}
+    \mathrm{st}=\subtext{K}{sat}\left(\frac{\theta-\theta_r}{\theta_s-\theta_r}\right)^c\\
     c=\frac{2+3\lambda}{\lambda}
+\end{gathered}
 $$
 
 Here $\SIb{}{mm t^{-1}}$ denotes milimeter per time step.
@@ -446,7 +448,7 @@ $$
     K_0e^{-fz} & \text{if $z < \subtext{z}{exp}$}\\
     K_0e^{-f\subtext{z}{exp}} & \text{if $z \ge \subtext{z}{exp}$}.
     \end{cases}
-```
+$$
 
 It is also possible to provide a $\subtext{K}{sat}$ value per soil layer by specifying
 `ksat_profile` "layered", these $\subtext{K}{sat}$ values are used directly to compute the vertical
@@ -517,10 +519,12 @@ A S-curve (see plot below) is used to make a smooth transition (a c-factor ($c$)
 used):
 
 $$
-    b = \frac{1.0}{1.0 - \subtext{\mathrm{cf}}{soil}}\\~\\
-    \mathrm{soilinfredu} = \frac{1.0}{b + \exp(-c (T_s - a))} + \subtext{\mathrm{cf}}{soil}\\~\\
+\begin{gathered}
+    b = \frac{1.0}{1.0 - \subtext{\mathrm{cf}}{soil}}\\
+    \mathrm{soilinfredu} = \frac{1.0}{b + \exp(-c (T_s - a))} + \subtext{\mathrm{cf}}{soil}\\
     a = 0.0\\
     c = 8.0
+\end{gathered}
 $$
 
 ![Infiltration correction factor as a function of soil temperature](../../images/soil_frozeninfilt.png)
@@ -658,7 +662,7 @@ apply an irrigation rate higher than the soil infiltration capacity. To account
 irrigation efficiency the net irrigation demand is divided by the irrigation efficiency for
 non-paddy crops (`irrigation_efficiency` $\SIb{}{-}$, default is $1.0$), resulting in gross irrigation
 demand $\SIb{}{mm t^{-1}}$. Finally, the gross irrigation demand is limited by the maximum
-irrigation rate (`maximum_irrigation_rate` $\SIb{}{mm t^{-1}}$, default is $\SI{25}^{mm\;day-1}$). If
+irrigation rate (`maximum_irrigation_rate` $\SIb{}{mm t^{-1}}$, default is $\SI{25}{mm\;day-1}$). If
 the maximum irrigation rate is applied, irrigation continues at subsequent time steps until
 field capacity is reached. Irrigation is added to the `SBM` variable `avail_forinfilt` $\SIb{}{mm t^{-1}}$, the amount of water available for infiltration.
 

docs/model_docs/vertical/sediment.qmd

@@ -57,7 +57,7 @@ use.
 
 Kinetic energies from both direct throughfall and leaf drainage are then multiplied by the
 respective depths of direct throughfall and leaf drainage (mm) and added to get the total
-rainfall kinetic energy ``\mathrm{KE}``. The soil detached by rainfall ``\SIb{D_R}{g m^{-2}}`` is
+rainfall kinetic energy $\mathrm{KE}$. The soil detached by rainfall $\SIb{D_R}{g m^{-2}}$ is
 then:
 $$
    D_R = k\,\mathrm{KE}\,e^{-\varphi h}
@@ -110,9 +110,11 @@ The other methods to estimate the USLE $K$ factor are to use either topsoil comp
 topsoil geometric mean diameter. $K$ estimation from topsoil composition is estimated with
 the equation developed in the EPIC model (Williams et al, 1983):
 $$
+\begin{gathered}
    \subtext{K}{USLE} = \left[ 0.2 + 0.3\exp\left(-0.0256\;\mathrm{SAN}\frac{(1-\mathrm{SIL})}{100}\right) \right]
-   \left(\frac{\mathrm{SIL}}{\mathrm{CLA}+\mathrm{SIL}}\right)^{0.3} \\~\\
+   \left(\frac{\mathrm{SIL}}{\mathrm{CLA}+\mathrm{SIL}}\right)^{0.3} \\
    \left(1-\frac{0.25\;\mathrm{OC}}{\mathrm{OC}+e^{3.72-2.95\;\mathrm{OC}}}\right)\left(1-\frac{0.75\;\mathrm{SN}}{\mathrm{SN}+e^{-5.51+22.9\;\mathrm{SN}}}\right)
+\end{gathered}
 $$
 where $\SIb{\mathrm{CLA}}{\%}$, $\SIb{\mathrm{SIL}}{\%}$, $\SIb{\mathrm{SAN}}{\%}$ are respectively the clay, silt and sand fractions of the
 topsoil, $\SIb{OC}{\%}$ is the topsoil organic carbon content and $\mathrm{SN} = 1-\mathrm{SAN}/100$.

docs/model_docs/vertical/shared_processes.qmd

@@ -19,7 +19,7 @@ The respective rates of snow melt and refreezing are:
 
 $$
 \begin{align*}
-    Q_m &=& \subtext{\mathrm{cf}}{max}(T_a−\mathrm{tt})\, &&T_a > \mathrm{tt} \\~\\
+    Q_m &=& \subtext{\mathrm{cf}}{max}(T_a−\mathrm{tt})\, &&T_a > \mathrm{tt} \\
     Q_r &=& \subtext{\mathrm{cf}}{max} \, \mathrm{cf}_r(\mathrm{tt}−T_a) &&T_a < \mathrm{tt}
 \end{align*}
 $$
@@ -161,21 +161,19 @@ can be determined through a lookup table with land cover based on literature (Pi
 Lui 1998). Next the `cmax` (leaves) is determined using:
 
 $$
-cmax(leaves)  = sl \, LAI
+    \mathrm{cmax}(\mathrm{leaves})  = \mathrm{sl} \cdot \mathrm{LAI}
 $$
 
-    \mathrm{cmax}(\mathrm{leaves})  = \mathrm{sl} \cdot \mathrm{LAI}
-```
 To get to total storage (`cmax`) the woody part of the vegetation also needs to be added. As
 for `sl`, the storage of the woody part `swood` can also be related to land cover (lookup
 table).
 
 The canopy gap fraction is determined using the extinction coefficient `kext` (van Dijk and
 Bruijnzeel 2001):
 
-```math
+$$
     \mathrm{canopygapfraction} = \exp(-\subtext{k}{ext} \cdot \mathrm{LAI})
-```
+$$
 
 The extinction coefficient `kext` can be related to land cover.