Hydrodynamics.md

@@ -4,14 +4,14 @@
 
 # Water transport
 
-The DEMO model has a very simple formulation for the hydrodynamics (exchange between the bordering compartments and the North Sea). It is assumed that the compartments are homogeneously mixed. For two neighboring compartments ($`i`$ and $`j`$), water is exchanged between both compartments with a constant rate of ($`Ex_{i,j}`$ m<sup>3</sup> d<sup>-1</sup>). The rate is bidirectional, so the water transport rate from compartment $`i`$ to compartment $`j`$ is the same as the water transport rate from compartment $`j`$ to $`i`$. As a result, there is no net transport of water between the compartments and the volume remains constant.
+The DEMO model has a very simple formulation for the hydrodynamics (exchange between the bordering compartments and the North Sea). It is assumed that the compartments are homogeneously mixed. For two neighboring compartments ($`i`$ and $`j`$), water is exchanged between both compartments with a constant rate of `Ex` `Ex_{i,j}` m<sup>3</sup> d<sup>\-1</sup>). The rate is bidirectional, so the water transport rate from compartment $`i`$ to compartment $`j`$ is the same as the water transport rate from compartment $`j`$ to $`i`$. As a result, there is no net transport of water between the compartments and the volume remains constant.
 
 ```mermaid
 flowchart LR;
   Comp_i <==>|Ex_i,j| Comp_j;
 ```
 
-The same formulation is used for the exchange between the North Sea and the compartment neighboring the North Sea ($`Ex_{i,NS}`$). The exchange parameters ($`Ex_{i,j}`$ and $`Ex_{i,NS}`$) are estimated by fitting a tracer model to data, artificially generated by a tracer simulation with the 3-D hydrodynamic model of Jiang et al. (2019)[<sup>1</sup>](#fn1-7947).
+The same formulation is used for the exchange between the North Sea and the compartment neighboring the North Sea ($`Ex_{i,NS}`$`). The exchange parameters (`$`Ex_{i,j}`$ and $`Ex_{i,NS}`$) are estimated by fitting a tracer model to data, artificially generated by a tracer simulation with the 3-D hydrodynamic model of Jiang et al. (2019)[<sup>1</sup>](#fn1-7947).
 
 [Top](Hydrodynamics)
 
@@ -37,7 +37,7 @@ The exchange rates between the neighboring compartments are estimated by fitting
 
 ## 0D model
 
-For the 0D model only 1 parameter (exchange rate between the North Sea and the Oosterschelde) had to be fitted. In the figure below, the fitted model is compared with the artificial data. The fitted model is used to calculate the average residence time ($`RT`$, d) and turnover time ($`TT`$, d) of the water within the compartment.
+For the 0D model only 1 parameter (exchange rate between the North Sea and the Oosterschelde) had to be fitted. In the figure below, the fitted model is compared with the artificial data. The fitted model is used to calculate the average residence time ($`RT`$`, d) and turnover time (`$`TT`$, d) of the water within the compartment.
 
 ![Tracer_0D](uploads/411c1435151b2cb814366c6c89dd4d1d/Tracer_0D.png)
 
@@ -51,13 +51,12 @@ The fitted exchange rate between the North Sea and the Oosterschelde is implemen
 
 For the model with 4 compartments, four exchange parameters had to be estimated:
 
-- Exchange rate between North Sea and compartment West (m<sup>3</sup> d<sup>-1</sup>);
-- Exchange rate between compartment West and Central (m<sup>3</sup> d<sup>-1</sup>);
-- Exchange rate between compartment Central and East (m<sup>3</sup> d<sup>-1</sup>);
-- Exchange rate between compartment Central and North (m<sup>3</sup> d<sup>-1</sup>)
+- Exchange rate between North Sea and compartment West (m<sup>3</sup> d<sup>\-1</sup>);
+- Exchange rate between compartment West and Central (m<sup>3</sup> d<sup>\-1</sup>);
+- Exchange rate between compartment Central and East (m<sup>3</sup> d<sup>\-1</sup>);
+- Exchange rate between compartment Central and North (m<sup>3</sup> d<sup>\-1</sup>)
 
-![Tracer_4Comp](uploads/78aa39be0504e896464edfd5c2328556/Tracer_4Comp.png) 
-_Results of the DEMO tracer model (blue lines), together with the artificial data from the 3D the GetM/GotM model (orange dots) for the compartments West, Central, East and North._
+![Tracer_4Comp](uploads/78aa39be0504e896464edfd5c2328556/Tracer_4Comp.png) _Results of the DEMO tracer model (blue lines), together with the artificial data from the 3D the GetM/GotM model (orange dots) for the compartments West, Central, East and North._
 
 The fitted exchange rates between the neighboring compartments are implemented in the function “Transp_4C()”.