Hydrodynamics.md

@@ -3,27 +3,25 @@
 [[_TOC_]]
 
 # 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 transported from compartment $`i`$ to compartment $`j`$ is the same as the water transported from compartment $`j`$ to $`i`$.  
 
-The DEMO model has a very simple formulation for the hydrodynamics (exchange between the compartments and the North Sea). It is assumed that the compartments are completely mixed. Each day a volume of water ($`Ex_{i,j}`$ ) is transported from compartment $`i`$ to compartment $`j`$ and the same amount of water is transported from compartment $`j`$ to $`i`$.  between The exchanges between the compartments are described by a diffusive process.
-
-```math
-Flux_{i,j} =  \frac{Ex_{i,j}\cdot(C_{j}-C_{i})}{Vol_{i}}
+```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. The exchange parameters ($`Ex_{i,j}`$) are estimated by fitting a tracer model to data, artificially generated by a tracer run with the 3-D hydrodynamic model of Jiang et al. (2019)[^3049].
 
+[Top](Hydrodynamics)
+# 3D Hydrodynamic model
+A 3D hydrodynamic model has been developed by Jiang et al. (2019) [^3049]. The model was developed in the open source General Estuarine Transport Model [GETM](https://getm.eu) in combination with the General Open Turbulence Model [GOTM](http://gotm.net). The model has a 300x300 meter rectangular grid in the Oosterschelde and a part of the Voordelta in the North Sea.
 
-State variables in the water column (DIN, Phyto, Zoo and Det) are transported by tidal currents. This transport is modeled as exchange rates between the neighboring compartments. It is assumed that the exchange rates are bi-directional, i.e. the exchange rate [m<sup>3</sup> d<sup>-1</sup>] from compartment $`i`$ to compartment $`j`$ is the same as the exchange rate from compartment $`j`$ to $`i`$.
- 
-
-Where $`Flux_{i,j}`$ is the increase in concentration in compartment $`i`$ [mmol-N m<sup>-3</sup> d<sup>-1</sup>] due to the water exchange between compartment $`i`$ and $`j`$. $`Ex_{i,j}`$ is the exchange rate between compartment $`i`$ and $`j`$ [m<sup>3</sup> d<sup>-1</sup>]. $`C_{i}`$ and $`C_{j}`$ are the concentrations of the state variables in compartment $`i`$ and $`j`$ [mmol-N m<sup>-3</sup>], respectively. $`Vol_{i}`$ is the volume of compartment $`i`$ [m<sup>3</sup>].
-
-
-
-The hydrodynamics in the DEMO model is based on the model that was developed by Jiang et al. (2019) [^3049]. The model was developed in the open source General Estuarine Transport Model [GETM](https://getm.eu) in combination with the General Open Turbulence Model [GOTM](http://gotm.net). The model has a 300x300 meter rectangular grid in the Oosterschelde and a part of the Voordelta in the North Sea.
-
-With the model a tracer simulation was run for a period of 1 year. At the start of the simulation the fraction of North Sea water in the North Sea was 1 (100%) and in he Oosterschelde the fraction of North Sea water was 0 (0%). The intrusion of North Sea water into the Oosterschelde with the tidal currents is shown in the movie below.
+With the model a tracer simulation was run. At the start of the simulation the fraction of North Sea water in the North Sea was 1 (100%) and in he Oosterschelde the fraction of North Sea water was 0 (0%). The model was run for one year from 1 January 2009 to 31 December 2009. For each hour, the depth-averaged tracer concentration and the water level in each (300x300 m) grid-cell was exported. The intrusion of North Sea water into the Oosterschelde with the tidal currents is shown in the movie below.
 
 ![0001lq](uploads/f2598a044853e2d233f4a731ed4683fe/0001lq.mp4)
 
+# Artificial data
+The results of the tracer simulation with the 3D hydrodynamic model were used to generate artificial data. For each DEMO model compartment, the depth-weighted average fraction North Sea water was calculated for each time step (hour). 
+
 [Top](Hydrodynamics)
 # Calibration exchange rates
 Hydrodynamics in DEMO is modeled as a diffusive process. Each timestep