Hydrodynamics.md

@@ -24,20 +24,40 @@ The results of the tracer simulation with the 3D hydrodynamic model were used to
 
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 # Calibration exchange rates
-Hydrodynamics in DEMO is modeled as a diffusive process. Each timestep 
-To calculate the exchange rates between the compartments and the North Sea, tracer simulations have also been run for the different schematizations (0D, 4Comp and 28Comp) of the DEMO model. The exchange rates between the compartments are calculated by fitting the model output of the DEMO model to the data generated by the GetM/GotM model. For each hour, the average tracer concentration within each compartment has been calculated. The models are fitted by changing the exchange rates between the compartments using the modFit function in R (Soetaert and Petzold, 2010)[^3228].
+The exchange rates between the neighboring compartments are estimated by fitting the output of the DEMO tracer model to the artificial data generated by the GetM/GotM model. Initial conditions for each compartment were calculated from the artificial data as the average fraction of North Sea water in each compartment during the first four tidal cycles. The models are fitted using the modFit function in R (Soetaert and Petzold, 2010)[^3228]. The 1D model and the models with the 4 and 28 compartments are fitted separately. The parameters were estimated using the Levenberg-Marquardt algorithm where the objective was to minimize the sum of squared residuals (SSR).
 
-## 1D model
+[Top](Hydrodynamics)
+## 0D model
+For the 0D model only 1 parameter (exchange rate between the North Sea and the Oosterschelde) had to be fitted. 
+
+![Tracer_0D](uploads/1330829c6ca42292905fc206459974bd/Tracer_0D.png)
+*Results of the DEMO tracer model (blue line), together with the artificial data from the 3D the GetM/GotM model (orange dots).*
 
+The fitted exchange rate between the North Sea and the Oosterschelde is implemented in the function “Transp_1C()”.
+
+[Top](Hydrodynamics)
 ## 4 Compartments
+For the model with 4 compartments, four exchange parameters had to be estimated:
+- Exchange rate between North Sea and compartment West
+- Exchange rate between compartment West and Central
+- Exchange rate between compartment Central and East
+- Exchange rate between compartment Central and North
 
+![Tracer_4Comp](uploads/3bb87851299dd8630769aa438754cdf3/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()”.
+
+[Top](Hydrodynamics)
 ## 28 Compartments
+For the model with 28 compartments, a total of 42 exchange rates had to be fitted. 
+
+The fitted exchange rates between the neighboring compartments are implemented in the function  “Transp_28C()”
 
-![Tracer_4Comp](uploads/435cc640eeca23673e5dfdf2186fbf62/Tracer_4Comp.png) 
 
 *Example of tracer fit of the 4Comp-DEMO model (blue lines) with the results of the GetM/GotM model (orange dots).*
 
-The exchanges between the neighbouring compartments is described in the functions “Transp_1C()”, “Transp_4C()” and “Transp_28C()”. Exchange rates are expressed in m<sup>3</sup> d<sup>-1</sup> and are the same in both directions. 
+The exchanges between the neighboring compartments is described in the functions “Transp_1C()”, “Transp_4C()” and “Transp_28C()”. Exchange rates are expressed in m<sup>3</sup> d<sup>-1</sup> and are the same in both directions. 
 
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